Epistemic Syllogistic: First Steps

TL;DR

This paper introduces and analyzes variants of epistemic syllogistic, inspired by natural logic, providing axiomatizations and completeness proofs for these modal logic fragments focused on knowledge reasoning.

Contribution

It presents new axiomatizations and completeness results for epistemic syllogistic variants, connecting Aristotle's modal logic with contemporary epistemic logic.

Findings

Axiomatizations of epistemic syllogistic variants

Completeness proofs for these logical systems

Analysis of natural fragments of first-order modal logic

Abstract

Aristotle's discussions on modal syllogistic have often been viewed as error-prone and have garnered significant attention in the literature due to historical and philosophical interests. However, from a contemporary standpoint, they also introduced natural fragments of first-order modal logic, warranting a comprehensive technical analysis. In this paper, drawing inspiration from the natural logic program, we propose and examine several variants of modal syllogistic within the epistemic context, thereby coining the term Epistemic Syllogistic. Specifically, we concentrate on the de re interpretation of epistemic syllogisms containing non-trivial yet natural expressions such as "all things known to be A are also known to be not B." We explore the epistemic apodeictic syllogistic and its extensions, which accommodate more complex terms. Our main contributions include several axiomatizations of these logics, with completeness proofs that may be of independent interest.