START - PEx preparation

Francisco Coelho
1 parent 1e8b2315
Showing 7 changed files with 128 additions and 14 deletions Show diff stats
2024-02-05--biblio.zip
code/asplang/ASPLang.jl
code/asplang/drafts.jl
code/asplang/sbf.plp
pex2024/candidatura.md
pex2024/candidatura.pdf
projecto-NovaLINCS.gdlink
 module ASPLang
  
-export parse_asp, debug_asp, 
+export parse_asp, debug_asp, pstring,
     literal_grammar, term_grammar, aggregate_grammar, asp_grammar,
-    Node, Variable, StringConstant, SymbolicConstant, AnonymousVariable, NumberConstant, Variable,
+    Node, Terminal, NonTerminal, Variable, StringConstant, SymbolicConstant, AnonymousVariable, NumberConstant, Variable,
     Functor, FunctionTerm,
     Negated, Inverted, Product, Sum,
     LT, LE, EQ, NE, GE, GT,
@@ -13,31 +13,47 @@ export parse_asp, debug_asp,
     Aggregate, Elements, InclusionCondition,
     Constraint, LeftBound, RightBound,
     Choice, RestrictedChoice, Choices,
-    Disjunction, Body, Rule, Restriction, WeakRestriction, Annotation,
+    Disjunction, Head, Body, Rule, Restriction, WeakRestriction, Annotation,
     Query, Program
  
+
+
+abstract type Node end
+Base.:(==)(n1::Node, n2::Node) = (typeof(n1) == typeof(n2)) && (n1.args == n2.args)
+
+pstring(x::Any, level=0) = repr(x)
+abstract type Terminal <: Node end
 macro terminal(lang)
     return quote
-        struct $lang <: Node end
+        struct $lang <: Terminal end
     end
 end
+pstring(x::Terminal, level=0) = "$(" "^level)$(typeof(x))"
  
+abstract type NonTerminal <: Node end
 macro variable(lang)
     return quote
-        struct $lang <: Node
+        struct $lang <: NonTerminal
             args
         end
     end
 end
  
+function pstring(x::NonTerminal, level=0)
+    if typeof(x.args) <: AbstractVector
+        pargs = x.args .|> (z -> pstring(z, level + 2))
+        "\n$(" "^level)$(typeof(x))($(join(pargs, ","))\n$(" "^level))"
+    else
+        pargs = join(pstring.(x.args), ",")
+        "\n$(" "^level)$(typeof(x))($pargs) - $(typeof(x.args))"
+    end
+end
+
 using ParserCombinator
 #=
     DATA STRUCTURES
     =#
  
-abstract type Node end
-Base.:(==)(n1::Node, n2::Node) = (typeof(n1) == typeof(n2)) && (n1.args == n2.args)
-
 @variable Variable
 @variable StringConstant
 @variable SymbolicConstant
@@ -92,6 +108,7 @@ Base.:(==)(n1::Node, n2::Node) = (typeof(n1) == typeof(n2)) &amp;&amp; (n1.args == n2.ar
 @variable Disjunction
 @variable Annotation
 @variable Body
+@variable Head
  
 @variable Rule
 @variable Restriction
@@ -316,7 +333,7 @@ statement =
     # strong restriction
     (E":-" + body + E"." > Restriction) |
     # rule
-    (head + Opt(annotation) + Opt(E":-" + body) + E"." |> Rule) |
+    ((head + Opt(annotation) |> Head) + Opt(E":-" + body) + E"." |> Rule) |
     # weak restriction
     (E":~" + Opt(body) + E"." + spc + E"[" + weight_at_level + E"]" |> WeakRestriction)
 statements = StarList(statement, E"")
@@ -4,8 +4,7 @@ using .ASPLang
  
 function test_parse(source, grammar=asp_grammar)
     expr = parse_asp(source, grammar)
-    println("$source => $(expr).\n")
-    print(pstring(expr))
+    println("$source\n$(pstring(expr))")
 end
  
