Constrained Pseudo-Propositional Logic

Propositional logic, with the aid of SAT solvers, has become capable of solving a range of important and complicated problems. Expanding this range, to contain additional varieties of problems, is subject to the complexity resulting from encoding counting constraints in conjunctive normal form (CNF)...

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Bibliographic Details
Published inLogica universalis Vol. 14; no. 4; pp. 523 - 535
Main Author Azizi-Sultan, Ahmad-Saher
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2020
Springer Nature B.V
Subjects
Boolean algebra
Canonical forms
Computer Science
Constraints
Logic
Mathematics
Mathematics and Statistics
Number theory
Propositional logic
Proof system
Pseudo-Boolean constraints
SAT
03F03
Primary 03B05
Secondary 03B22
05A05
Online AccessGet full text
ISSN1661-8297
1661-8300
DOI10.1007/s11787-020-00266-x

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Summary:Propositional logic, with the aid of SAT solvers, has become capable of solving a range of important and complicated problems. Expanding this range, to contain additional varieties of problems, is subject to the complexity resulting from encoding counting constraints in conjunctive normal form (CNF). Due to the limitation of the expressive power of propositional logic, generally, such an encoding increases the numbers of variables and clauses excessively. This work eliminates the indicated drawback by interpolating constraint symbols and the set of natural numbers N into the alphabet of propositional logic and adjusting the underlying language accordingly. In the extended logic counting constraints are naturally formulated, while many important aspects, such as Boolean nature and the soundness and completeness theorems, are kept preserved.
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content type line 14
ISSN:1661-8297
1661-8300
DOI:10.1007/s11787-020-00266-x