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Article
Data sources: zbMATH Open
Journal of Logic and Computation
Article . 1994 . Peer-reviewed
Data sources: Crossref
DBLP
Article . 1994
Data sources: DBLP
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Short Conjunctive Normal Forms in Finitely Valued Logics

Short conjunctive normal forms in finitely valued logics
Authors: Reiner Hähnle;

Short Conjunctive Normal Forms in Finitely Valued Logics

Abstract

This paper deals with resolution theorem proving in many-valued logic. The latter has found increasing applications in such diverse fields as nonmonotonic reasoning, error-correcting codes, and software/hardware verification. Here, very long nonclausal formulae naturally come out, and efficient normal form reductions are, if not a \textit{sine qua non}, at least a very interesting tool for the algorithmic manipulation of these formulas. The author develops a satisfiability preserving CNF reduction of formulas in finite-valued calculi. Generalizing Tseitin's structure preserving clause forms, and adapting the notion of polarity to the many- valued case, he is able to keep the length of the resulting formulas polynomially bounded with respect to the length of the input formulas, while avoiding the generation of redundant clauses. Formulas are labelled by signs which, in contrast to the two-valued case, are sets of truth values, rather than truth values. The author compares his work with previous results on many-valued normal forms by Baaz, Carnielli, Fernmüller, Morgan, Murray, O'Hearn, Orlowska, Rosenthal, Stachniak, and others. In a final section he discusses applications of his techniques to the many-valued counterparts of the existential and universal quantifiers.

Country
Germany
Related Organizations
Keywords

ddc:004, DATA processing & computer science, many-valued logic, Łukasiewicz logic, 004, satisfiability preserving CNF reduction of formulas in finite-valued calculi, Mechanization of proofs and logical operations, Logical aspects of Łukasiewicz and Post algebras, Many-valued logic, resolution theorem proving, info:eu-repo/classification/ddc/004, Theorem proving (deduction, resolution, etc.)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
58
Top 10%
Top 10%
Average
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