prolog - 用于查找可证明目标缺少哪些谓词的程序

Question

底部的程序应该返回目标缺失的子句，在这种情况下 p(1, 3, fire) 是可证明的。

问题是它返回一个“太多”的解决方案，如输出中的最后一个解决方案所示:

?- main.
MISSING PREMISES:
p(A,2,presenceOfFlammableMaterial)
p(B,2,johnDroppedAMatch)
true ;

MISSING PREMISES:
p(A,2,presenceOfFlammableMaterial)
p(B,1,johnWasTired)
true ;

MISSING PREMISES:
precedes(3,3)
p(A,3,presenceOfFlammableMaterial)
p(B,2,johnWasTired)
true ;
false.

我想要的只是:

MISSING PREMISES:
p(A,2,presenceOfFlammableMaterial)
p(B,2,johnDroppedAMatch)
true ;

MISSING PREMISES:
p(A,2,presenceOfFlammableMaterial)
p(B,1,johnWasTired)
true ;

我很难理解哪里出了问题，希望能得到一些改进的提示 :-)，或者一些文献提示(我已经熟悉 Markus Triska 的优秀页面)。

重要的谓词是missing0(G, M)，其中G 是目标，M 是缺失子句的列表。我对这个问题的怀疑之一是可能有无数个失败的子句，所以我错过了某种“停止”条件。

我发布了相同的 question在 SWI Prolog 论坛上，但没有得到任何回应。我正在运行 SWI Prolog。

% https://www.swi-prolog.org/pldoc/doc/_SWI_/library/clp/clpr.pl

:-use_module(library(clpr)).

% time is ordered

precedes(1, 2).
precedes(2, 3).

% knowledge

p(X1, T2, johnDroppedAMatch):-
    p(X2, T1, johnWasTired),
    precedes(T1, T2),
    {X1 = 0.5 * X2}.

p(X1, T2, fire):-
    p(X2, T1, presenceOfFlammableMaterial),
    p(X3, T1, johnDroppedAMatch),
    precedes(T1, T2),
    {X1 = 0.7 * X2 * X3}.

% --- Reasoning about knowledge

missing(G, M) :- call(G), 
                 M = ['There are no missing premises.'].

missing(G, M) :- \+clause(G, _),
                 M = ['There are no clauses for the goal.'].

missing(G, M) :- clause(G, B), \+G, missing0(B, M).

% -- Look for missing clauses in a conjunction

missing0(G, M) :- G = (G1, G2), !, 
                  missing0(G1, M1), missing0(G2, M2), append(M1, M2, M).

% -- Look for missing clauses in a disjunction 

missing0(G, M) :- G = (G1; _), missing0(G1, M). 

% -- Look for missing clauses in a disjunction

missing0(G, M) :- G = (_; G2), missing0(G2, M). 

% -- If G is callable then it is not missing

missing0(G, M) :- call(G), M = []. 

% G fails, and is neither a conjunction nor a disjunction, so
% put in in M. Here I collect missing clauses.

missing0(G, M) :- \+G, G \= (_, _), G \= (_; _), M = [G]. 

% If G fails and if B is in the body of G, check what predicates are
% missing for B to be provable. G \= {_} is to avoid an error when
% using clause/2 on clpr predicates.

missing0(G, M) :- \+G, G \= {_}, clause(G, B), missing0(B, M). 


showMissing(M) :- copy_term_nat(M, M1), 
                  numbervars(M1, 0, _, [attvar(bind)]),
                  sort(M1, M2), 
                  nl, writeln('MISSING PREMISES:'),
                  maplist(writeln, M2).

main :- missing(p(1, 3, fire), M), showMissing(M).

Answer 1

不是答案，但我对代码进行了一些尝试，添加了一些打印输出并使其具有确定性。它现在报告一个解决方案。

原始代码，略有审查

这是原始代码，带有一些打印输出。它的报告与以前完全一样，输出没有排序，以便能够跟踪它首先命中的内容。

:-use_module(library(clpr)).

% ======================
% knowledge
% ======================

% time is ordered
% Note: Time is not transitive as precedes(1,3) is missing!

precedes(1, 2).
precedes(2, 3).

p(X1, T2, johnDroppedAMatch):-
    p(X2, T1, johnWasTired),
    precedes(T1, T2),
    {X1 = 0.5 * X2}.

p(X1, T2, fire):-
    p(X2, T1, presenceOfFlammableMaterial),
    p(X3, T1, johnDroppedAMatch),
    precedes(T1, T2),
    {X1 = 0.7 * X2 * X3}.