 # test_parse("\"a\"", term_grammar)
 a::"0.3".
-b | c :- a.
 \ No newline at end of file
+b | c ::"0.7" :- a.
+:- not c.
 \ No newline at end of file
-# Candidatura PeX - Zugzwang
+# Candidatura PEx - Zugzwang
+
+
+## 2024-01-05 - Next Research Lines
+
+> After the base-setting work of "_An Algebraic Approach to Stochastic ASP_" these are the next tasks to consider. Is summary:
+> 1. **Logic Programming** - Stratified & Non-stratified programs
+> 2. **Computer Science** - Inductive Logic Programming
+> 3. **Software** - Integration with Potassco and other frameworks
+> 4. **Applications**
+
+#### Line 1: Logic Programming - Stratified & Non-stratified programs
+
+##### Line 1a - Logic Programs Structure and Properties
+
+> _Stratified_ & _non-stratified_ programs are quoted in the "CREDAL" papers as important classes of logic programs.
+
+Minimal example of a **non-stratified program**.
+
+The following annotated LP, with clauses $c_1, c_2, c_3$ respectively, is non-stratified (because has a cycle with negated arcs) but no head is disjunctive:
+```prolog
+0.3::a.                 % c1
+b :- not c, not a.      % c2
+c :- not b.             % c3
+```
+
+This program has three stable models:
+$$
+\begin{aligned}
+m_1 &= \set{ a, c } \cr
+m_2 &= \set{ \neg a, b } \cr
+m_3 &= \set{ \neg a, c }
+\end{aligned}
+$$
+
+> We should **investigate** _What are stratified programs and why are they important?_ and how does our approach deals with such programs?
+
+##### Line 1b - Investigate the expressiveness of PASP
+
+Consider:
+
+- Recursion
+- Variables,
+- Functional symbols,
+
+##### Line 1c - The equivalence relation
+
+Consider the cases where only $s \subseteq e$ and $e \subseteq s$. Or other refinements. Also consider the inconsistent and independent events.
+
+##### Line 1d - Stability of the error function
+
+Consider alternative error functions. See statistics, Kullback-Leibler divergence
+
+#### Line 2: Computer Science - Inductive Logic Programming
+
+> Proceed from scoring programs to support genetic algorithms or other program space exploration methods.
+
+Scoring programs, as described in our paper, is just a step into **Inductive Logic Programming**. To go further, we need to explore algorithms that:
+
+1. Use **background knowledge**, expressed as a PLP.
+2. Consult **positive examples** that should be _soft_ induced.
+3. Consult **negative examples** that should be _soft_ excluded.
+4. Generate **PLPs** that are scored.
+5. Recombine the **best scored** into a new _population_, using recombination rules.
+
+> In order to do that, **PLPs must be expressed as data structures** to be manipulated. Also **recombination rules** must investigated before become formally expressed and supported with adequate methods.
+
+#### Line 3: Software - Integration with Potassco and other frameworks
+
+> Support annotated programs with zugzwang semantics.
+
+- Bayesian Networks (BII Alice)
+  - Generate an annotated asp program from a bayesian network and run it trough `clingo`.
+  - Recover the stable models from the previous ste and compute the respective probabilities.
+- Program Manipulation
+  - Annotated ASP program _representation_ and a _parser_.
+
+#### Line 4: Applications
+
+> Apply zugzwang to a few showcases, besides the theoretic corner stones (non-stratified, disjunctive, bayes networks), preferably based in real world scenarios, with complex structure and large datasets.
+
+- (Stochastic) Plan Generation
+- Yale-Shooting Problem
+- (Stochastic) Situation Calculus
+- Frame Problem
+- Latent Facts - and core assumptions.
+- Given a **Bayesian Network** (or a **Markov Networks**):
+  - Represent it. (**done** for BNs; MNs?)
+  - Solve the common probability tasks: join (**done**), marginals, conditionals, parameter learning, inferring unobserved variables, sample generation, _etc._
+- Given a _solved_ ASP specification:
+  - What is the marginal probability of the atom `a`? (**done**)
+  - What other probability queries are important to consider?
+- Given an _unsolved_ ASP specification:
+  - What is the probability (distribution?) of the probabilistic fact `a`?
+  - What other questions are relevant? _E.g._ the distribution family of a fact?
+- Given a _solved_ ASP specification and a set of _samples_:
+  - How do the probabilities inferred from the specification match the ones from the empiric distribution? (**done** might see alternative approaches)
+- Given two _solved_ ASP specification and a set of _samples_:
+  - Which specification best describes the empiric distribution? (**done**)
  
