Francisco Coelho / zugzwang

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Commit 353a8086aab8f46c7610ea1a544f7078e57f479f

Authored by Francisco Coelho
1 parent 0ca70415
Exists in master

alterações feitas pelo bruno à sub-secção 4.2

Showing 27 changed files with 1180 additions and 882 deletions   Show diff stats
code/drafts/.ipynb_checkpoints/EventLattice-checkpoint.ipynb 0 → 100644
  Diff comments   View file @353a808
... ... @@ -0,0 +1,113 @@
  1 +{
  2 + "cells": [
  3 + {
  4 + "cell_type": "code",
  5 + "execution_count": null,
  6 + "id": "57fc5921-9d6b-4b43-a8f6-743a03650d63",
  7 + "metadata": {},
  8 + "outputs": [],
  9 + "source": [
  10 + "import event_lattice as el"
  11 + ]
  12 + },
  13 + {
  14 + "cell_type": "code",
  15 + "execution_count": null,
  16 + "id": "00f0eb68",
  17 + "metadata": {},
  18 + "outputs": [],
  19 + "source": [
  20 + "def zoom_event(event_str, lattice, lower_op=el.sum_op, upper_op=el.prod_op):\n",
  21 + " event = el.Event.from_str(event_str)\n",
  22 + " event_class = lattice.event_class(event)\n",
  23 + " propagated = lattice.propagated_value(\n",
  24 + " event, lower_op=lower_op, upper_op=upper_op)\n",
  25 + "\n",
  26 + " print(\n",
  27 + " f\"Event: {event}\\n\\tClass: {event_class} \\n\\tValue: {propagated}\")"
  28 + ]
  29 + },
  30 + {
  31 + "cell_type": "code",
  32 + "execution_count": null,
  33 + "id": "cdd8c6d6",
  34 + "metadata": {},
  35 + "outputs": [],
  36 + "source": [
  37 + "smodels = el.Lattice.parse({\n",
  38 + " \"A\": 2,\n",
  39 + " \"ab\": 3,\n",
  40 + " \"ac\": 5\n",
  41 + "})\n",
  42 + "\n",
  43 + "lattice = el.Lattice(smodels)\n",
  44 + "\n",
  45 + "print(lattice)"
  46 + ]
  47 + },
  48 + {
  49 + "cell_type": "code",
  50 + "execution_count": null,
  51 + "id": "2b445339",
  52 + "metadata": {},
  53 + "outputs": [],
  54 + "source": [
  55 + "zoom_event(\"abc\", lattice)\n",
  56 + "zoom_event(\"a\", lattice)\n",
  57 + "zoom_event(\"b\", lattice)\n",
  58 + "zoom_event(\"bc\", lattice)\n",
  59 + "zoom_event(\"ac\", lattice)"
  60 + ]
  61 + },
  62 + {
  63 + "cell_type": "code",
  64 + "execution_count": null,
  65 + "id": "f1b85255",
  66 + "metadata": {},
  67 + "outputs": [],
  68 + "source": [
  69 + "from itertools import *\n",
  70 + "\n",
  71 + "lits = lattice.literals()\n",
  72 + "for len_lit in range(len(lits)+1):\n",
  73 + " events = list(\"\".join(c) for c in combinations(lits, len_lit))\n",
  74 + " for event in events:\n",
  75 + " zoom_event(event, lattice)"
  76 + ]
  77 + },
  78 + {
  79 + "cell_type": "code",
  80 + "execution_count": null,
  81 + "id": "07973a47",
  82 + "metadata": {},
  83 + "outputs": [],
  84 + "source": []
  85 + }
  86 + ],
  87 + "metadata": {
  88 + "kernelspec": {
  89 + "display_name": "Python 3.9.13 ('base')",
  90 + "language": "python",
  91 + "name": "python3"
  92 + },
  93 + "language_info": {
  94 + "codemirror_mode": {
  95 + "name": "ipython",
  96 + "version": 3
  97 + },
  98 + "file_extension": ".py",
  99 + "mimetype": "text/x-python",
  100 + "name": "python",
  101 + "nbconvert_exporter": "python",
  102 + "pygments_lexer": "ipython3",
  103 + "version": "3.9.13"
  104 + },
  105 + "vscode": {
  106 + "interpreter": {
  107 + "hash": "a59afa236e16843183c59a167f072b6fa0409044b3c4938e82ac98aad91bf217"
  108 + }
  109 + }
  110 + },
  111 + "nbformat": 4,
  112 + "nbformat_minor": 5
  113 +}
... ...
code/drafts/EventLattice.ipynb 0 → 100644
  Diff comments   View file @353a808
... ... @@ -0,0 +1,154 @@
  1 +{
  2 + "cells": [
  3 + {
  4 + "cell_type": "code",
  5 + "execution_count": 4,
  6 + "id": "57fc5921-9d6b-4b43-a8f6-743a03650d63",
  7 + "metadata": {},
  8 + "outputs": [
  9 + {
  10 + "name": "stdout",
  11 + "output_type": "stream",
  12 + "text": [
  13 + "The autoreload extension is already loaded. To reload it, use:\n",
  14 + " %reload_ext autoreload\n"
  15 + ]
  16 + }
  17 + ],
  18 + "source": [
  19 + "%load_ext autoreload\n",
  20 + "%autoreload 1\n",
  21 + "%aimport event_lattice"
  22 + ]
  23 + },
  24 + {
  25 + "cell_type": "code",
  26 + "execution_count": 5,
  27 + "id": "00f0eb68",
  28 + "metadata": {},
  29 + "outputs": [],
  30 + "source": [
  31 + "def zoom_event(event_str, lattice):\n",
  32 + " event = event_lattice.Event.from_str(event_str)\n",
  33 + " event_class = lattice.event_class(event)\n",
  34 + " propagated = lattice.extended_value(\n",
  35 + " event)\n",
  36 + "\n",
  37 + " print(\n",
  38 + " f\"Event: {event}\\n\\tClass: {event_class} \\n\\tValue: {propagated}\")"
  39 + ]
  40 + },
  41 + {
  42 + "cell_type": "code",
  43 + "execution_count": 6,
  44 + "id": "cdd8c6d6",
  45 + "metadata": {},
  46 + "outputs": [
  47 + {
  48 + "name": "stdout",
  49 + "output_type": "stream",
  50 + "text": [
  51 + "{\n",
  52 + "\t'stable_models': {\n",
  53 + "\t\t A: 2,\n",
  54 + "\t\tab: 3,\n",
  55 + "\t\tac: 5 \n",
  56 + "\t}\n",
  57 + "\t'literals': { A,B,C,a,b,c } \n",
  58 + "}\n"
  59 + ]
  60 + }
  61 + ],
  62 + "source": [
  63 + "smodels = event_lattice.Lattice.parse({\n",
  64 + " \"A\": 2,\n",
  65 + " \"ab\": 3,\n",
  66 + " \"ac\": 5\n",
  67 + "})\n",
  68 + "\n",
  69 + "lattice = event_lattice.Lattice(smodels)\n",
  70 + "\n",
  71 + "print(lattice)"
  72 + ]
  73 + },
  74 + {
  75 + "cell_type": "code",
  76 + "execution_count": 7,
  77 + "id": "2b445339",
  78 + "metadata": {},
  79 + "outputs": [
  80 + {
  81 + "ename": "TypeError",
  82 + "evalue": "__init__() missing 1 required positional argument: 'lattice'",
  83 + "output_type": "error",
  84 + "traceback": [
  85 + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
  86 + "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)",
  87 + "\u001b[0;32m/tmp/ipykernel_361713/2581811254.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mzoom_event\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"abc\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlattice\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2\u001b[0m \u001b[0mzoom_event\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"a\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlattice\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mzoom_event\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"b\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlattice\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0mzoom_event\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"bc\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlattice\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0mzoom_event\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"ac\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlattice\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
  88 + "\u001b[0;32m/tmp/ipykernel_361713/1675915232.py\u001b[0m in \u001b[0;36mzoom_event\u001b[0;34m(event_str, lattice)\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mzoom_event\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mevent_str\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlattice\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0mevent\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mevent_lattice\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mEvent\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfrom_str\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mevent_str\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mevent_class\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlattice\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mevent_class\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mevent\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 4\u001b[0m propagated = lattice.extended_value(\n\u001b[1;32m 5\u001b[0m event)\n",
  89 + "\u001b[0;32m~/sci/projetos/zugzwang/code/python/event_lattice.py\u001b[0m in \u001b[0;36mevent_class\u001b[0;34m(self, event)\u001b[0m\n\u001b[1;32m 146\u001b[0m \u001b[0;34m@\u001b[0m\u001b[0mcache\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 147\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mevent_class\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mevent\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 148\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mEventsClass\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstable_core\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mevent\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 149\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 150\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mrelated\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mu\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mv\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
  90 + "\u001b[0;31mTypeError\u001b[0m: __init__() missing 1 required positional argument: 'lattice'"
  91 + ]
  92 + }
  93 + ],
  94 + "source": [
  95 + "zoom_event(\"abc\", lattice)\n",
  96 + "zoom_event(\"a\", lattice)\n",
  97 + "zoom_event(\"b\", lattice)\n",
  98 + "zoom_event(\"bc\", lattice)\n",
  99 + "zoom_event(\"ac\", lattice)"
  100 + ]
  101 + },
  102 + {
  103 + "cell_type": "code",
  104 + "execution_count": null,
  105 + "id": "f1b85255",
  106 + "metadata": {},
  107 + "outputs": [],
  108 + "source": [
  109 + "from itertools import *\n",
  110 + "\n",
  111 + "lits = lattice.literals()\n",
  112 + "events = []\n",
  113 + "for len_lit in range(len(lits)+1):\n",
  114 + " events = events + list(\"\".join(c) for c in combinations(lits, len_lit))\n",
  115 + "for event in events:\n",
  116 + " zoom_event(event, lattice)"
  117 + ]
  118 + },
  119 + {
  120 + "cell_type": "code",
  121 + "execution_count": null,
  122 + "id": "07973a47",
  123 + "metadata": {},
  124 + "outputs": [],
  125 + "source": []
  126 + }
  127 + ],
  128 + "metadata": {
  129 + "kernelspec": {
  130 + "display_name": "Python 3 (ipykernel)",
  131 + "language": "python",
  132 + "name": "python3"
  133 + },
  134 + "language_info": {
  135 + "codemirror_mode": {
  136 + "name": "ipython",
  137 + "version": 3
  138 + },
  139 + "file_extension": ".py",
  140 + "mimetype": "text/x-python",
  141 + "name": "python",
  142 + "nbconvert_exporter": "python",
  143 + "pygments_lexer": "ipython3",
  144 + "version": "3.9.15"
  145 + },
  146 + "vscode": {
  147 + "interpreter": {
  148 + "hash": "a59afa236e16843183c59a167f072b6fa0409044b3c4938e82ac98aad91bf217"
  149 + }
  150 + }
  151 + },
  152 + "nbformat": 4,
  153 + "nbformat_minor": 5
  154 +}
... ...
