Evidence and plausibility in neighborhood structures

Annals of Pure and Applied Logic 165 (1):106-133 (2014)
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Abstract

The intuitive notion of evidence has both semantic and syntactic features. In this paper, we develop an evidence logic for epistemic agents faced with possibly contradictory evidence from different sources. The logic is based on a neighborhood semantics, where a neighborhood N indicates that the agent has reason to believe that the true state of the world lies in N. Further notions of relative plausibility between worlds and beliefs based on the latter ordering are then defined in terms of this evidence structure, yielding our intended models for evidence-based beliefs. In addition, we also consider a second more general flavor, where belief and plausibility are modeled using additional primitive relations, and we prove a representation theorem showing that each such general model is a p-morphic image of an intended one. This semantics invites a number of natural special cases, depending on how uniform we make the evidence sets, and how coherent their total structure. We give a structural study of the resulting ‘uniform’ and ‘flat’ models. Our main result are sound and complete axiomatizations for the logics of all four major model classes with respect to the modal language of evidence, belief and safe belief. We conclude with an outlook toward logics for the dynamics of changing evidence, and the resulting language extensions and connections with logics of plausibility change

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Author Profiles

Eric Pacuit
University of Maryland, College Park
Johan Van Benthem
University of Amsterdam

Citations of this work

Dynamic Hyperintensional Belief Revision.Aybüke Özgün & Francesco Berto - 2021 - Review of Symbolic Logic (3):766-811.
Substructural epistemic logics.Igor Sedlár - 2015 - Journal of Applied Non-Classical Logics 25 (3):256-285.
A Hyperintensional Logic of Non-prime Evidence.Pietro Vigiani - 2024 - Journal of Philosophical Logic 53 (3):761-788.
Epistemic logic.Vincent Hendricks - 2008 - Stanford Encyclopedia of Philosophy.

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References found in this work

An essay in classical modal logic.Krister Segerberg - 1971 - Uppsala,: Filosofiska föreningen och Filosofiska institutionen vid Uppsala universitet.
What 'must' and 'can' must and can mean.Angelika Kratzer - 1977 - Linguistics and Philosophy 1 (3):337--355.
Dynamic logic for belief revision.Johan van Benthem - 2007 - Journal of Applied Non-Classical Logics 17 (2):129-155.
On Logics of Knowledge and Belief.Robert Stalnaker - 2006 - Philosophical Studies 128 (1):169-199.

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