后关系代数及其证明系统

[1991] Proceedings of the Twenty-First International Symposium on Multiple-Valued Logic Pub Date : 1991-05-26 DOI:10.1109/ISMVL.1991.130746

E. Orlowska

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引用次数: 6

摘要

介绍了一类与后逻辑相对应的非经典关系代数，并提出了一种后逻辑的代数化方法。Post逻辑的关系语义导致了一个Rasiowa-Sikorski风格的Post逻辑证明系统。定义了一个逻辑LPo，旨在提供一个正式的工具来验证后关系代数中的方程。定义了两种关系逻辑规则:根据公式中出现的关系操作的符号，将关系公式分解为一些更简单的公式的分解规则;以及特定的规则，这些规则对应于关系逻辑模型中假设的语义假设。这些规则适用于有限的公式序列。由于应用了一个规则，得到了一组新的序列

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Post relation algebras and their proof system

A class of nonclassical relation algebras that correspond to Post logics is introduced and a method of algebraization of those logics is proposed. Relational semantics for Post logics leads to a Rasiowa-Sikorski style proof system for Post logics. A logic LPo intended to provide a formal tool to verify equations in Post relation algebras is defined. Two kinds of rules for the relational logic are defined: decomposition rules enabling the decomposition of relational formulas into some simpler formulas, depending on symbols of relational operations occurring in the formulas; and specific rules, which correspond to semantical postulates assumed in the models of the relational logic. The rules apply to finite sequences of formulas. As a result of application of a rule, a family of new sequences is obtained.<>

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[1991] Proceedings of the Twenty-First International Symposium on Multiple-Valued Logic

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