code/drafts/__init__.py 0 → 100644
  Diff comments   View file @353a808
code/drafts/__pycache__/event_lattice.cpython-39.pyc 0 → 100644
View file @353a808
No preview for this file type
code/drafts/algebra.py 0 → 100644
  Diff comments   View file @353a808
... ... @@ -0,0 +1,30 @@
  1 +from itertools import combinations, product
  2 +
  3 +def fmt(expr):
  4 + """Doc string"""
  5 + return ",".join(f"{x:>2}" for x in expr)
  6 +
  7 +def c(expr):
  8 + """Doc string"""
  9 + def litcomp(x):
  10 + if x == "⊤":
  11 + return "⊥"
  12 + elif x == "⊥":
  13 + return "⊤"
  14 + elif x[0] == "¬":
  15 + return x[1:]
  16 + else:
  17 + return f"¬{x}"
  18 + return [litcomp(x) for x in expr]
  19 +
  20 +def domain(symbols, unary="¬"):
  21 + """Doc string"""
  22 + atoms = list(symbols)
  23 + literals = [
  24 + [f"{u}{a}" for u in unary] +
  25 + [a, "⊤", "⊥"] for a in atoms ]
  26 + return product(*literals)
  27 +
  28 +d = sorted(domain("abc"))
  29 +for x in d:
  30 + print(f"{fmt(x)} | {fmt(c(x))}")
... ...
code/drafts/api_01.py 0 → 100644
  Diff comments   View file @353a808
... ... @@ -0,0 +1,26 @@
  1 +from clingo.symbol import Number
  2 +from clingo.control import Control
  3 +
  4 +class Context:
  5 + def inc(self, x):
  6 + return Number(x.number + 1)
  7 +
  8 + def seq(self, x, y):
  9 + return [x, y]
  10 +
  11 +def on_model(m):
  12 + print(m)
  13 +
  14 +ctl = Control()
  15 +ctl.add("base", [], """\
  16 +p(@inc(10)).
  17 +q(@seq(1,2)).
  18 +""")
  19 +
  20 +ctl.ground(
  21 + [("base", [])],
  22 + context=Context())
  23 +
  24 +s = ctl.solve(on_model=on_model)
  25 +
  26 +print(s)
0 27 \ No newline at end of file
... ...
code/drafts/event_lattice.py 0 → 100644
  Diff comments   View file @353a808
... ... @@ -0,0 +1,301 @@
  1 +import math
  2 +from functools import cache
  3 +from itertools import accumulate, combinations, chain, groupby
  4 +import operator
  5 +
  6 +
  7 +
  8 +def uniform_op(x):
  9 + n = len(list(x))
  10 + return 1.0 if n == 0 else 1.0/n
  11 +
  12 +
  13 +def max_op(x):
  14 + return max(x)
  15 +
  16 +
  17 +def min_op(x):
  18 + return min(x)
  19 +
  20 +
  21 +def sum_op(x):
  22 + return sum(x)
  23 +
  24 +
  25 +def stableprod_op(x):
  26 + log_x = map(math.log, x)
  27 + return math.exp(sum(log_x))
  28 +
  29 +
  30 +def prod_op(x):
  31 + return list(accumulate(x, func=lambda a,b: a*b))[-1]
  32 +
  33 +
  34 +class Event:
  35 + """Events.
  36 +
  37 + An event is a set of literals - atoms and negated atoms.
  38 +
  39 + The convention is that atoms are represented by lower case single letters
  40 + and a negated atom by upper case single letters.
  41 + """
  42 +
  43 + @staticmethod
  44 + def _parse(text):
  45 + return frozenset(text)
  46 +
  47 + @staticmethod
  48 + def parse(text):
  49 + """Convert a string to an event.
  50 +
  51 + Each letter in the string represents a literal.
  52 + """
  53 + return Event(Event._parse(text))
  54 +
  55 +
  56 + def __init__(self, literals):
  57 + """Instantiate from a (frozen) set of literals.
  58 + For example: e = Event(frozenset("abc"))."""
  59 + self._literals = frozenset(literals)
  60 +
  61 +
  62 + def literals(self):
  63 + return self._literals
  64 +
  65 +
  66 + def __iter__(self):
  67 + return self._literals.__iter__()
  68 +
  69 + @cache
  70 + def is_consistent(self):
  71 + """True if this event is consistent."""
  72 + return all(x.swapcase() not in self._literals for x in self._literals)
  73 +
  74 +
  75 + def co(self):
  76 + """Negation of this event.
  77 +
  78 + Negation is case based: A = not a; a = not A."""
  79 + return Event(x.swapcase() for x in self._literals)
  80 +
  81 + def invert(self):
  82 + """Negation of this event.
  83 +
  84 + See the method "co"
  85 + """
  86 + return self.co()
  87 +
  88 + def __repr__(self) -> str:
  89 + return ''.join(str(x) for x in sorted(self._literals)) if len(self._literals) > 0 else '0'
  90 +
  91 + def latex(self):
  92 + """LaTeX representation of this even.
  93 +
  94 + Negation is represented by overline and the empty event by
  95 +
  96 + """
  97 + return ''.join(
  98 + (str(x) if x.islower() else f"\co{{{x.lower()}}}") \
  99 + for x in sorted(self._literals)
  100 + ) if len(self._literals) > 0 else "\set{}"
  101 +
  102 + def __hash__(self) -> int:
  103 + return self._literals.__hash__()
  104 +
  105 +
  106 + def __eq__(self, other):
  107 + """Event equality test."""
  108 + return self._literals.__eq__(other._literals)
  109 +
  110 + def __or__(self, other):
  111 + """Event union operation."""
  112 + return Event(self._literals | other._literals)
  113 +
  114 + def __le__(self, other):
  115 + """Event subset test."""
  116 + return self._literals.__le__(other._literals)
  117 +
  118 +
  119 + def __lt__(self, other):
  120 + """Event strict subset test."""
  121 + return self._literals.__lt__(other._literals)
  122 +
  123 +
  124 + def __ne__(self, other):
  125 + """Event not-equal test."""
  126 + return self._literals.__ne__(other._literals)
  127 +
  128 +
  129 + def __ge__(self, other):
  130 + """Event superset test."""
  131 + return self._literals.__ge__(other._literals)
  132 +
  133 +
  134 + def __gt__(self, other):
  135 + """Event strict superset test."""
  136 + return self._literals.__gt__(other._literals)
  137 +
  138 +
  139 +class Lattice:
  140 +
  141 + @staticmethod
  142 + def parse(d):
  143 + """Input stable models.
  144 +
  145 + The input format is a dictionary associating a stable model in string form to an weight.
  146 +
  147 + For example:
  148 +
  149 + input_dict = {
  150 + "A": 0.3,
  151 + "ab": 0.2,
  152 + "ac": 0.5
  153 + }
  154 + smodels = Lattice.parse(input_dict)
  155 + """
  156 + result = dict()
  157 + for k, v in d.items():
  158 + key = Event.parse(k)
  159 + result[key] = v
  160 + return result
  161 +
  162 +
  163 + @staticmethod
  164 + def close_literals(events):
  165 + """Closed set of literals entailed by a set of events.
  166 +
  167 + Includes the literals in the set of events and any missing negation."""
  168 + base_lits = list(accumulate(events, func=operator.or_))[-1]
  169 + lits = set()
  170 + for x in base_lits.literals():
  171 + lits.add(x)
  172 + lits.add(x.swapcase())
  173 + return sorted(lits)
  174 +
  175 + def __init__(self, smodels_dict):
  176 + """Create an Events lattice."""
  177 + self._smodels = smodels_dict
  178 + self._literals = Lattice.close_literals(self._smodels.keys())
  179 +
  180 + def literals(self):
  181 + """The literals in this lattice."""
  182 + return self._literals
  183 +
  184 + @cache
  185 + def stable_models(self):
  186 + """The stable models that generate this lattice."""
  187 + return self._smodels.keys()
  188 +
  189 + #@cache
  190 + def events(self):
  191 + """All the events of this lattice."""
  192 + return chain.from_iterable(map(Event, combinations(self._literals, r)) for r in range(len(self._literals)+1))
  193 +
  194 + @cache
  195 + def stable_core(self, event):
  196 + """The stable core of an event in this lattice."""
  197 + return set(filter(lambda sm: sm <= event or event <= sm, self.stable_models()))
  198 +
  199 + # @cache
  200 + # def event_class(self, event):
  201 + # """The equivalence class of an event."""
  202 + # return EventsClass(self.stable_core(event), self)
  203 +
  204 + @cache
  205 + def classes(self):
  206 + """The classes of this lattice.
  207 +
  208 + Each class is presented as a key:value pair where the "key" is the stable core of the elements in "value"."""
  209 + map_ev_classes = [(e, tuple(self.stable_core(e))) for e in self.events() if e.is_consistent()]
  210 + groups = dict()
  211 + for e,c in map_ev_classes:
  212 + if c in groups.keys():
  213 + groups[c].add(e)
  214 + else:
  215 + groups[c] = set([e])
  216 + inconsistent = list(e for e in self.events() if not e.is_consistent())
  217 + inconsistent_repr = inconsistent[0]
  218 + groups[(inconsistent_repr,)] = set(inconsistent)
  219 + return groups
  220 +
  221 +
  222 + def related(self, u, v):
  223 + """Tests if two events are related."""
  224 + u_consistent = u.is_consistent()
  225 + v_consistent = v.is_consistent()
  226 + if u_consistent and (u_consistent == v_consistent):
  227 + return self.stable_core(u) == self.stable_core(v)
  228 + else:
  229 + return u_consistent == v_consistent
  230 +
  231 + def extended_value(self, event:Event,
  232 + op=prod_op):
  233 + """TODO: well..."""
