📄 fig23_16.pl
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% Figure 23.16 Translating a propositional calculus formula into
% a set of (asserted) clauses.
% Translating a propositional formula into (asserted) clauses
:- op( 100, fy, ~). % Negation
:- op( 110, xfy, &). % Conjunction
:- op( 120, xfy, v). % Disjunction
:- op( 130, xfy, =>). % Implication
% translate( Formula): translate propositional Formula
% into clauses and assert each resulting clause C as clause( C)
translate( F & G) :- % Translate conjunctive formula
!, % Red cut
translate( F),
translate( G).
translate( Formula) :-
transform( Formula, NewFormula), % Transformation step on Formula
!, % Red cut
translate( NewFormula).
translate( Formula) :- % No more transformation possible
assert( clause( Formula)).
% Transformation rules for propositional formulas
% transform( Formula1, Formula2) if
% Formula2 is equivalent to Formula1, but closer to clause form
transform( ~(~X), X). % Eliminate double negation
transform( X => Y, ~X v Y). % Eliminate implication
transform( ~ (X & Y), ~X v ~Y). % De Morgan's law
transform( ~ (X v Y), ~X & ~Y). % De Morgan's law
transform( X & Y v Z, (X v Z) & (Y v Z)). % Distribution
transform( X v Y & Z, (X v Y) & (X v Z)). % Distribution
transform( X v Y, X1 v Y) :-
transform( X, X1). % Transform subexpression
transform( X v Y, X v Y1) :-
transform( Y, Y1). % Transform subexpression
transform( ~ X, ~ X1) :-
transform( X, X1). % Transform subexpression
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