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)

Abstract

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
• Status: Published
• Refereed: Yes
• 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
• Publisher: Springer
• ISSN: 0039-7857
• 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

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
65770	1	The Whole Truth	Stephan Leuenberger	Arts & Humanities Research Council (AHRC)	AH/M009610/1	HU - PHILOSOPHY
57255	1	The Contingency of Contingency	Stephan Leuenberger	Arts & Humanities Research Council (AHRC)	AH/J004189/1	HU - PHILOSOPHY