  234 + value = 0
  235 + #
  236 + # INCONSISTENT EVENTS
  237 + #
  238 + if not event.is_consistent():
  239 + return value
  240 + #
  241 + # CONSISTENT EVENTS
  242 + #
  243 + score = self.stable_core(event)
  244 + len_score = len(score)
  245 + # CONSISTENT, INDEPENDENT
  246 + if len_score == 0:
  247 + value = 0
  248 + elif len_score == 1:
  249 + value = self._smodels[score[0]]
  250 + else:
  251 + value = op(map(lambda sm: self._smodels[sm], score))
  252 +
  253 + return value
  254 +
  255 + def __repr__(self):
  256 + smodels_repr = ',\n\t\t'.join(f"{k}: {v:<}" for k,v in self._smodels.items())
  257 + lits_repr = ','.join(sorted(self._literals))
  258 +
  259 + return "{\n" +\
  260 + f"\t'stable_models': {{\n\t\t {smodels_repr} \n\t}}\n" +\
  261 + f"\t'literals': {{ {lits_repr} }} \n" +\
  262 + "}"
  263 +
  264 +# class EventsClass:
  265 +# def __init__(self, core, lattice:Lattice):
  266 +# self._core = core
  267 +# self._lattice = lattice
  268 +
  269 +# def __repr__(self):
  270 +# core_repr = "" if len(self._core) == 0 else ",".join(str(x) for x in self._core)
  271 +# return f"<{core_repr}>"
  272 +
  273 +# def __contains__(self, event:Event):
  274 +# return self.lattice.stable_core(event) == self._core
  275 +
  276 +if __name__ == "__main__":
  277 + def zoom_event(event_str, lattice):
  278 + event = Event.parse(event_str)
  279 + event_class = lattice.event_class(event)
  280 + propagated = lattice.extended_value(
  281 + event)
  282 +
  283 + print(
  284 + f"Event: {event}\n\tClass: {event_class} \n\tValue: {propagated}")
  285 +
  286 + smodels = Lattice.parse({
  287 + "A": 2,
  288 + "ab": 3,
  289 + "ac": 5
  290 + })
  291 +
  292 + lattice = Lattice(smodels)
  293 +
  294 + ev_classes = lattice.classes()
  295 + for k,g in ev_classes.items():
  296 + print(f"{tuple(s.latex() for s in k)} {set(e.latex() for e in g)}")
  297 + # zoom_event("abc", lattice)
  298 + # zoom_event("a", lattice)
  299 + # zoom_event("b", lattice)
  300 + # zoom_event("bc", lattice)
  301 + # zoom_event("ac", lattice)
0 302 \ No newline at end of file
... ...
code/drafts/explore_01.py 0 → 100644
  Diff comments   View file @353a808
... ... @@ -0,0 +1,13 @@
  1 +from clingo.control import Control
  2 +from clingox.program import Program, ProgramObserver, Remapping
  3 +
  4 +prg = Program()
  5 +ctl_a = Control()
  6 +ctl_a.register_observer(ProgramObserver(prg))
  7 +print(f"<1>\n{prg}\n</1>")
  8 +
  9 +prog = "code/asp/alarm.lp"
  10 +ctl_a.load(prog)
  11 +ctl_a.ground([('base', [])])
  12 +print(f"<2>\n{prg}\n</2>")
  13 +
... ...
code/drafts/sample.csv 0 → 100644
  Diff comments   View file @353a808
... ... @@ -0,0 +1,101 @@
  1 +event
  2 +b
  3 +b
  4 +b
  5 +C
  6 +λ
  7 +BC
  8 +C
  9 +λ
  10 +bC
  11 +BC
  12 +Ac
  13 +λ
  14 +λ
  15 +abC
  16 +λ
  17 +BC
  18 +abC
  19 +A
  20 +a
  21 +B
  22 +b
  23 +abc
  24 +λ
  25 +B
  26 +λ
  27 +AC
  28 +C
  29 +Ac
  30 +C
  31 +B
  32 +Bc
  33 +c
  34 +aB
  35 +Ab
  36 +λ
  37 +C
  38 +aC
  39 +λ
  40 +a
  41 +aBC
  42 +abc
  43 +Ac
  44 +λ
  45 +c
  46 +c
  47 +λ
  48 +Bc
  49 +B
  50 +bc
  51 +aB
  52 +aB
  53 +ABc
  54 +C
  55 +λ
  56 +B
  57 +λ
  58 +ac
  59 +Ac
  60 +b
  61 +Abc
  62 +b
  63 +C
  64 +a
  65 +ab
  66 +C
  67 +ab
  68 +λ
  69 +A
  70 +bc
  71 +AC
  72 +λ
  73 +C
  74 +ABc
  75 +AC
  76 +ac
  77 +BC
  78 +c
  79 +Ac
  80 +ab
  81 +ABC
  82 +A
  83 +aB
  84 +bc
  85 +λ
  86 +aB
  87 +ABc
  88 +Ac
  89 +Ac
  90 +B
  91 +aB
  92 +Ac
  93 +c
  94 +λ
  95 +λ
  96 +b
  97 +c
  98 +Ab
  99 +BC
  100 +A
  101 +BC
... ...
code/drafts/sample_analysis.jl 0 → 100644
  Diff comments   View file @353a808
... ... @@ -0,0 +1,5 @@
  1 +using CSV
  2 +using DataFrames
  3 +
  4 +data = CSV.read("sample.csv", DataFrame)
  5 +println(describe(data, :all))
0 6 \ No newline at end of file
... ...
code/drafts/sampling.jl 0 → 100644
  Diff comments   View file @353a808
... ... @@ -0,0 +1,28 @@
  1 +neg(a) = islowercase(a) ? uppercase(a) : lowercase(a)
  2 +
  3 +function sample(atoms)
  4 + result = Char[]
  5 + for a in atoms
  6 + if rand(Bool)
  7 + push!(result, rand(Bool) ? a : neg(a))
  8 + end
  9 + end
  10 + return length(result) > 0 ? join(result) : "λ"
  11 +end
  12 +
  13 +function sample(n::Int, atoms)
  14 + result = String[]
  15 + for _ in 1:n
  16 + push!(result, sample(atoms))
  17 + end
  18 + return result
  19 +end
  20 +
  21 +using DelimitedFiles
  22 +
  23 +abc_atoms = [ 'a', 'b', 'c']
  24 +
  25 +open("sample.csv", "w") do io
  26 + writedlm(io, [ "event" ])
  27 + writedlm(io, sample(100, abc_atoms), )
  28 +end
0 29 \ No newline at end of file
... ...
code/drafts/symbops.py 0 → 100644
  Diff comments   View file @353a808
... ... @@ -0,0 +1,41 @@
  1 +from unicodedata import numeric
  2 +from sympy import *
  3 +from sympy.plotting import plot
  4 +
  5 +def variants(expr, with_plot=False):
  6 + print(f"Expr: {latex(expr)}")
  7 + print(f"Simplify: {latex(simplify(expr))}")
  8 + print(f"Expand: {latex(expand(expr))}")
  9 + print(f"Factor: {latex(factor(expr))}")
  10 + if with_plot:
  11 + plot(expr, (d, 0, 1, 10),ylabel="$\\mathrm{P(expr \\mid \\alpha = 0.3)}$")
  12 +
  13 +init_printing(use_unicode=True)
  14 +
  15 +a, d = symbols('a d')
  16 +A = 1 - a
  17 +D = 1 - d
  18 +
  19 +wab = a * d
  20 +wac = a * D
  21 +wA = A
  22 +
  23 +wabc = wab * wac
  24 +wAb = wA
  25 +wa = wab + wac
  26 +wb = wab
  27 +wc = wac
  28 +wE = wab + wab + wA
  29 +
  30 +z = wabc + 9 * wA + wab + wac + wa + wb +wc + wE
  31 +pabc = wabc/z
  32 +
  33 +z_03 = z.subs(a, 0.3)
  34 +wabc_03 = wabc.subs(a, 0.3)
  35 +pabc_03 = pabc.subs(a, 0.3)
  36 +
  37 +variants(z_03)
  38 +variants(wabc_03)
  39 +variants(pabc_03)
  40 +print(solve(wabc_03 - 0.0015 * z_03, d))
  41 +
... ...
code/drafts/teste.ipynb 0 → 100644
  Diff comments   View file @353a808
... ... @@ -0,0 +1,116 @@
  1 +{
  2 + "cells": [
  3 + {
  4 + "cell_type": "code",
  5 + "execution_count": 1,
  6 + "metadata": {},
  7 + "outputs": [
  8 + {
  9 + "data": {
  10 + "text/plain": [
  11 + "4"
  12 + ]
  13 + },
  14 + "execution_count": 1,
  15 + "metadata": {},
  16 + "output_type": "execute_result"
  17 + }
  18 + ],
  19 + "source": [
  20 + "2+2"
  21 + ]
  22 + },
  23 + {
  24 + "cell_type": "code",
  25 + "execution_count": 3,
  26 + "metadata": {},
  27 + "outputs": [],
  28 + "source": [
  29 + "import matplotlib.pyplot as plt\n",
  30 + "import numpy as np"
  31 + ]
  32 + },
  33 + {
  34 + "cell_type": "code",
  35 + "execution_count": 4,
  36 + "metadata": {},
  37 + "outputs": [],
  38 + "source": [
  39 + "x = np.linspace(-6, 6)"
  40 + ]
  41 + },
  42 + {
  43 + "cell_type": "code",
  44 + "execution_count": 5,
  45 + "metadata": {},
  46 + "outputs": [],
  47 + "source": [
  48 + "y = np.sin(x)"
  49 + ]
  50 + },
  51 + {
  52 + "cell_type": "code",
  53 + "execution_count": 6,
  54 + "metadata": {},
  55 + "outputs": [
  56 + {
  57 + "data": {
  58 + "text/plain": [
  59 + "[<matplotlib.lines.Line2D at 0x7f2d55566b50>]"
  60 + ]
  61 + },
  62 + "execution_count": 6,
  63 + "metadata": {},
  64 + "output_type": "execute_result"
  65 + },
  66 + {
  67 + "data": {
  68 + "image/png": 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",
  69 + "text/plain": [
  70 + "<Figure size 640x480 with 1 Axes>"
  71 + ]
  72 + },
  73 + "metadata": {},
  74 + "output_type": "display_data"
  75 + }
  76 + ],
  77 + "source": [
  78 + "plt.plot(x,y)"
  79 + ]
  80 + },
  81 + {
  82 + "cell_type": "code",
  83 + "execution_count": null,
  84 + "metadata": {},
  85 + "outputs": [],
  86 + "source": []
  87 + }
  88 + ],
  89 + "metadata": {
  90 + "kernelspec": {
  91 + "display_name": "Python 3.9.15 ('base')",
  92 + "language": "python",
  93 + "name": "python3"
  94 + },
  95 + "language_info": {
  96 + "codemirror_mode": {
  97 + "name": "ipython",
  98 + "version": 3
  99 + },
  100 + "file_extension": ".py",
  101 + "mimetype": "text/x-python",
  102 + "name": "python",
  103 + "nbconvert_exporter": "python",
  104 + "pygments_lexer": "ipython3",
  105 + "version": "3.9.15"
  106 + },
  107 + "orig_nbformat": 4,
  108 + "vscode": {
  109 + "interpreter": {
  110 + "hash": "a59afa236e16843183c59a167f072b6fa0409044b3c4938e82ac98aad91bf217"
  111 + }
  112 + }
  113 + },
  114 + "nbformat": 4,
  115 + "nbformat_minor": 2
  116 +}
... ...
