First Degree Entailment with Group Attitudes and Information Updates

TL;DR

This paper extends epistemic logic with group knowledge and information updates, providing sound, complete, and decidable axiomatizations for these enhanced logical systems.

Contribution

It introduces operators for universal and common knowledge in groups and formalizes information updates using non-associative Lambek calculus, expanding the expressiveness of epistemic logic.

Findings

Sound and complete axiomatizations for the extended logics

Decidability of both logics established

Formalization of information updates using non-associative Lambek calculus

Abstract

We extend the epistemic logic with De Morgan negation by Fagin et al. (Artif. Intell. 79, 203-240, 1995) by adding operators for universal and common knowledge in a group of agents, and with a formalization of information update using a generalized version of the left division connective of the non-associative Lambek calculus. We provide sound and complete axiomatizations of the basic logic with the group operators and the basic logic with group operators and updates. Both logics are shown to be decidable.