cs7120 (prasad)l16-meaning1 procedural and declarative meaning of prolog [email protected]
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cs7120 (Prasad) L16-Meaning 1
Procedural and Declarative Meaning of Prolog
http://www.knoesis.org/tkprasad/
p :- q, r.q.
• Declarative – Machine independent. Formalized through
propositional and predicate logic.p is true if q is true and r is true.
q is true.
• Procedural To solve p: first solve q, and then solve r.
q is solved.
cs7120 (Prasad) L16-Meaning 2
Consequences : EquivalenceDeclarative Reading
p :- q, r.
q.
equivalent to
p :- r, q.
q.
since “OR”and “AND” are commutative.
p :- p.
p.
equivalent to
p.
p :- p.
since “AND” is commutative.cs7120 (Prasad) L16-Meaning 3
(cont’d)Procedural Reading
p :- p.
p.
is not equivalent to
p.
p :- p.
• The former program loops on the query ?-p, while the latter program succeeds.
• Prolog strategy is computationally efficient but incomplete.
cs7120 (Prasad) L16-Meaning 4
Declarative Meaning
• Specifies whether or not a given goal G is true, and if so, for what values of the variables is it true.
• Instance of a clause C is obtained by substituting terms for each of its variables.
• Variant of a clause C is obtained by renam- ing the variables of C.
cs7120 (Prasad) L16-Meaning 5
Example
• Clause: p(X) :- q(X,Y), r(Y).
• Instance:p(a) :- q(a,Y), r(Y).
p(b) :- q(b,b), r(b).
• Variant:p(A) :- q(A,B), r(B).
cs7120 (Prasad) L16-Meaning 6
Declarative Meaning
• Given a program P and a goal G,
G is true ( i.e., logically follows from P)
if and only if:
(1) There is a clause C in P such that
(2) there is a clause instance I of C such that
(a) the head of I is identical to G, and
(b) all the goals in the body of I are true.
(Recursive definition of satisfaction)
cs7120 (Prasad) L16-Meaning 7
• An instance of a clause C is obtained by renaming each variable in C and possibly substituting the variable by some term.
• E.g. an instance of p(X,Y) :- q(Y,Z).
is
p(U,a) :- q(a,V).• Recall that scope of a variable is the clause (locality
of reference) and same variable name implies equality constraint.
cs7120 (Prasad) L16-Meaning 8
• Specifies how Prolog answers questions.
• Procedural meaning is an algorithm to execute a list of goals given a Prolog program:
program
success/failure indication
goal list execute
instantiation of variables
Procedural Meaning
9
procedure execute( Program, GoalList, Success)
• execute = declarative meaning + procedural elements
G is true ( i.e. logically follows from P) if and only if:
(1) there is a clause C in P such that
(2) there is a clause instance I of C such that
(a) the head of I is identical to G, and
(b) all the goals in the body of I are true
Search program from top to bottom to find such clause
Match G and head of C Execute goals in order as they
appear in program
procedure execute( Program, GoalList, Success)
begin
if empty(GoalList) then Success := true
else begin Goal := head(GoalList);
OtherGoals := tail(GoalList);
Satisfied := false;
while not Satisfied and
“more clauses in Program” do
begin (* NEXT GoalList GENERATION *)
end;
Success := Satisfied
end
end;
cs7120 (Prasad) L16-Meaning 11
Let next clause in Program be
H :- B1, B2, …, Bn.
Construct a variant of this clause (variables disjoint from GoalList)
H’ :- B1’, B2’, …, Bn’.
match(Goal, H’, MatchOK, substitution);
if MatchOK then
begin
NewGoals := apply(substitution,
append( [B1’,B2’,…,Bn’], OtherGoals) );
execute(Program, NewGoals, Satisfied);
end
cs7120 (Prasad) L16-Meaning 12
Debugging PrologWelcome to SWI-Prolog (Multi-threaded, 32 bits, Version 5.6.62)
Copyright (c) 1990-2008 University of Amsterdam.…
For help, use ?- help(Topic). or ?- apropos(Word).
1 ?- consult(user).
| likes(mary,food).
likes(mary,wine).
likes(john,wine).
likes(john,mary).
| % user://2 compiled 0.00 sec, 632 bytes
cs7120 (Prasad) L16-Meaning 13
2 ?- trace, likes(X,Y).
Call: (9) likes(_G597, _G598) ? creep
Exit: (9) likes(mary, food) ? creep
X = mary,
Y = food ;
Redo: (9) likes(_G597, _G598) ? creep
Exit: (9) likes(mary, wine) ? creep
X = mary,
Y = wine ;
Redo: (9) likes(_G597, _G598) ? creep
Exit: (9) likes(john, wine) ? creep
…
[debug] 4 ?- likes(tom,john).
false.
cs7120 (Prasad) L16-Meaning 14
Debugging----------------
trace.spy(…).
;
…?creep…?leap…?abort
Propositional Prologp. p :- true.
p :- q.
p if q
cs7120 (Prasad) L16-Meaning 15
pq
p => q true false
true true false
false true true
pq
Facts
Rules
Boolean Logic
De Morgan’s Laws
cs7120 (Prasad) L16-Meaning 16
)()()( qpqp
)()()( qpqp
prq
prq
)()(
)(
p :- q,r.
cs7120 (Prasad) L16-Meaning 17
)()(
)(
prpq
prq
p :- q.p :- r. p :- q ; r.
cf. Normal Form / Clausal form
Sum of product form disjunctive normal form product of sum forms conjunctive normal form