code/python/.ipynb_checkpoints/EventLattice-checkpoint.ipynb
View file @0ca7041
... ... @@ -1,113 +0,0 @@
1   -{
2   - "cells": [
3   - {
4   - "cell_type": "code",
5   - "execution_count": null,
6   - "id": "57fc5921-9d6b-4b43-a8f6-743a03650d63",
7   - "metadata": {},
8   - "outputs": [],
9   - "source": [
10   - "import event_lattice as el"
11   - ]
12   - },
13   - {
14   - "cell_type": "code",
15   - "execution_count": null,
16   - "id": "00f0eb68",
17   - "metadata": {},
18   - "outputs": [],
19   - "source": [
20   - "def zoom_event(event_str, lattice, lower_op=el.sum_op, upper_op=el.prod_op):\n",
21   - " event = el.Event.from_str(event_str)\n",
22   - " event_class = lattice.event_class(event)\n",
23   - " propagated = lattice.propagated_value(\n",
24   - " event, lower_op=lower_op, upper_op=upper_op)\n",
25   - "\n",
26   - " print(\n",
27   - " f\"Event: {event}\\n\\tClass: {event_class} \\n\\tValue: {propagated}\")"
28   - ]
29   - },
30   - {
31   - "cell_type": "code",
32   - "execution_count": null,
33   - "id": "cdd8c6d6",
34   - "metadata": {},
35   - "outputs": [],
36   - "source": [
37   - "smodels = el.Lattice.parse({\n",
38   - " \"A\": 2,\n",
39   - " \"ab\": 3,\n",
40   - " \"ac\": 5\n",
41   - "})\n",
42   - "\n",
43   - "lattice = el.Lattice(smodels)\n",
44   - "\n",
45   - "print(lattice)"
46   - ]
47   - },
48   - {
49   - "cell_type": "code",
50   - "execution_count": null,
51   - "id": "2b445339",
52   - "metadata": {},
53   - "outputs": [],
54   - "source": [
55   - "zoom_event(\"abc\", lattice)\n",
56   - "zoom_event(\"a\", lattice)\n",
57   - "zoom_event(\"b\", lattice)\n",
58   - "zoom_event(\"bc\", lattice)\n",
59   - "zoom_event(\"ac\", lattice)"
60   - ]
61   - },
62   - {
63   - "cell_type": "code",
64   - "execution_count": null,
65   - "id": "f1b85255",
66   - "metadata": {},
67   - "outputs": [],
68   - "source": [
69   - "from itertools import *\n",
70   - "\n",
71   - "lits = lattice.literals()\n",
72   - "for len_lit in range(len(lits)+1):\n",
73   - " events = list(\"\".join(c) for c in combinations(lits, len_lit))\n",
74   - " for event in events:\n",
75   - " zoom_event(event, lattice)"
76   - ]
77   - },
78   - {
79   - "cell_type": "code",
80   - "execution_count": null,
81   - "id": "07973a47",
82   - "metadata": {},
83   - "outputs": [],
84   - "source": []
85   - }
86   - ],
87   - "metadata": {
88   - "kernelspec": {
89   - "display_name": "Python 3.9.13 ('base')",
90   - "language": "python",
91   - "name": "python3"
92   - },
93   - "language_info": {
94   - "codemirror_mode": {
95   - "name": "ipython",
96   - "version": 3
97   - },
98   - "file_extension": ".py",
99   - "mimetype": "text/x-python",
100   - "name": "python",
101   - "nbconvert_exporter": "python",
102   - "pygments_lexer": "ipython3",
103   - "version": "3.9.13"
104   - },
105   - "vscode": {
106   - "interpreter": {
107   - "hash": "a59afa236e16843183c59a167f072b6fa0409044b3c4938e82ac98aad91bf217"
108   - }
109   - }
110   - },
111   - "nbformat": 4,
112   - "nbformat_minor": 5
113   -}
code/python/EventLattice.ipynb
View file @0ca7041
... ... @@ -1,154 +0,0 @@
1   -{
2   - "cells": [
3   - {
4   - "cell_type": "code",
5   - "execution_count": 4,
6   - "id": "57fc5921-9d6b-4b43-a8f6-743a03650d63",
7   - "metadata": {},
8   - "outputs": [
9   - {
10   - "name": "stdout",
11   - "output_type": "stream",
12   - "text": [
13   - "The autoreload extension is already loaded. To reload it, use:\n",
14   - " %reload_ext autoreload\n"
15   - ]
16   - }
17   - ],
18   - "source": [
19   - "%load_ext autoreload\n",
20   - "%autoreload 1\n",
21   - "%aimport event_lattice"
22   - ]
23   - },
24   - {
25   - "cell_type": "code",
26   - "execution_count": 5,
27   - "id": "00f0eb68",
28   - "metadata": {},
29   - "outputs": [],
30   - "source": [
31   - "def zoom_event(event_str, lattice):\n",
32   - " event = event_lattice.Event.from_str(event_str)\n",
33   - " event_class = lattice.event_class(event)\n",
34   - " propagated = lattice.extended_value(\n",
35   - " event)\n",
36   - "\n",
37   - " print(\n",
38   - " f\"Event: {event}\\n\\tClass: {event_class} \\n\\tValue: {propagated}\")"
39   - ]
40   - },
41   - {
42   - "cell_type": "code",
43   - "execution_count": 6,
44   - "id": "cdd8c6d6",
45   - "metadata": {},
46   - "outputs": [
47   - {
48   - "name": "stdout",
49   - "output_type": "stream",
50   - "text": [
51   - "{\n",
52   - "\t'stable_models': {\n",
53   - "\t\t A: 2,\n",
54   - "\t\tab: 3,\n",
55   - "\t\tac: 5 \n",
56   - "\t}\n",
57   - "\t'literals': { A,B,C,a,b,c } \n",
58   - "}\n"
59   - ]
60   - }
61   - ],
62   - "source": [
63   - "smodels = event_lattice.Lattice.parse({\n",
64   - " \"A\": 2,\n",
65   - " \"ab\": 3,\n",
66   - " \"ac\": 5\n",
67   - "})\n",
68   - "\n",
69   - "lattice = event_lattice.Lattice(smodels)\n",
70   - "\n",
71   - "print(lattice)"
72   - ]
73   - },
74   - {
75   - "cell_type": "code",
76   - "execution_count": 7,
77   - "id": "2b445339",
78   - "metadata": {},
79   - "outputs": [
80   - {
81   - "ename": "TypeError",
82   - "evalue": "__init__() missing 1 required positional argument: 'lattice'",
83   - "output_type": "error",
84   - "traceback": [
85   - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
86   - "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)",
87   - "\u001b[0;32m/tmp/ipykernel_361713/2581811254.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mzoom_event\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"abc\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlattice\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2\u001b[0m \u001b[0mzoom_event\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"a\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlattice\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mzoom_event\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"b\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlattice\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0mzoom_event\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"bc\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlattice\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0mzoom_event\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"ac\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlattice\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
88   - "\u001b[0;32m/tmp/ipykernel_361713/1675915232.py\u001b[0m in \u001b[0;36mzoom_event\u001b[0;34m(event_str, lattice)\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mzoom_event\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mevent_str\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlattice\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0mevent\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mevent_lattice\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mEvent\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfrom_str\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mevent_str\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mevent_class\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlattice\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mevent_class\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mevent\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 4\u001b[0m propagated = lattice.extended_value(\n\u001b[1;32m 5\u001b[0m event)\n",
89   - "\u001b[0;32m~/sci/projetos/zugzwang/code/python/event_lattice.py\u001b[0m in \u001b[0;36mevent_class\u001b[0;34m(self, event)\u001b[0m\n\u001b[1;32m 146\u001b[0m \u001b[0;34m@\u001b[0m\u001b[0mcache\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 147\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mevent_class\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mevent\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 148\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mEventsClass\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstable_core\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mevent\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 149\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 150\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mrelated\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mu\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mv\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
90   - "\u001b[0;31mTypeError\u001b[0m: __init__() missing 1 required positional argument: 'lattice'"
91   - ]
92   - }
93   - ],
94   - "source": [
95   - "zoom_event(\"abc\", lattice)\n",
96   - "zoom_event(\"a\", lattice)\n",
97   - "zoom_event(\"b\", lattice)\n",
98   - "zoom_event(\"bc\", lattice)\n",
99   - "zoom_event(\"ac\", lattice)"
100   - ]
101   - },
102   - {
103   - "cell_type": "code",
104   - "execution_count": null,
105   - "id": "f1b85255",
106   - "metadata": {},
107   - "outputs": [],
108   - "source": [
109   - "from itertools import *\n",
110   - "\n",
111   - "lits = lattice.literals()\n",
112   - "events = []\n",
113   - "for len_lit in range(len(lits)+1):\n",
114   - " events = events + list(\"\".join(c) for c in combinations(lits, len_lit))\n",
115   - "for event in events:\n",
116   - " zoom_event(event, lattice)"
117   - ]
118   - },
119   - {
120   - "cell_type": "code",
121   - "execution_count": null,
122   - "id": "07973a47",
123   - "metadata": {},
124   - "outputs": [],
125   - "source": []
126   - }
127   - ],
128   - "metadata": {
129   - "kernelspec": {
130   - "display_name": "Python 3 (ipykernel)",
131   - "language": "python",
132   - "name": "python3"
133   - },
134   - "language_info": {
135   - "codemirror_mode": {
136   - "name": "ipython",
137   - "version": 3
138   - },
139   - "file_extension": ".py",
140   - "mimetype": "text/x-python",
141   - "name": "python",
142   - "nbconvert_exporter": "python",
143   - "pygments_lexer": "ipython3",
144   - "version": "3.9.15"
145   - },
146   - "vscode": {
147   - "interpreter": {
148   - "hash": "a59afa236e16843183c59a167f072b6fa0409044b3c4938e82ac98aad91bf217"
149   - }
150   - }
151   - },
152   - "nbformat": 4,
153   - "nbformat_minor": 5
154   -}
code/python/__init__.py
View file @0ca7041
code/python/__pycache__/event_lattice.cpython-39.pyc
View file @0ca7041
No preview for this file type
code/python/algebra.py
View file @0ca7041
... ... @@ -1,30 +0,0 @@
1   -from itertools import combinations, product
2   -
3   -def fmt(expr):
4   - """Doc string"""
5   - return ",".join(f"{x:>2}" for x in expr)
6   -
7   -def c(expr):
8   - """Doc string"""
9   - def litcomp(x):
10   - if x == "⊤":
11   - return "⊥"
12   - elif x == "⊥":
13   - return "⊤"
14   - elif x[0] == "¬":
15   - return x[1:]
16   - else:
17   - return f"¬{x}"
18   - return [litcomp(x) for x in expr]
19   -
20   -def domain(symbols, unary="¬"):
21   - """Doc string"""
22   - atoms = list(symbols)
23   - literals = [
24   - [f"{u}{a}" for u in unary] +
25   - [a, "⊤", "⊥"] for a in atoms ]
26   - return product(*literals)
27   -
28   -d = sorted(domain("abc"))
29   -for x in d:
30   - print(f"{fmt(x)} | {fmt(c(x))}")
code/python/api_01.py
View file @0ca7041
... ... @@ -1,26 +0,0 @@
1   -from clingo.symbol import Number
2   -from clingo.control import Control
3   -
4   -class Context:
5   - def inc(self, x):
6   - return Number(x.number + 1)
7   -
8   - def seq(self, x, y):
9   - return [x, y]
10   -
11   -def on_model(m):
12   - print(m)
13   -
14   -ctl = Control()
15   -ctl.add("base", [], """\
16   -p(@inc(10)).