% ======================
% reasoning about knowledge
% ======================

% Note: What exactly does it mean for a premise to be "missing"?
% Are variables to be resolved when reporting? 

missing(G, M) :- call(G), 
                 M = ['There are no missing premises.'].

missing(G, M) :- \+clause(G, _),
                 M = ['There are no clauses for the goal.'].

missing(G, M) :- clause(G, B), \+G, missingr(B, M, 0).

% --- Recursively look for missing stuff in a goal 
% D is the Depth of the analysis
% SP is a string of spaces for indentation

missingr(G, M, D) :- G = (G1, G2), !,
                     sp(D,SP), format("~w«~w» AND «~w»\n",[SP,G1,G2]), spinc(D,DP),
                     missingr(G1, M1, DP), 
                     missingr(G2, M2, DP),                  
                     append(M1, M2, M).

missingr(G, M, D) :- G = (G1; _), !,
                     sp(D,SP), format("~w«~w» OR «~w»\n",[SP,G1,"..."]), spinc(D,DP),
                     missingr(G1, M, DP).

missingr(G, M, D) :- G = (_ ; G2), !,
                     sp(D,SP), format("~w«~w» OR «~w»\n",[SP,"...",G2]), spinc(D,DP),
                     missingr(G2, M, DP).

missingr(G, M, D) :- sp(D,SP), format("~wMaybe «~w» can be called?\n",[SP,G]),
                     call(G),
                     format("~w«~w» succeeds; nothing is missing here.\n",[SP,G]),
                     M = [].

missingr(G, M, D) :- \+G, G \= (_,_), G \= (_;_),
                     sp(D,SP), format("~w«~w» is not provable, not a conjunction, not a disjunction: Consider missing!\n",[SP,G]),
                     M = [G].

missingr(G, M, D) :- \+G, G \= {_}, clause(G, B),
                     sp(D,SP), format("~w«~w» is not provable, not a constraint, and a clause with body «~w», continue with body\n",[SP,G,B]), spinc(D,DP),
                     missingr(B, M, DP).

% Igniter

showMissing(M) :- copy_term_nat(M, M1), 
                  numbervars(M1, 0, _, [attvar(bind)]),
                  % sort(M1, M2), % do not sort so that terms are output in found order
                  M2 =  M1,
                  nl, writeln('MISSING PREMISES:'),
                  maplist(writeln, M2).

main :- missing(p(1, 3, fire), M), showMissing(M).


% Generate string of N spaces fast. 

spinc(In,Out) :- Out is In+2.

sp(0,"") :- !.
sp(1,".") :- !.
sp(Len,Str) :- Len > 1,
               Lenx is Len div 2, Remx is Len rem 2, 
               sp(Lenx,Strx), 
               string_concat(Strx,Strx,Stry),
               (Remx == 0 -> Str = Stry ; string_concat(Stry,".",Str)),!.

输出

?- main.  
«p(_7002,_7004,presenceOfFlammableMaterial)» AND «p(_7010,_7004,johnDroppedAMatch),precedes(_7004,3),{1=0.7*_7002*_7010}»
..Maybe «p(_7002,_7004,presenceOfFlammableMaterial)» can be called?
..«p(_7002,_7004,presenceOfFlammableMaterial)» is not provable, not a conjunction, not a disjunction: Consider missing!
..«p(_7010,_7004,johnDroppedAMatch)» AND «precedes(_7004,3),{1=0.7*_7002*_7010}»
....Maybe «p(_7010,_7004,johnDroppedAMatch)» can be called?
....«p(_7010,_7004,johnDroppedAMatch)» is not provable, not a conjunction, not a disjunction: Consider missing!
....«precedes(_7004,3)» AND «{1=0.7*_7002*_7010}»
......Maybe «precedes(_7004,3)» can be called?
......«precedes(2,3)» succeeds; nothing is missing here.
......Maybe «{1=0.7*_7002*_7010}» can be called?
......«{1=0.7*_7914*_7940}» succeeds; nothing is missing here.

