q 
¬p 
q
:- op(1100, xfy, implies).
:- op(1000, xfy, or). :- op(900, xfy, and). :- op(800, fy, ~). |
or, and and implies are defined as infix operators. is defined as a prefix operator. Note that these definitions are unusual in that they must be preceded by the :- operator. Omit this and you will get an error message to the effect that you are trying to redefine a system predicate. Defining a new operator consists of satisfying a goal which as a side-effect assigns the relevant precedence and associativity value to the operator.
or is defined as Prolog disjunction:
or(X, Y):- X;Y.
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and is defined as Prolog conjunction:
and(X, Y) :- X, Y.
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is defined as Prolog negation as failure:
~X :- \+ X.
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The definition of implies is a little more cunning. The following is a standard tautology of propositional logic:
p q ¬p q
as can be seen from the following truth table:
| (p | | q) | | ((¬ | p) | | q) |
| t | t | t | t | f | t | t | t |
| t | f | f | t | f | t | f | f |
| f | t | t | t | t | f | t | t |
| f | t | t | t | t | f | t | f |
We can use this equivalence to define implies like this:
implies(X, Y):- \+ X ; Y.
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Declare p and q to be true.
p.
q. |
We assume that everything other than p and q is false, but we need to tell Prolog that we haven’t simply forgotten some of our definitions
:- prolog_flag(unknown, _, fail).
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This allows Prolog to simply fail if given an unknown predicate.
The top-level predicate play/0 writes a prompt and accepts input with the built-in read/1 predicate, then evaluates the input.
play:-
write('> '), read(X), evaluate(X). |
evaluate/1 has three cases:
evaluate(X):-
X = stop, write(goodbye), nl. |
evaluate(X):-
X, write(true), nl, play. |
evaluate(_):-
write(false), nl, play. |
Finally, we insert a directive at the end of the file which Prolog will attempt to evaluate as soon as it consults it:
:-play.
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/* file logic.pl */
/* A simple program to demonstrate the use of operators in Prolog. Logical connectives and, or, if and ~ (negation) are defined as operators and given the same semantics as their Prolog counterparts. A small procedure play/0 is provided to allow the answers 'true' and 'false' to be supplied. To run the program, type 'play.' and then input a propositional calculus expression, followed by a full stop and carriage return. e.g. ?- play. > |: p and q. true > p and r. false > r and r. false > q and r. false > q or r. true > p implies q. true > p implies q and r. false > p implies q or r. true > stop. Goodbye Type 'stop.' to finish. */ % Operator definitions :- op(1000, xfy, or). :- op(900, xfy, and). :- op(800, fy, ~). :- op(1100, xfx, implies). % Allow Prolog to simply fail if given an unknown % predicate :- prolog_flag(unknown, _, fail). % Definitions of connectives ~X :- \+ X. and(X, Y):- X , Y. or(X, Y):- X ; Y. % This one is cunning, 'X implies Y' is defined with % the semantics of (~X) or Y -- which has the same % truth conditions. implies(X, Y):- \+ X ; Y. % p and q are true. p. q. % Top level. Write a prompt and accept input. Then % evaluate input. play:- write('> '), read(X), evaluate(X). % If X is 'stop', then output 'goodbye' and terminate. evaluate(X):- X = stop, write(goodbye), nl. % If X succeeds, write 'true' and continue. evaluate(X):- X, write(true), nl, play. % Otherwise, output 'false' and continue. evaluate(_):- write(false), nl, play. :-play. |