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Resolution and model building in the infinite-valued calculus of Łukasiewicz. (English) Zbl 0921.03013
The paper presents a resolution procedure for the infinite-valued calculus of Łukasiewicz. Problems of resolution, model building and their complexity are discussed. The notion of $$\Theta$$-satisfiability is introduced. Then the authors prove that the $$\Theta$$-satisfiability problem is NP-complete. In the particular case of a finite set of Horn-clauses the authors provide decision and model building algorithms that are polynomial. The same is proved for a finite set of Krom-clauses.
Reviewer: N.Zamov (Kazan’)

##### MSC:
 03B35 Mechanization of proofs and logical operations 03B50 Many-valued logic
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##### References:
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