17   -q(@seq(1,2)).
18   -""")
19   -
20   -ctl.ground(
21   - [("base", [])],
22   - context=Context())
23   -
24   -s = ctl.solve(on_model=on_model)
25   -
26   -print(s)
27 0 \ No newline at end of file
code/python/event_lattice.py
View file @0ca7041
... ... @@ -1,301 +0,0 @@
1   -import math
2   -from functools import cache
3   -from itertools import accumulate, combinations, chain, groupby
4   -import operator
5   -
6   -
7   -
8   -def uniform_op(x):
9   - n = len(list(x))
10   - return 1.0 if n == 0 else 1.0/n
11   -
12   -
13   -def max_op(x):
14   - return max(x)
15   -
16   -
17   -def min_op(x):
18   - return min(x)
19   -
20   -
21   -def sum_op(x):
22   - return sum(x)
23   -
24   -
25   -def stableprod_op(x):
26   - log_x = map(math.log, x)
27   - return math.exp(sum(log_x))
28   -
29   -
30   -def prod_op(x):
31   - return list(accumulate(x, func=lambda a,b: a*b))[-1]
32   -
33   -
34   -class Event:
35   - """Events.
36   -
37   - An event is a set of literals - atoms and negated atoms.
38   -
39   - The convention is that atoms are represented by lower case single letters
40   - and a negated atom by upper case single letters.
41   - """
42   -
43   - @staticmethod
44   - def _parse(text):
45   - return frozenset(text)
46   -
47   - @staticmethod
48   - def parse(text):
49   - """Convert a string to an event.
50   -
51   - Each letter in the string represents a literal.
52   - """
53   - return Event(Event._parse(text))
54   -
55   -
56   - def __init__(self, literals):
57   - """Instantiate from a (frozen) set of literals.
58   - For example: e = Event(frozenset("abc"))."""
59   - self._literals = frozenset(literals)
60   -
61   -
62   - def literals(self):
63   - return self._literals
64   -
65   -
66   - def __iter__(self):
67   - return self._literals.__iter__()
68   -
69   - @cache
70   - def is_consistent(self):
71   - """True if this event is consistent."""
72   - return all(x.swapcase() not in self._literals for x in self._literals)
73   -
74   -
75   - def co(self):
76   - """Negation of this event.
77   -
78   - Negation is case based: A = not a; a = not A."""
79   - return Event(x.swapcase() for x in self._literals)
80   -
81   - def invert(self):
82   - """Negation of this event.
83   -
84   - See the method "co"
85   - """
86   - return self.co()
87   -
88   - def __repr__(self) -> str:
89   - return ''.join(str(x) for x in sorted(self._literals)) if len(self._literals) > 0 else '0'
90   -
91   - def latex(self):
92   - """LaTeX representation of this even.
93   -
94   - Negation is represented by overline and the empty event by
95   -
96   - """
97   - return ''.join(
98   - (str(x) if x.islower() else f"\co{{{x.lower()}}}") \
99   - for x in sorted(self._literals)
100   - ) if len(self._literals) > 0 else "\set{}"
101   -
102   - def __hash__(self) -> int:
103   - return self._literals.__hash__()
104   -
105   -
106   - def __eq__(self, other):
107   - """Event equality test."""
108   - return self._literals.__eq__(other._literals)
109   -
110   - def __or__(self, other):
111   - """Event union operation."""
112   - return Event(self._literals | other._literals)
113   -
114   - def __le__(self, other):
115   - """Event subset test."""
116   - return self._literals.__le__(other._literals)
117   -
118   -
119   - def __lt__(self, other):
120   - """Event strict subset test."""
121   - return self._literals.__lt__(other._literals)
122   -
123   -
124   - def __ne__(self, other):
125   - """Event not-equal test."""
126   - return self._literals.__ne__(other._literals)
127   -
128   -
129   - def __ge__(self, other):
130   - """Event superset test."""
131   - return self._literals.__ge__(other._literals)
132   -
133   -
134   - def __gt__(self, other):
135   - """Event strict superset test."""
136   - return self._literals.__gt__(other._literals)
137   -
138   -
139   -class Lattice:
140   -
141   - @staticmethod
142   - def parse(d):
143   - """Input stable models.
144   -
145   - The input format is a dictionary associating a stable model in string form to an weight.
146   -
147   - For example:
148   -
149   - input_dict = {
150   - "A": 0.3,
151   - "ab": 0.2,
152   - "ac": 0.5
153   - }
154   - smodels = Lattice.parse(input_dict)
155   - """
156   - result = dict()
157   - for k, v in d.items():
158   - key = Event.parse(k)
159   - result[key] = v
160   - return result
161   -
162   -
163   - @staticmethod
164   - def close_literals(events):
165   - """Closed set of literals entailed by a set of events.
166   -
167   - Includes the literals in the set of events and any missing negation."""
168   - base_lits = list(accumulate(events, func=operator.or_))[-1]
169   - lits = set()
170   - for x in base_lits.literals():
171   - lits.add(x)
172   - lits.add(x.swapcase())
173   - return sorted(lits)
174   -
175   - def __init__(self, smodels_dict):
176   - """Create an Events lattice."""
177   - self._smodels = smodels_dict
178   - self._literals = Lattice.close_literals(self._smodels.keys())
179   -
180   - def literals(self):
181   - """The literals in this lattice."""
182   - return self._literals
183   -
184   - @cache
185   - def stable_models(self):
186   - """The stable models that generate this lattice."""
187   - return self._smodels.keys()
188   -
189   - #@cache
190   - def events(self):
191   - """All the events of this lattice."""
192   - return chain.from_iterable(map(Event, combinations(self._literals, r)) for r in range(len(self._literals)+1))
193   -
194   - @cache
195   - def stable_core(self, event):
196   - """The stable core of an event in this lattice."""
197   - return set(filter(lambda sm: sm <= event or event <= sm, self.stable_models()))
198   -
199   - # @cache
200   - # def event_class(self, event):
201   - # """The equivalence class of an event."""
202   - # return EventsClass(self.stable_core(event), self)
203   -
204   - @cache
205   - def classes(self):
206   - """The classes of this lattice.
207   -
208   - Each class is presented as a key:value pair where the "key" is the stable core of the elements in "value"."""
209   - map_ev_classes = [(e, tuple(self.stable_core(e))) for e in self.events() if e.is_consistent()]
210   - groups = dict()
211   - for e,c in map_ev_classes:
212   - if c in groups.keys():
213   - groups[c].add(e)
214   - else:
215   - groups[c] = set([e])
216   - inconsistent = list(e for e in self.events() if not e.is_consistent())
217   - inconsistent_repr = inconsistent[0]
218   - groups[(inconsistent_repr,)] = set(inconsistent)
219   - return groups
220   -
221   -
222   - def related(self, u, v):
223   - """Tests if two events are related."""
224   - u_consistent = u.is_consistent()
225   - v_consistent = v.is_consistent()
226   - if u_consistent and (u_consistent == v_consistent):
227   - return self.stable_core(u) == self.stable_core(v)
228   - else:
229   - return u_consistent == v_consistent
230   -
231   - def extended_value(self, event:Event,
232   - op=prod_op):
233   - """TODO: well..."""
