Bulletin of Symbolic Logic

On the computational complexity of the numerically definite syllogistic and related logics

Ian Pratt-Hartmann

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Abstract

The numerically definite syllogistic is the fragment of English obtained by extending the language of the classical syllogism with numerical quantifiers. The numerically definite relational syllogistic is the fragment of English obtained by extending the numerically definite syllogistic with predicates involving transitive verbs. This paper investigates the computational complexity of the satisfiability problem for these fragments. We show that the satisfiability problem (= finite satisfiability problem) for the numerically definite syllogistic is strongly NP-complete, and that the satisfiability problem (= finite satisfiability problem) for the numerically definite relational syllogistic is NEXPTIME-complete, but perhaps not strongly so. We discuss the related problem of probabilistic (propositional) satisfiability, and thereby demonstrate the incompleteness of some proof-systems that have been proposed for the numerically definite syllogistic.

Article information

Source
Bull. Symbolic Logic, Volume 14, Issue 1 (2008), 1-28.

Dates
First available in Project Euclid: 16 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.bsl/1208358842

Digital Object Identifier
doi:10.2178/bsl/1208358842

Mathematical Reviews number (MathSciNet)
MR2395045

Zentralblatt MATH identifier
1166.03011

Citation

Pratt-Hartmann, Ian. On the computational complexity of the numerically definite syllogistic and related logics. Bull. Symbolic Logic 14 (2008), no. 1, 1--28. doi:10.2178/bsl/1208358842. https://projecteuclid.org/euclid.bsl/1208358842


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