MISSING PREMISES:
p(A,2,presenceOfFlammableMaterial)
p(B,2,johnDroppedAMatch)
true ;

....«p(_7010,_7004,johnDroppedAMatch)» is not provable, not a constraint, and a clause with body «p(_7278,_7280,johnWasTired),precedes(_7280,_7004),{_7010=0.5*_7278}», continue with body
......«p(_7278,_7280,johnWasTired)» AND «precedes(_7280,_7004),{_7010=0.5*_7278}»
........Maybe «p(_7278,_7280,johnWasTired)» can be called?
........«p(_7278,_7280,johnWasTired)» is not provable, not a conjunction, not a disjunction: Consider missing!
........«precedes(_7280,_7004)» AND «{_7010=0.5*_7278}»
..........Maybe «precedes(_7280,_7004)» can be called?
..........«precedes(1,2)» succeeds; nothing is missing here.
..........Maybe «{_7010=0.5*_7278}» can be called?
..........«{_8266=0.5*_8368}» succeeds; nothing is missing here.
....«precedes(2,3)» AND «{1=0.7*_7002*_8266}»
......Maybe «precedes(2,3)» can be called?
......«precedes(2,3)» succeeds; nothing is missing here.
......Maybe «{1=0.7*_7002*_8266}» can be called?
......«{1=0.7*_9472*_8266}» succeeds; nothing is missing here.

MISSING PREMISES:
p(A,2,presenceOfFlammableMaterial)
p(B,1,johnWasTired)
true ;

..........«precedes(2,3)» succeeds; nothing is missing here.
..........Maybe «{_7010=0.5*_7278}» can be called?
..........«{_8266=0.5*_8368}» succeeds; nothing is missing here.
....«precedes(3,3)» AND «{1=0.7*_7002*_8266}»
......Maybe «precedes(3,3)» can be called?
......«precedes(3,3)» is not provable, not a conjunction, not a disjunction: Consider missing!
......Maybe «{1=0.7*_7002*_8266}» can be called?
......«{1=0.7*_9476*_8266}» succeeds; nothing is missing here.

MISSING PREMISES:
p(A,3,presenceOfFlammableMaterial)
p(B,2,johnWasTired)
precedes(3,3)
true ;
false.

考虑到这一点，就不清楚“缺少谓词” 是什么意思，甚至不清楚在解释过程中遇到合取或析取时应该发生什么。需要更多细节!

修改代码尝试

这里是修改后的代码，它似乎符合要求，但更具确定性，只输出一个解决方案:

:-use_module(library(clpr)).

% ======================
% knowledge
% ======================

% time is ordered
% Note: Time is not transitive as precedes(1,3) is missing!

precedes(1, 2).
precedes(2, 3).

p(X1, T2, johnDroppedAMatch):-
    p(X2, T1, johnWasTired),
    precedes(T1, T2),
    {X1 = 0.5 * X2}.

p(X1, T2, fire):-
    p(X2, T1, presenceOfFlammableMaterial),
    p(X3, T1, johnDroppedAMatch),
    precedes(T1, T2),
    {X1 = 0.7 * X2 * X3}.

% ======================
% reasoning about knowledge
% ======================

% Note: What exactly does it mean for a premise to be "missing"?
% Are variables to be resolved when reporting? 

missing(G, M) :- call(G), 
                 M = ['There are no missing premises.'].

missing(G, M) :- \+clause(G, _),
                 M = ['There are no clauses for the goal.'].

missing(G, M) :- clause(G, B), \+G, missingr(B, M, 0).

% --- Recursively look for missing stuff in a goal

% Conjunction
% In a conjunction we can fail on left or right, go down both branches.

missingr(G, M, D) :- G = (G1, G2), !,
                     sp(D,SP), format("~w«~w» AND «~w»\n",[SP,G1,G2]), spinc(D,DP),
                     missingr(G1, M1, DP), 
                     missingr(G2, M2, DP),                  
                     append(M1, M2, M).

% Disjunction. Finagle a proper guard!
% Note: In a disjunction we fail if we fail on both sides, but then what to report???

missingr(G, M, D) :- G = (G1; G2), !,
                     sp(D,SP), format("~w«~w» OR «~w»\n",[SP,G1,G2]), spinc(D,DP),
                     (missingr(G1, M, DP) ; missingr(G2, M, DP)).

