Inferentialist Public Announcement Logic: Base-extension Semantics

TL;DR

This paper develops a base-extension semantics for public announcement logic rooted in inferentialist proof-theoretic semantics, extending prior modal semantics to account for information updates through announcements.

Contribution

It introduces a novel base-extension semantics for public announcement logic that explicitly models information updates via modal relations on bases, grounded in inferentialist principles.

Findings

Analyzed the three-player card game example.

Examined the muddy children puzzle.

Extended semantics to handle announcement updates.

Abstract

Proof-theoretic semantics, and base-extension semantics in particular, can be seen as a logical realization of inferentialism, in which the meaning of expressions is understood through their use. We present a base-extension semantics for public announcement logic, building on earlier work giving a base-extension semantics for the modal logic $S5$, which in turn builds on earlier such work for $K$, $KT$, $K4$, and $S4$. These analyses rely on a notion of `modal relation' on bases. The main difficulty in extending the existing B-eS for $S5$ to public announcement logic is to account announcements of the form $[\psi]\phi$, which, in this setting, update the modal relations on bases. We provide a detailed analysis of two classical examples, namely the three-player card game and the muddy children puzzle. These examples illustrate how the inferentialist perspective requires fully explicit information about the state of the participating agents.