Epistemic logic without closure

Leuenberger, S. and Smith, M. (2021) Epistemic logic without closure. Synthese, 198(5), pp. 4751-4774. (doi: 10.1007/s11229-019-02368-6)

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All standard epistemic logics legitimate something akin to the principle of closure, according to which knowledge is closed under competent deductive inference. And yet the principle of closure, particularly in its multiple premise guise, has a somewhat ambivalent status within epistemology. One might think that serious concerns about closure point us away from epistemic logic altogether—away from the very idea that the knowledge relation could be fruitfully treated as a kind of modal operator. This, however, need not be so. The abandonment of closure may yet leave in place plenty of formal structure amenable to systematic logical treatment. In this paper we describe a family of weak epistemic logics in which closure fails, and describe two alternative semantic frameworks in which these logics can be modelled. One of these—which we term plurality semantics—is relatively unfamiliar. We explore under what conditions plurality frames validate certain much-discussed principles of epistemic logic. It turns out that plurality frames can be interpreted in a very natural way in light of one motivation for rejecting closure, adding to the significance of our technical work. The second framework that we employ—neighbourhood semantics—is much better known. But we show that it too can be interpreted in a way that comports with a certain motivation for rejecting closure.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Leuenberger, Professor Stephan
Authors: Leuenberger, S., and Smith, M.
College/School:College of Arts > School of Humanities > Philosophy
Journal Name:Synthese
ISSN (Online):1573-0964
Published Online:27 August 2019
Copyright Holders:Copyright © 2019 The Authors
First Published:First published in Synthese 198(5): 4751-4774
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
657701The Whole TruthStephan LeuenbergerArts & Humanities Research Council (AHRC)AH/M009610/1HU - PHILOSOPHY
572551The Contingency of ContingencyStephan LeuenbergerArts & Humanities Research Council (AHRC)AH/J004189/1HU - PHILOSOPHY