Towards Syntactic Epistemic Logic

TL;DR

This paper introduces Syntactic Epistemic Logic (SEL), a new approach that models epistemic situations as sets of syntactic conditions, enabling representation of incomplete descriptions and bridging gaps in Epistemic Game Theory.

Contribution

It proposes SEL as a novel framework for representing incomplete epistemic descriptions, addressing limitations of traditional model-based approaches.

Findings

Successfully applied to a case study demonstrating effectiveness.

Bridges the gap between syntactic descriptions and semantic game representations.

Enhances modeling of incomplete epistemic information.

Abstract

Traditionally, Epistemic Logic represents epistemic scenarios using a single model. This, however, covers only complete descriptions that specify truth values of all assertions. Indeed, many -- and perhaps most -- epistemic descriptions are not complete. Syntactic Epistemic Logic, SEL, suggests viewing an epistemic situation as a set of syntactic conditions rather than as a model. This allows us to naturally capture incomplete descriptions; we discuss a case study in which our proposal is successful. In Epistemic Game Theory, this closes the conceptual and technical gap, identified by R. Aumann, between the syntactic character of game-descriptions and semantic representations of games.