Simple Hyperintensional Belief Revision

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.

The Fundamental Problem of Logical Omniscience

“…Logical tools help with (1), (2), (3). Take a modal propositional language E L with knowledge modality K and update modality [ ].…”

“…On another approach, content is as structured as a syntax: an agent's total knowledge at @ is modeled as a set of sentences K @ in a suitable formal language (say, E L itself). 3 (One may then understand the contents of a knowledge attitude as sentences in a language of thought; but see [13] for a critique.) Kϕ is true at @ exactly when ϕ ∈ K @ .…”

“…Hence, by the definition of W c , Aϕ ∈ f or all ∈ W c . (4) @ 0 ⊆ @ follows directly from item (3). For @ ⊆ @ 0 , suppose ϕ ∈ @ , i.e., that Aϕ ∈ .…”

Taming the runabout imagination ticket

“… Besides Berto (2017a), a version of the semantics used in this paper, which resorts to a plausibility metric, can be found inBerto (2018). There, the relevant operators are interpreted precisely as a kind of conditional belief or (static) belief revision operators, in the context of a discussion of the AGM postulates for belief revision.…”

“…There, the relevant operators are interpreted precisely as a kind of conditional belief or (static) belief revision operators, in the context of a discussion of the AGM postulates for belief revision. 4 These were called 'contents' inBerto (2017aBerto ( , 2018. I'm not so happy with that terminology anymore: it has topic-preservation expressed as 'content containment', and this reminds one of some Kantian analyticity, which is misleading in this context.…”