Simple Hyperintensional Belief Revision

F Berto

doi:10.1007/s10670-018-9971-1

Abstract

I present a possible worlds semantics for a hyperintensional belief revision operator, which reduces the logical idealization of cognitive agents affecting similar operators in doxastic and epistemic logics, as well as in standard AGM belief revision theory. (Revised) belief states are not closed under classical logical consequence; revising by inconsistent information does not perforce lead to trivialization; and revision can be subject to ‘framing effects’: logically or necessarily equivalent contents can lead to different revisions. Such results are obtained without resorting to non-classical logics, or to non-normal or impossible worlds semantics. The framework combines, instead, a standard semantics for propositional S5 with a simple mereology of contents.

Highlights

Standard AGM belief revision theory imposes a high amount of idealization on cognitive agents who revise their beliefs in the light of new information1
Our mental states—believing, supposing, desiring, hoping, fearing—can treat logically or necessarily equivalent contents differently: Lois Lane can wish that Superman is in love with her without wishing that Clark Kent is in love with her, it is metaphysically impossible for Superman to be other than Clark Kent
While general transitivity fails for our B as a consequence of its variable strictness, C3 validates a kind of limited transitivity or Cut principle for belief revision: (CUT) fB/w; B/^wvgB/v

Summary

Introduction

Standard AGM belief revision theory imposes a high amount of idealization on cognitive agents who revise their beliefs in the light of new information. It should allow us to reason about below, that it models the aforementioned hyperintensional phenomena without weakening the underlying classical and (normal) modal logic (as it happens, e.g., in paraconsistent logics for the management of inconsistent information: see Tanaka et al 2013), and without resorting to so-called non-normal or impossible worlds (Kiourti 2010; Berto 2013), which have often been proposed as a tool to deal with logical omniscience (see Rantala 1982; Wansing 1990; Nolan 1997; Jago 2007, 2014) It employs, instead, only semantic notions acceptable by, and already available in the toolkit of, a classical modal logician (I will mention, though, a revenge of non-classical frameworks in a footnote below). The latter can lead to very complex frameworks, or to logics that are too weak to be of serious interest

A Hyperintensional Semantics

Disjunction and Indeterminacy

Hyperintensionality

Revising by Inconsistent Information

Conclusion and Further Work