论数值确定三段论及相关逻辑的计算复杂度

IF 0.7 3区数学 Q1 LOGIC

Bulletin of Symbolic Logic Pub Date : 2008-03-01 DOI:10.2178/bsl/1208358842

Ian Pratt-Hartmann

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引用次数: 38

摘要

数值定三段论是用数值量词对经典三段论的语言进行扩展而得到的英语片段。数量型关系三段论是将数量型三段论用及物动词谓词扩展而成的英语片段。本文研究了这些碎片的可满足性问题的计算复杂度。我们证明了数值确定三段论的可满足性问题(=有限可满足性问题)是强np完全的，而数值确定关系三段论的可满足性问题(=有限可满足性问题)是nexptime完全的，但可能不是强np完全的。我们讨论了概率(命题)可满足性的相关问题，从而证明了数值定三段论的一些证明系统的不完备性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the Computational Complexity of the Numerically Definite Syllogistic and Related Logics

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.

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来源期刊

Bulletin of Symbolic Logic 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Bulletin of Symbolic Logic was established in 1995 by the Association for Symbolic Logic to provide a journal of high standards that would be both accessible and of interest to as wide an audience as possible. It is designed to cover all areas within the purview of the ASL: mathematical logic and its applications, philosophical and non-classical logic and its applications, history and philosophy of logic, and philosophy and methodology of mathematics.