Exploring the Landscape of Relational Syllogistic Logics

TL;DR

This paper investigates relational syllogistic logics, establishing their decidability, completeness, and complexity, and explores how different constructors influence these properties in logical reasoning about relations.

Contribution

It provides the first completeness and complexity results for a broad family of relational syllogistic logics parametrized by constructors.

Findings

All considered systems are decidable.

Completeness theorems are established for the subfamily.

Complexity results are derived for the parametrized logics.

Abstract

This paper explores relational syllogistic logics, a family of logical systems related to reasoning about relations in extensions of the classical syllogistic. These are all decidable logical systems. We prove completeness theorems and complexity results for a natural subfamily of relational syllogistic logics, parametrized by constructors for terms and for sentences.