Decidability of weak logics with deterministic transitive closure

Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2014-07-14 DOI:10.1145/2603088.2603134

Witold Charatonik, Emanuel Kieronski, Filip Mazowiecki

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引用次数: 10

Abstract

The deterministic transitive closure operator, added to languages containing even only two variables, allows to express many natural properties of a binary relation, including being a linear order, a tree, a forest or a partial function. This makes it a potentially attractive ingredient of computer science formalisms. In this paper we consider the extension of the two-variable fragment of first-order logic by the deterministic transitive closure of a single binary relation, and prove that the satisfiability and finite satisfiability problems for the obtained logic are decidable and ExpSpace-complete. This contrasts with the undecidability of two-variable logic with the deterministic transitive closures of several binary relations, known before. We also consider the class of universal first-order formulas in prenex form. Its various extensions by deterministic closure operations were earlier considered by other authors, leading to both decidability and undecidability results. We examine this scenario in more details.

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具有确定性传递闭包的弱逻辑的可判定性

确定性传递闭包运算符添加到只包含两个变量的语言中，允许表达二元关系的许多自然属性，包括线性顺序、树、森林或部分函数。这使得它成为计算机科学形式化中一个潜在的有吸引力的成分。本文考虑了单二元关系的确定性传递闭包对一阶逻辑的二变量片段的扩展，并证明了所得到的逻辑的可满足性和有限可满足性问题是可决定的和expspace完全的。这与之前已知的几个二元关系的确定性传递闭包的两变量逻辑的不可判定性形成对比。我们也考虑一类前缀形式的一阶通称公式。其他作者先前考虑过通过确定性闭包操作对其进行各种扩展，从而导致可判定性和不可判定性结果。我们将更详细地研究这个场景。

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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Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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