234   - value = 0
235   - #
236   - # INCONSISTENT EVENTS
237   - #
238   - if not event.is_consistent():
239   - return value
240   - #
241   - # CONSISTENT EVENTS
242   - #
243   - score = self.stable_core(event)
244   - len_score = len(score)
245   - # CONSISTENT, INDEPENDENT
246   - if len_score == 0:
247   - value = 0
248   - elif len_score == 1:
249   - value = self._smodels[score[0]]
250   - else:
251   - value = op(map(lambda sm: self._smodels[sm], score))
252   -
253   - return value
254   -
255   - def __repr__(self):
256   - smodels_repr = ',\n\t\t'.join(f"{k}: {v:<}" for k,v in self._smodels.items())
257   - lits_repr = ','.join(sorted(self._literals))
258   -
259   - return "{\n" +\
260   - f"\t'stable_models': {{\n\t\t {smodels_repr} \n\t}}\n" +\
261   - f"\t'literals': {{ {lits_repr} }} \n" +\
262   - "}"
263   -
264   -# class EventsClass:
265   -# def __init__(self, core, lattice:Lattice):
266   -# self._core = core
267   -# self._lattice = lattice
268   -
269   -# def __repr__(self):
270   -# core_repr = "" if len(self._core) == 0 else ",".join(str(x) for x in self._core)
271   -# return f"<{core_repr}>"
272   -
273   -# def __contains__(self, event:Event):
274   -# return self.lattice.stable_core(event) == self._core
275   -
276   -if __name__ == "__main__":
277   - def zoom_event(event_str, lattice):
278   - event = Event.parse(event_str)
279   - event_class = lattice.event_class(event)
280   - propagated = lattice.extended_value(
281   - event)
282   -
283   - print(
284   - f"Event: {event}\n\tClass: {event_class} \n\tValue: {propagated}")
285   -
286   - smodels = Lattice.parse({
287   - "A": 2,
288   - "ab": 3,
289   - "ac": 5
290   - })
291   -
292   - lattice = Lattice(smodels)
293   -
294   - ev_classes = lattice.classes()
295   - for k,g in ev_classes.items():
296   - print(f"{tuple(s.latex() for s in k)} {set(e.latex() for e in g)}")
297   - # zoom_event("abc", lattice)
298   - # zoom_event("a", lattice)
299   - # zoom_event("b", lattice)
300   - # zoom_event("bc", lattice)
301   - # zoom_event("ac", lattice)
302 0 \ No newline at end of file
code/python/explore_01.py
View file @0ca7041
... ... @@ -1,13 +0,0 @@
1   -from clingo.control import Control
2   -from clingox.program import Program, ProgramObserver, Remapping
3   -
4   -prg = Program()
5   -ctl_a = Control()
6   -ctl_a.register_observer(ProgramObserver(prg))
7   -print(f"<1>\n{prg}\n</1>")
8   -
9   -prog = "code/asp/alarm.lp"
10   -ctl_a.load(prog)
11   -ctl_a.ground([('base', [])])
12   -print(f"<2>\n{prg}\n</2>")
13   -
code/python/symbops.py
View file @0ca7041
... ... @@ -1,41 +0,0 @@
1   -from unicodedata import numeric
2   -from sympy import *
3   -from sympy.plotting import plot
4   -
5   -def variants(expr, with_plot=False):
6   - print(f"Expr: {latex(expr)}")
7   - print(f"Simplify: {latex(simplify(expr))}")
8   - print(f"Expand: {latex(expand(expr))}")
9   - print(f"Factor: {latex(factor(expr))}")
10   - if with_plot:
11   - plot(expr, (d, 0, 1, 10),ylabel="$\\mathrm{P(expr \\mid \\alpha = 0.3)}$")
12   -
13   -init_printing(use_unicode=True)
14   -
15   -a, d = symbols('a d')
16   -A = 1 - a
17   -D = 1 - d
18   -
19   -wab = a * d
20   -wac = a * D
21   -wA = A
22   -
23   -wabc = wab * wac
24   -wAb = wA
25   -wa = wab + wac
26   -wb = wab
27   -wc = wac
28   -wE = wab + wab + wA
29   -
30   -z = wabc + 9 * wA + wab + wac + wa + wb +wc + wE
31   -pabc = wabc/z
32   -
33   -z_03 = z.subs(a, 0.3)
34   -wabc_03 = wabc.subs(a, 0.3)
35   -pabc_03 = pabc.subs(a, 0.3)
36   -
37   -variants(z_03)
38   -variants(wabc_03)
39   -variants(pabc_03)
40   -print(solve(wabc_03 - 0.0015 * z_03, d))
41   -
code/python/teste.ipynb
View file @0ca7041
... ... @@ -1,116 +0,0 @@
1   -{
2   - "cells": [
3   - {
4   - "cell_type": "code",
5   - "execution_count": 1,
6   - "metadata": {},
7   - "outputs": [
8   - {
9   - "data": {
10   - "text/plain": [
11   - "4"
12   - ]
13   - },
14   - "execution_count": 1,
15   - "metadata": {},
16   - "output_type": "execute_result"
17   - }
18   - ],
19   - "source": [
20   - "2+2"
21   - ]
22   - },
23   - {
24   - "cell_type": "code",
25   - "execution_count": 3,
26   - "metadata": {},
27   - "outputs": [],
28   - "source": [
29   - "import matplotlib.pyplot as plt\n",
30   - "import numpy as np"
31   - ]
32   - },
33   - {
34   - "cell_type": "code",
35   - "execution_count": 4,
36   - "metadata": {},
37   - "outputs": [],
38   - "source": [
39   - "x = np.linspace(-6, 6)"
40   - ]
41   - },
42   - {
43   - "cell_type": "code",
44   - "execution_count": 5,
45   - "metadata": {},
46   - "outputs": [],
47   - "source": [
48   - "y = np.sin(x)"
49   - ]
50   - },
51   - {
52   - "cell_type": "code",
53   - "execution_count": 6,
54   - "metadata": {},
55   - "outputs": [
56   - {
57   - "data": {
58   - "text/plain": [
59   - "[<matplotlib.lines.Line2D at 0x7f2d55566b50>]"
60   - ]
61   - },
62   - "execution_count": 6,
63   - "metadata": {},
64   - "output_type": "execute_result"
65   - },
66   - {
67   - "data": {
68   - "image/png": 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",
69   - "text/plain": [
70   - "<Figure size 640x480 with 1 Axes>"
71   - ]
72   - },
73   - "metadata": {},
74   - "output_type": "display_data"
75   - }
76   - ],
77   - "source": [
78   - "plt.plot(x,y)"
79   - ]
80   - },
81   - {
82   - "cell_type": "code",
83   - "execution_count": null,
84   - "metadata": {},
85   - "outputs": [],
86   - "source": []
87   - }
88   - ],
89   - "metadata": {
90   - "kernelspec": {
91   - "display_name": "Python 3.9.15 ('base')",
92   - "language": "python",
93   - "name": "python3"
94   - },
95   - "language_info": {
96   - "codemirror_mode": {
97   - "name": "ipython",
98   - "version": 3
99   - },
100   - "file_extension": ".py",
101   - "mimetype": "text/x-python",
102   - "name": "python",
103   - "nbconvert_exporter": "python",
104   - "pygments_lexer": "ipython3",
105   - "version": "3.9.15"
106   - },
107   - "orig_nbformat": 4,
108   - "vscode": {
109   - "interpreter": {
110   - "hash": "a59afa236e16843183c59a167f072b6fa0409044b3c4938e82ac98aad91bf217"
111   - }
112   - }
113   - },
114   - "nbformat": 4,
115   - "nbformat_minor": 2
116   -}
sample.csv 0 → 100644
  Diff comments   View file @353a808
... ... @@ -0,0 +1,100 @@
  1 +c
  2 +a
  3 +B
  4 +c
  5 +ab
  6 +Ac
  7 +aBC
  8 +BC
  9 +Ab
  10 +b
  11 +c
  12 +AB
  13 +Ac
  14 +B
  15 +bC
  16 +Ab
  17 +
  18 +aB
  19 +B
  20 +a
  21 +aC
  22 +B
  23 +AB
  24 +B
  25 +
  26 +C
  27 +bc
  28 +
  29 +B
  30 +bc
  31 +AC
  32 +ABC
  33 +a
  34 +b
  35 +ac
  36 +AC
  37 +B
  38 +bC
  39 +b
  40 +C
  41 +
  42 +aC
  43 +AbC
  44 +
  45 +C
  46 +AC
  47 +bc
  48 +
  49 +
  50 +C
  51 +b
  52 +
  53 +b
  54 +abc
  55 +a
  56 +abc
  57 +
  58 +B
  59 +a
  60 +C
  61 +aB
  62 +
  63 +A
  64 +Bc
  65 +C
  66 +AB
  67 +aBc
  68 +A
  69 +b
  70 +
  71 +a
  72 +a
  73 +c
  74 +b
  75 +a
  76 +A
  77 +Ab
  78 +aC
  79 +
  80 +B
  81 +C
  82 +Ab
  83 +Bc
  84 +A
  85 +Ac
  86 +c
  87 +B
  88 +AC
  89 +ABC
  90 +Ab
  91 +aC
  92 +bC
  93 +
  94 +
  95 +C
  96 +a
  97 +
  98 +ABC
  99 +b
  100 +aB
... ...
students/amartins/tarefas/tarefa2.py
  Diff comments   View file @353a808
... ... @@ -26,13 +26,20 @@ if __name__ == &quot;__main__&quot;:
26 26 parents = model.get_parents(node)
27 27 s = ""
28 28 if len(parents) == 0:
29   - s += str(yes_prob) + " :: " + str(node)
  29 + s += str(yes_prob) + " :: " + str(node) +"\n"
30 30 print(s)
31 31 elif len(parents) == 1:
32   - s += str(yes_prob[0]) + " :: " + str(node) + " <- " + str(parents) + "\n"
33   - s += str(yes_prob[1]) + " :: " + str(node) + " <- -" + str(parents) + "\n"
  32 + p = parents[0]
  33 + s += str(yes_prob[0]) + " :: " + str(node) + " <- " + str(p) + "\n"
  34 + s += str(yes_prob[1]) + " :: " + str(node) + " <- -" + str(p) + "\n"
34 35 print(s)
35 36 else:
36   - print("Node:", node)
37   - print("Probability of 'yes':", yes_prob)
38   - print()
  37 + yes1 = yes_prob[0]
  38 + yes2 = yes_prob[1]
  39 + p0 = parents[0]
  40 + p1 = parents[1]
  41 + s += str(yes1[0]) + " :: " + str(node) + " <- " + str(p0) + ", " + str(p1) + "\n"
  42 + s += str(yes2[0]) + " :: " + str(node) + " <- -" + str(p0) + ", " + str(p1) + "\n"
  43 + s += str(yes1[1]) + " :: " + str(node) + " <- " + str(p0) + ", -" + str(p1) + "\n"
  44 + s += str(yes2[1]) + " :: " + str(node) + " <- -" + str(p0) + ", -" + str(p1) + "\n"
  45 + print(s)
... ...
text/paper_01/pre-paper.pdf
View file @353a808
No preview for this file type
text/paper_01/pre-paper.tex
  Diff comments   View file @353a808
... ... @@ -17,7 +17,7 @@ proptc/.style = {-latex, dashed},
17 17 propsm/.style = {-latex, thick},
18 18 doubt/.style = {gray}
19 19 }
20   -\usetikzlibrary{calc, positioning}
  20 +\usetikzlibrary{calc, positioning, patterns}
21 21  
22 22 \usepackage{hyperref}
23 23 \hypersetup{
... ... @@ -93,16 +93,18 @@ citecolor=blue,
93 93 \acrodef{SC}[SC]{stable core}
94 94 \acrodef{KL}[KL]{Kullback-Leibler}
95 95  
96   -\title{Zugzwang\\\emph{Logic and Artificial Intelligence}\\{\bruno Why this title?}}
  96 +\title{An Algebraic Approach to Stochastic ASP
  97 + %Zugzwang\\\emph{Logic and Artificial Intelligence}\\{\bruno Why this title?}
  98 + }
97 99  
98 100 \author{
99 101 \begin{tabular}{ccc}
100 102 Francisco Coelho
101   - \footnote{Universidade de Évora}
  103 + \footnote{Universidade de Évora, NOVALINCS, High Performance Computing Chair}
102 104 & Bruno Dinis
103   - \footnote{Universidade de Évora}
  105 + \footnote{Universidade de Évora, CIMA, CMAFcIO}
104 106 & Salvador Abreu
105   - \footnote{Universidade de Évora}
  107 + \footnote{Universidade de Évora, NOVALINCS}
106 108 \\
107 109 \texttt{fc@uevora.pt}
108 110 & \texttt{bruno.dinis@uevora.pt}
... ... @@ -148,8 +150,9 @@ Our idea to extend probabilities starts with the stance that a specification des
148 150 Extending probability from \acp{TC} to \acp{SM} faces a critical problem, illustrated by the example in \cref{sec:example.1}, concerning situations where multiple \acp{SM}, $ab$ and $ac$, result from a single \ac{TC}, $a$, but there is not enough information (in the specification) to assign a single probability to each \ac{SM}. We propose to address this issue by using algebraic variables to describe that lack of information and then estimate the value of those variables from empirical data.