 ## Tarefas
  
@@ -1 +0,0 @@
-{"url": "https://drive.google.com/file/d/1liS-0PGFXZVVPtfiRZix2JXjXzshbNKw/view?usp=drivesdk", "file_id": "1liS-0PGFXZVVPtfiRZix2JXjXzshbNKw", "account_email": "mangon@gmail.com"}
 \ No newline at end of file
1	1	module ASPLang
2	2
3		-export parse_asp, debug_asp,
	3	+export parse_asp, debug_asp, pstring,
4	4	literal_grammar, term_grammar, aggregate_grammar, asp_grammar,
5		- Node, Variable, StringConstant, SymbolicConstant, AnonymousVariable, NumberConstant, Variable,
	5	+ Node, Terminal, NonTerminal, Variable, StringConstant, SymbolicConstant, AnonymousVariable, NumberConstant, Variable,
6	6	Functor, FunctionTerm,
7	7	Negated, Inverted, Product, Sum,
8	8	LT, LE, EQ, NE, GE, GT,
...	...	@@ -13,31 +13,47 @@ export parse_asp, debug_asp,
13	13	Aggregate, Elements, InclusionCondition,
14	14	Constraint, LeftBound, RightBound,
15	15	Choice, RestrictedChoice, Choices,
16		- Disjunction, Body, Rule, Restriction, WeakRestriction, Annotation,
	16	+ Disjunction, Head, Body, Rule, Restriction, WeakRestriction, Annotation,
17	17	Query, Program
18	18
	19	+
	20	+
	21	+abstract type Node end
	22	+Base.:(==)(n1::Node, n2::Node) = (typeof(n1) == typeof(n2)) && (n1.args == n2.args)
	23	+
	24	+pstring(x::Any, level=0) = repr(x)
	25	+abstract type Terminal <: Node end
19	26	macro terminal(lang)
20	27	return quote
21		- struct $lang <: Node end
	28	+ struct $lang <: Terminal end
22	29	end
23	30	end
	31	+pstring(x::Terminal, level=0) = "$(" "^level)$(typeof(x))"
24	32
	33	+abstract type NonTerminal <: Node end
25	34	macro variable(lang)
26	35	return quote
27		- struct $lang <: Node
	36	+ struct $lang <: NonTerminal
28	37	args
29	38	end
30	39	end
31	40	end
32	41
	42	+function pstring(x::NonTerminal, level=0)
	43	+ if typeof(x.args) <: AbstractVector
	44	+ pargs = x.args .\|> (z -> pstring(z, level + 2))
	45	+ "\n$(" "^level)$(typeof(x))($(join(pargs, ","))\n$(" "^level))"
	46	+ else
	47	+ pargs = join(pstring.(x.args), ",")
	48	+ "\n$(" "^level)$(typeof(x))($pargs) - $(typeof(x.args))"
	49	+ end
	50	+end
	51	+
33	52	using ParserCombinator
34	53	#=
35	54	DATA STRUCTURES
36	55	=#
37	56
38		-abstract type Node end
39		-Base.:(==)(n1::Node, n2::Node) = (typeof(n1) == typeof(n2)) && (n1.args == n2.args)
40		-
41	57	@variable Variable
42	58	@variable StringConstant
43	59	@variable SymbolicConstant
...	...	@@ -92,6 +108,7 @@ Base.:(==)(n1::Node, n2::Node) = (typeof(n1) == typeof(n2)) && (n1.args == n2.ar
92	108	@variable Disjunction
93	109	@variable Annotation
94	110	@variable Body
	111	+@variable Head
95	112
96	113	@variable Rule
97	114	@variable Restriction
...	...	@@ -316,7 +333,7 @@ statement =
316	333	# strong restriction
317	334	(E":-" + body + E"." > Restriction) \|
318	335	# rule
319		- (head + Opt(annotation) + Opt(E":-" + body) + E"." \|> Rule) \|
	336	+ ((head + Opt(annotation) \|> Head) + Opt(E":-" + body) + E"." \|> Rule) \|
320	337	# weak restriction
321	338	(E":~" + Opt(body) + E"." + spc + E"[" + weight_at_level + E"]" \|> WeakRestriction)
322	339	statements = StarList(statement, E"")
...	...
...	...	@@ -4,8 +4,7 @@ using .ASPLang
4	4
5	5	function test_parse(source, grammar=asp_grammar)
6	6	expr = parse_asp(source, grammar)
7		- println("$source => $(expr).\n")
8		- print(pstring(expr))
	7	+ println("$source\n$(pstring(expr))")
9	8	end
10	9
11	10	# test_parse("\"a\"", term_grammar)
...	...
1	1	a::"0.3".
2		-b \| c :- a.
3	2	\ No newline at end of file
	3	+b \| c ::"0.7" :- a.
	4	+:- not c.
4	5	\ No newline at end of file
...	...
1		-# Candidatura PeX - Zugzwang
	1	+# Candidatura PEx - Zugzwang
	2	+
	3	+
	4	+## 2024-01-05 - Next Research Lines
	5	+
	6	+> After the base-setting work of "_An Algebraic Approach to Stochastic ASP_" these are the next tasks to consider. Is summary:
	7	+> 1. Logic Programming - Stratified & Non-stratified programs
	8	+> 2. Computer Science - Inductive Logic Programming
	9	+> 3. Software - Integration with Potassco and other frameworks
	10	+> 4. Applications
	11	+
	12	+#### Line 1: Logic Programming - Stratified & Non-stratified programs
	13	+
	14	+##### Line 1a - Logic Programs Structure and Properties
	15	+
	16	+> _Stratified_ & _non-stratified_ programs are quoted in the "CREDAL" papers as important classes of logic programs.