% If G is callable and succeeds then it is not missing. 
% The call will unify variables, which may or may not be what we want.

missingr(G, M, D) :- sp(D,SP), format("~wMaybe «~w» can be called?\n",[SP,G]),
                     call(G), !,
                     format("~w«~w» succeeds; nothing is missing here.\n",[SP,G]),
                     M = [].

% If G fails and if B is the body of G, check what predicates are
% missing for B to be provable. G \= {_} is to avoid an error when
% using clause/2 on clpr predicates.

missingr(G, M, D) :- \+G, !, 
                     sp(D,SP), format("~w«~w» is nonprovable\n",[SP,G]), spinc(D,DP),
                     nonprovable(G, M, DP).

nonprovable(G, M, D) :- G \= {_}, clause(G, B), !,
                        sp(D,SP), format("~w«~w» is a nonprovable clause with body «~w», continue with body\n",[SP,G,B]), spinc(D,DP),
                        missingr(B, M, DP). 

nonprovable(G, M, D) :- G \= {_}, !,
                        sp(D,SP), format("~w«~w» is a nonprovable non-clause: considered missing!\n",[SP,G]),
                        M = [G].

nonprovable(G, M, D) :- sp(D,SP), format("~w«~w» is a constraint; dropped!\n",[SP,G]),
                        M = [].

% Igniter

showMissing(M) :- copy_term_nat(M, M1), 
                  numbervars(M1, 0, _, [attvar(bind)]),
                  nl, writeln('MISSING PREMISES:'),
                  maplist(writeln, M1).

main :- missing(p(1, 3, fire), M), showMissing(M).


% Generate string of N spaces fast. 

spinc(In,Out) :- Out is In+2.

sp(0,"") :- !.
sp(1,".") :- !.
sp(Len,Str) :- Len > 1,
               Lenx is Len div 2, Remx is Len rem 2, 
               sp(Lenx,Strx), 
               string_concat(Strx,Strx,Stry),
               (Remx == 0 -> Str = Stry ; string_concat(Stry,".",Str)),!.

新输出

运行它会生成一个解决方案:

?- main.
«p(_5182,_5184,presenceOfFlammableMaterial)» AND «p(_5190,_5184,johnDroppedAMatch),precedes(_5184,3),{1=0.7*_5182*_5190}»
..Maybe «p(_5182,_5184,presenceOfFlammableMaterial)» can be called?
..«p(_5182,_5184,presenceOfFlammableMaterial)» is nonprovable
....«p(_5182,_5184,presenceOfFlammableMaterial)» is a nonprovable non-clause: considered missing!
..«p(_5190,_5184,johnDroppedAMatch)» AND «precedes(_5184,3),{1=0.7*_5182*_5190}»
....Maybe «p(_5190,_5184,johnDroppedAMatch)» can be called?
....«p(_5190,_5184,johnDroppedAMatch)» is nonprovable
......«p(_5190,_5184,johnDroppedAMatch)» is a nonprovable clause with body «p(_5572,_5574,johnWasTired),precedes(_5574,_5184),{_5190=0.5*_5572}», 
........«p(_5572,_5574,johnWasTired)» AND «precedes(_5574,_5184),{_5190=0.5*_5572}»
..........Maybe «p(_5572,_5574,johnWasTired)» can be called?
..........«p(_5572,_5574,johnWasTired)» is nonprovable
............«p(_5572,_5574,johnWasTired)» is a nonprovable non-clause: considered missing!
..........«precedes(_5574,_5184)» AND «{_5190=0.5*_5572}»
............Maybe «precedes(_5574,_5184)» can be called?
............«precedes(1,2)» succeeds; nothing is missing here.
............Maybe «{_5190=0.5*_5572}» can be called?
............«{_6626=0.5*_6728}» succeeds; nothing is missing here.
....«precedes(2,3)» AND «{1=0.7*_5182*_6626}»
......Maybe «precedes(2,3)» can be called?
......«precedes(2,3)» succeeds; nothing is missing here.
......Maybe «{1=0.7*_5182*_6626}» can be called?
......«{1=0.7*_7658*_6626}» succeeds; nothing is missing here.

MISSING PREMISES:
p(A,2,presenceOfFlammableMaterial)
p(B,1,johnWasTired)
true.

但如前所述，我们真正想要的是什么？