149 151  
150 152 In a related work, \cite{verreet2022inference}, epistemic uncertainty (or model uncertainty) is considered as a lack of knowledge about the underlying model, that may be mitigated via further observations. This seems to presuppose a Bayesian approach to imperfect knowledge in the sense that having further observations allows to improve/correct the model. Indeed, the approach in that work uses Beta distributions in order to be able to learn the full distribution. This approach seems to be specially fitted to being able to tell when some probability lies beneath some given value. \todo{Our approach seems to be similar in spirit. If so, we should mention this in the introduction.}
  153 +\todo{Also remark that our apporach remains algebraic in the way that we address the problems concerning the extension of probabilities.}
151 154  
152   -\todo{cite \cite{sympy} \franc{--- why here? but cite \cite{cozman2020joy} and relate with our work.}}
  155 +\todo{cite \citetitle{sympy} \franc{--- why here? but cite \citetitle{cozman2020joy} and relate with our work.}}
153 156  
154 157 \todo{Discuss the least informed strategy and the corolary that \aclp{SM} should be conditionally independent on the \acl{TC}.}
155 158  
... ... @@ -239,6 +242,8 @@ The \aclp{SM} $ab, ac$ from \cref{running.example} result from the clause $b \v
239 242  
240 243 \draw[doubt] (ac) to[bend right] (abc);
241 244 \draw[doubt] (ac) to[bend left] (aBc);
  245 +
  246 + \draw[doubt, dash dot] (Ac) to (Abc);
242 247  
243 248 \draw[doubt] (A) to (Ac);
244 249 \draw[doubt] (A) to (Abc);
... ... @@ -251,10 +256,10 @@ The \aclp{SM} $ab, ac$ from \cref{running.example} result from the clause $b \v
251 256 \draw[doubt] (ac) to (c);
252 257 % \draw[doubt] (ab) to[bend left] (a);
253 258 % \draw[doubt] (ac) to[bend right] (a);
254   - \draw[doubt] (c) to[bend right] (bc);
255   - \draw[doubt] (abc) to[bend left] (bc);
256   - \draw[doubt] (Abc) to (bc);
257   - \draw[doubt] (c) to[bend right] (Ac);
  259 + \draw[doubt, dash dot] (c) to[bend right] (bc);
  260 + \draw[doubt, dash dot] (abc) to[bend left] (bc);
  261 + \draw[doubt, dash dot] (bc) to (Abc);
  262 + \draw[doubt, dash dot] (c) to[bend right] (Ac);
258 263 \end{tikzpicture}
259 264 \end{center}
260 265  
... ... @@ -287,7 +292,7 @@ The diagram in \cref{fig:running.example} illustrates the problem of extending p
287 292 \node[event, above = of A] (Ac) {$\co{a}c$};
288 293 \node[event, above right = of Ac] (Abc) {$\co{a}bc$};
289 294 % ----
290   - \path[draw, rounded corners, fill=cyan, fill opacity=0.1]
  295 + \path[draw, rounded corners, pattern=north west lines, opacity=0.2]
291 296 (ab.west) --
292 297 (ab.north west) --
293 298 %
... ... @@ -316,7 +321,7 @@ The diagram in \cref{fig:running.example} illustrates the problem of extending p
316 321 (ab.west)
317 322 ;
318 323 % ----
319   - \path[draw, rounded corners, fill=magenta, fill opacity=0.1]
  324 + \path[draw, rounded corners, pattern=north east lines, opacity=0.2]
320 325 (ac.south west) --
321 326 (ac.west) --
322 327 (ac.north west) --
... ... @@ -346,7 +351,7 @@ The diagram in \cref{fig:running.example} illustrates the problem of extending p
346 351 (ac.south west)
347 352 ;
348 353 % ----
349   - \path[draw, rounded corners, fill=yellow, fill opacity=0.1]
  354 + \path[draw, rounded corners, pattern=horizontal lines, opacity=0.2]
350 355 % (A.north west) --
351 356 %
352 357 (Ac.north west) --
... ... @@ -373,7 +378,7 @@ The diagram in \cref{fig:running.example} illustrates the problem of extending p
373 378 \end{tikzpicture}
374 379 \end{center}
375 380  
376   - \caption{Classes (of consistent events) related to the \aclp{SM} of \cref{running.example} are defined through inclusions. \todo{write the caption}}
  381 + \caption{Classes (of consistent events) related to the \aclp{SM} of \cref{running.example} are defined through intersections and inclusions. \todo{write the caption}}
377 382 \label{fig:running.example.classes}
378 383 \end{figure}
379 384  
... ... @@ -559,7 +564,7 @@ The ``extension&#39;&#39; phase, traced by equations (\ref{eq:prob.total.choice}) and (\
559 564 \pw{\class{e}} := \sum_{t \in \fml{T}} \pw{\class{e}, t}\pw{t}.
560 565 \label{eq:weight.class.unconditional}
561 566 \end{equation}
562   - \remark{}{Changed from $\prod$ to $\sum$ to represent ``either'' instead of ``both'' since the later is not consistent with the ``only one stable model at a time'' assumption.}
  567 +
563 568 \end{description}
564 569 %
565 570 \item[Events.] \label{item:event.cases} Each (general) event $e$ is in the class defined by its \acl{SC}, $\stablecore{e}$. So, we set:
... ... @@ -618,9 +623,9 @@ We continue with the specification from Equation \eqref{eq:example.1}.
618 623 \item[\Aclp{SM}.] The $\theta_{s,t}$ parameters in this example are
619 624 $$
620 625 \theta_{ab,\co{a}} = \theta_{ac,\co{a}} = \theta_{\co{a}, a} = 0
621   - $$
622   - and
623   - $$
  626 + %
  627 + \text{~and~}
  628 + %
624 629 \theta_{\co{a}, \co{a}} = 1, \theta_{ab, a} = \theta, \theta_{ac, a} = \co{\theta}
625 630 $$
626 631 with $\theta \in \intcc{0, 1}$.
... ... @@ -675,7 +680,7 @@ We continue with the specification from Equation \eqref{eq:example.1}.
675 680 & 1
676 681 \end{array}
677 682 \end{equation*}
678   - \item[Normalization.] To get a weight that sums up to one, we compute the \emph{normalization factor}. Since $\pw{\cdot}$ is constant on classes,
  683 + \item[Normalization.] To get a weight that sums up to one, we compute the \emph{normalization factor}. Since $\pw{\cdot}$ is constant on classes,\todo{prove that we get a probability.}
679 684 \begin{equation*}
680 685 Z := \sum_{e\in\fml{E}} \pw{e}
681 686 = \sum_{\class{e} \in\class{\fml{E}}} \frac{\pw{\class{e}}}{\#\class{e}},
... ... @@ -704,95 +709,81 @@ We continue with the specification from Equation \eqref{eq:example.1}.
704 709 & 0
705 710 & 0
706 711 & 0
707   - \\
  712 + \\[4pt]
708 713 %
709 714 \indepclass
710 715 & 9
711 716 & 0
712 717 & 0
713 718 & 0
714   - \\
  719 + \\[4pt]
715 720 %
716 721 \co{a}
717 722 & 9
718   - & \lfrac{7}{10}
719   - & \lfrac{7}{90}
720   - & \lfrac{7}{792}
721   - \\
  723 + & \frac{7}{10}
  724 + & \frac{7}{90}
  725 + & \frac{7}{792}
  726 + \\[4pt]
722 727 %
723 728 ab
724 729 & 3
725   - & \lfrac{3\theta}{10}
726   - & \lfrac{\theta}{10}
727   - & \lfrac{\theta}{88}
728   - \\
  730 + & \frac{3\theta}{10}
  731 + & \frac{\theta}{10}
  732 + & \frac{\theta}{88}
  733 + \\[4pt]
729 734 %
730 735 ac
731 736 & 3
732   - & \lfrac{3\co{\theta}}{10}
733   - & \lfrac{\co{\theta}}{10}
734   - & \lfrac{\co{\theta}}{88}
735   - \\
  737 + & \frac{3\co{\theta}}{10}
  738 + & \frac{\co{\theta}}{10}
  739 + & \frac{\co{\theta}}{88}
  740 + \\[4pt]
736 741 %
737 742 \co{a}, ab
738 743 & 0
739   - &
740   - &
741   - &
742   - \\
  744 + & \frac{7 + 3\theta}{10}
  745 + & 0
  746 + & 0
  747 + \\[4pt]
743 748 %
744 749 \co{a}, ac
745 750 & 0
746   - &
747   - &
748   - &
  751 + & \frac{7 + 3\co{\theta}}{10}
  752 + & 0
  753 + & 0
749 754 %
750   - \\
  755 + \\[4pt]
751 756 %
752 757 ab, ac
753 758 & 2
754   - & \lfrac{3}{10}
755   - & \lfrac{3}{20}
756   - & \lfrac{3}{176}
757   - \\
  759 + & \frac{3}{10}
  760 + & \frac{3}{20}
  761 + & \frac{3}{176}
  762 + \\[4pt]
758 763 %
759 764 \co{a}, ab, ac
760 765 & 1
761 766 & 1
762 767 & 1
763   - & \lfrac{5}{176}
764   - \\
  768 + & \frac{5}{176}
  769 + \\[4pt]
765 770 %
766 771 \hline
767 772 &
768   - & Z = 8.8
  773 + & Z = \frac{44}{5}
769 774 \end{array}
770 775 \end{equation*}
771 776 \end{description}
  777 +
  778 +\todo{Continue this example with a set of observations to estimate $\theta$ and try to show some more. For example, that the resulting distribution is not very good when $t = \co{a}$. Also gather a sample following the specification.}
772 779 %
773 780 %
774 781 %
775   -\subsection{A Not So Simple Example}
776   -
777   -\todo{this subsection}
778   -
779   -In this section we see how the classical example of the Burglary, Earthquake, Alarm \cite{Judea88} works in our setting. This example is a commonly used example in Bayesian networks because it illustrates reasoning under uncertainty. The gist of example is given in \cref{Figure_Alarm}. It involves a simple network of events and conditional probabilities.