	17	+
	18	+Minimal example of a non-stratified program.
	19	+
	20	+The following annotated LP, with clauses $c_1, c_2, c_3$ respectively, is non-stratified (because has a cycle with negated arcs) but no head is disjunctive:
	21	+```prolog
	22	+0.3::a. % c1
	23	+b :- not c, not a. % c2
	24	+c :- not b. % c3
	25	+```
	26	+
	27	+This program has three stable models:
	28	+$$
	29	+\begin{aligned}
	30	+m_1 &= \set{ a, c } \cr
	31	+m_2 &= \set{ \neg a, b } \cr
	32	+m_3 &= \set{ \neg a, c }
	33	+\end{aligned}
	34	+$$
	35	+
	36	+> We should investigate _What are stratified programs and why are they important?_ and how does our approach deals with such programs?
	37	+
	38	+##### Line 1b - Investigate the expressiveness of PASP
	39	+
	40	+Consider:
	41	+
	42	+- Recursion
	43	+- Variables,
	44	+- Functional symbols,
	45	+
	46	+##### Line 1c - The equivalence relation
	47	+
	48	+Consider the cases where only $s \subseteq e$ and $e \subseteq s$. Or other refinements. Also consider the inconsistent and independent events.
	49	+
	50	+##### Line 1d - Stability of the error function
	51	+
	52	+Consider alternative error functions. See statistics, Kullback-Leibler divergence
	53	+
	54	+#### Line 2: Computer Science - Inductive Logic Programming
	55	+
	56	+> Proceed from scoring programs to support genetic algorithms or other program space exploration methods.
	57	+
	58	+Scoring programs, as described in our paper, is just a step into Inductive Logic Programming. To go further, we need to explore algorithms that:
	59	+
	60	+1. Use background knowledge, expressed as a PLP.
	61	+2. Consult positive examples that should be _soft_ induced.
	62	+3. Consult negative examples that should be _soft_ excluded.
	63	+4. Generate PLPs that are scored.
	64	+5. Recombine the best scored into a new _population_, using recombination rules.
	65	+
	66	+> In order to do that, PLPs must be expressed as data structures to be manipulated. Also recombination rules must investigated before become formally expressed and supported with adequate methods.
	67	+
	68	+#### Line 3: Software - Integration with Potassco and other frameworks
	69	+
	70	+> Support annotated programs with zugzwang semantics.
	71	+
	72	+- Bayesian Networks (BII Alice)
	73	+ - Generate an annotated asp program from a bayesian network and run it trough `clingo`.
	74	+ - Recover the stable models from the previous ste and compute the respective probabilities.
	75	+- Program Manipulation
	76	+ - Annotated ASP program _representation_ and a _parser_.
	77	+
	78	+#### Line 4: Applications
	79	+
	80	+> Apply zugzwang to a few showcases, besides the theoretic corner stones (non-stratified, disjunctive, bayes networks), preferably based in real world scenarios, with complex structure and large datasets.
	81	+
	82	+- (Stochastic) Plan Generation
	83	+- Yale-Shooting Problem
	84	+- (Stochastic) Situation Calculus
	85	+- Frame Problem
	86	+- Latent Facts - and core assumptions.
	87	+- Given a Bayesian Network (or a Markov Networks):
	88	+ - Represent it. (done for BNs; MNs?)
	89	+ - Solve the common probability tasks: join (done), marginals, conditionals, parameter learning, inferring unobserved variables, sample generation, _etc._
	90	+- Given a _solved_ ASP specification:
	91	+ - What is the marginal probability of the atom `a`? (done)
	92	+ - What other probability queries are important to consider?
	93	+- Given an _unsolved_ ASP specification:
	94	+ - What is the probability (distribution?) of the probabilistic fact `a`?
	95	+ - What other questions are relevant? _E.g._ the distribution family of a fact?
	96	+- Given a _solved_ ASP specification and a set of _samples_:
	97	+ - How do the probabilities inferred from the specification match the ones from the empiric distribution? (done might see alternative approaches)
	98	+- Given two _solved_ ASP specification and a set of _samples_:
	99	+ - Which specification best describes the empiric distribution? (done)
2	100
3	101	## Tarefas
4	102
...	...
...	...	@@ -1 +0,0 @@
1		-{"url": "https://drive.google.com/file/d/1liS-0PGFXZVVPtfiRZix2JXjXzshbNKw/view?usp=drivesdk", "file_id": "1liS-0PGFXZVVPtfiRZix2JXjXzshbNKw", "account_email": "mangon@gmail.com"}
2	0	\ No newline at end of file