780   -
781   -The events are: Burglary ($B$), Earthquake ($E$), Alarm ($A$), Mary calls ($M$) and John calls ($J$). The initial events $B$ and $E$ are assumed to be independent events that occur with probabilities $P(B)$ and $P(E)$, respectively. There is an alarm system that can be triggered by either of the initial events $B$ and $E$. The probability of the alarm going off is a conditional probability depending on whether $B$, or $E$ as occurred. One denotes these probabilities, as per usual, by $P(A|B)$, and $P(A|E)$. There are two neighbours, Mary and John who have agreed to call if they hear the alarm. The probability that they do actually call is also a conditional probability denoted by $P(M|A)$ and $P(J|A)$, respectively.
782   -
783   -Considering the probabilities given in \cref{Figure_Alarm} we obtain the following specification
784   -
785   -\begin{equation*}
786   - \begin{aligned}
787   - \probfact{0.001}{B}&,\cr
788   - \probfact{0.002}{E}&,\cr
789   - \probfact{??}{A}&,\cr
790   - ... &. \cr
791   - \end{aligned}
792   - \label{eq:not_so_simple_example}
793   -\end{equation*}
  782 +\subsection{An example involving Bayesian networks}
794 783  
  784 +As it turns out, our framework is suitable to deal with more sophisticated cases, for example cases involving Bayesian networks. In order to illustrate this, in this section we see how the classical example of the Burglary, Earthquake, Alarm \cite{Judea88} works in our setting. This example is a commonly used example in Bayesian networks because it illustrates reasoning under uncertainty. The gist of example is given in \cref{Figure_Alarm}. It involves a simple network of events and conditional probabilities.
795 785  
  786 +The events are: Burglary ($B$), Earthquake ($E$), Alarm ($A$), Mary calls ($M$) and John calls ($J$). The initial events $B$ and $E$ are assumed to be independent events that occur with probabilities $P(B)$ and $P(E)$, respectively. There is an alarm system that can be triggered by either of the initial events $B$ and $E$. The probability of the alarm going off is a conditional probability given that $B$ and $E$ have occurred. One denotes these probabilities, as per usual, by $P(A|B)$, and $P(A|E)$. There are two neighbours, Mary and John who have agreed to call if they hear the alarm. The probability that they do actually call is also a conditional probability denoted by $P(M|A)$ and $P(J|A)$, respectively.
796 787  
797 788  
798 789  
... ... @@ -808,8 +799,8 @@ Considering the probabilities given in \cref{Figure_Alarm} we obtain the followi
808 799 \node[tchoice, below right of=A] (J) {J};
809 800  
810 801 % Edges
811   - \draw[->] (B) to[bend left] (A) node[right,xshift=1.1cm,yshift=0.8cm] {\footnotesize{$P(B)=0,001$}} ;
812   - \draw[->] (E) to[bend right] (A) node[left, xshift=-1.4cm,yshift=0.8cm] {\footnotesize{$P(E)=0,002$}} ;
  802 + \draw[->] (B) to[bend left] (A) node[right,xshift=1.1cm,yshift=0.8cm] {\footnotesize{$P(B)=0.001$}} ;
  803 + \draw[->] (E) to[bend right] (A) node[left, xshift=-1.4cm,yshift=0.8cm] {\footnotesize{$P(E)=0.002$}} ;
813 804 \draw[->] (A) to[bend right] (M) node[left,xshift=0.2cm,yshift=0.7cm] {\footnotesize{$P(M|A)$}};
814 805 \draw[->] (A) to[bend left] (J) node[right,xshift=-0.2cm,yshift=0.7cm] {\footnotesize{$P(J|A)$}} ;
815 806 \end{tikzpicture}
... ... @@ -822,10 +813,10 @@ Considering the probabilities given in \cref{Figure_Alarm} we obtain the followi
822 813 \begin{split}
823 814 &P(M|A)\\
824 815 & \begin{array}{c|cc}
825   - A & T & F \
  816 + & m & \neg m \
826 817 \hline
827   - T & 0,9 & 0,1\\
828   - F& 0,05 & 0,95
  818 + a & 0.9 & 0.1\\
  819 + \neg a& 0.05 & 0.95
829 820 \end{array}
830 821 \end{split}
831 822 \end{equation*}
... ... @@ -836,10 +827,10 @@ Considering the probabilities given in \cref{Figure_Alarm} we obtain the followi
836 827 \begin{split}
837 828 &P(J|A)\\
838 829 & \begin{array}{c|cc}
839   - A & T & F \
  830 + & j & \neg j \
840 831 \hline
841   - T & 0,7 & 0,3\\
842   - F& 0,01 & 0,99
  832 + a & 0.7 & 0.3\\
  833 + \neg a& 0.01 & 0.99
843 834 \end{array}
844 835 \end{split}
845 836 \end{equation*}
... ... @@ -847,14 +838,14 @@ Considering the probabilities given in \cref{Figure_Alarm} we obtain the followi
847 838 \footnotesize{
848 839 \begin{equation*}
849 840 \begin{split}
850   - P(A|B \vee E)\
  841 + P(A|B \wedge E)\
851 842 \begin{array}{c|c|cc}
852   - B & E& T & F \
  843 + & & a & \neg a \
853 844 \hline
854   - T & T & 0,95 & 0,05\\
855   - T & F & 0,94 & 0,06\\
856   - F & T & 0,29 & 0,71\\
857   - F & F & 0,001 & 0,999
  845 + b & e & 0.95 & 0.05\\
  846 + b & \neg e & 0.94 & 0.06\\
  847 + \neg b & e & 0.29 & 0.71\\
  848 + \neg b & \neg e & 0.001 & 0.999
858 849 \end{array}
859 850 \end{split}
860 851 \end{equation*}
... ... @@ -865,6 +856,64 @@ Considering the probabilities given in \cref{Figure_Alarm} we obtain the followi
865 856 \end{figure}
866 857  
867 858  
  859 +Considering the probabilities given in \cref{Figure_Alarm} we obtain the following specification
  860 +
  861 +\begin{equation*}
  862 + \begin{aligned}
  863 + \probfact{0.001}{b}&,\cr
  864 + \probfact{0.002}{e}&,\cr
  865 + \end{aligned}
  866 + \label{eq:not_so_simple_example}
  867 +\end{equation*}
  868 +
  869 +For the table giving the probability $P(M|A)$ we obtain the specification:
  870 +
  871 +
  872 +\begin{equation*}
  873 + \begin{aligned}
  874 + &\probfact{0.9}{pm\_a},\cr
  875 + &\probfact{0.05}{pm\_na},\cr
  876 + m & \leftarrow a, pm\_a,\cr
  877 + \neg m & \leftarrow a, \neg pm\_a.
  878 + \end{aligned}
  879 +\end{equation*}
  880 +
  881 +This latter specification can be simplified by writing $\probfact{0.9}{m \leftarrow a}$ and $\probfact{0.05}{m \leftarrow \neg a}$.
  882 +
  883 +Similarly, for the probability $P(J|A)$ we obtain
  884 +
  885 +\begin{equation*}
  886 + \begin{aligned}
  887 + &\probfact{0.7}{pj\_a},\cr
  888 + &\probfact{0.01}{pj\_na},\cr
  889 + j & \leftarrow a, pj\_a,\cr
  890 + \neg j & \leftarrow a, \neg pj\_a.\cr
  891 + \end{aligned}
  892 +\end{equation*}
  893 +
  894 +Again, this can be simplified by writing $\probfact{0.7}{j \leftarrow a}$ and $\probfact{0.01}{j \leftarrow \neg a}$.
  895 +
  896 +Finally, for the probability $P(A|B \wedge E)$ we obtain
  897 +
  898 +\begin{equation*}
  899 + \begin{aligned}
  900 + &\probfact{0.95}{a\_be},\cr
  901 + &\probfact{0.94}{a\_bne},\cr
  902 + &\probfact{0.29}{a\_nbe},\cr
  903 + &\probfact{0.001}{a\_nbne},\cr
  904 + a & \leftarrow b, e, a\_be,\cr
  905 + \neg a & \leftarrow b,e, \neg a\_be, \cr
  906 + a & \leftarrow b,e, a\_bne,\cr
  907 + \neg a & \leftarrow b,e, \neg a\_bne, \cr
  908 + a & \leftarrow b,e, a\_nbe,\cr
  909 + \neg a & \leftarrow b,e, \neg a\_nbe, \cr
  910 + a & \leftarrow b,e, a\_nbne,\cr
  911 + \neg a & \leftarrow b,e, \neg a\_nbne. \cr
  912 + \end{aligned}
  913 +\end{equation*}
  914 +
  915 +One can then proceed as in the previous subsection and analyse this example. The details of such analysis are not given here since they are analogous, albeit admittedly more cumbersome.
  916 +
868 917  
869 918 \section{Discussion}
870 919  
... ... @@ -906,6 +955,14 @@ Considering the probabilities given in \cref{Figure_Alarm} we obtain the followi
906 955 %
907 956 % ================================================================
908 957 %
  958 + \begin{itemize}
  959 + \item Changed from $\prod$ to $\sum$ to represent ``either'' instead of ``both'' since the later is not consistent with the ``only one stable model at a time'' assumption.
  960 + \item \todo{The `up and down' choice in the equivalence relation and the possibility of describing any probability distribution.}
  961 + \item \todo{Remark that no benchmark was done with other SOTA efforts.}
  962 + \item \todo{The possibility to `import' bayesian theory and tools to this study.}
  963 + \end{itemize}
  964 +
  965 +
909 966 \subsection{Dependence}
910 967 \label{subsec:dependence}
911 968  
... ... @@ -963,7 +1020,7 @@ Considering the probabilities given in \cref{Figure_Alarm} we obtain the followi
963 1020 Prove the four world cases (done), support the product (done) and sum (tbd) options, with the independence assumptions.
964 1021 \end{quotation}
965 1022  
966   - \section{Final Remarks}
  1023 + \subsection{Future Work}
967 1024  
968 1025 \todo{develop this section.}
969 1026  
... ...