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Knowledge means ‘all’, belief means ‘most’

Knowledge means ‘all’, belief means ‘most’ We introduce a bimodal epistemic logic intended to capture knowledge as truth in all epistemically alternative states and belief as a generalised ‘majority’ quantifier, interpreted as truth in most (i.e. a ‘majority’) of the epistemically alternative states. This doxastic interpretation is of interest in knowledge-representation applications and it also holds an independent philosophical and technical appeal. The logic comprises an epistemic modal operator, a doxastic modal operator of consistent and complete belief and ‘bridge’ axioms which relate knowledge to belief. To capture the notion of a ‘majority’ we use the ‘large sets’ introduced independently by K. Schlechta and V. Jauregui, augmented with a requirement of completeness, which furnishes a ‘weak ultrafilter’ concept. We provide semantics in the form of possible-worlds frames, properly blending relational semantics with a version of general Scott–Montague (neighbourhood) frames and we obtain soundness and completeness results. We examine the validity of certain epistemic principles discussed in the literature, in particular some of the ‘bridge’ axioms discussed by W. Lenzen and R. Stalnaker, as well as the ‘paradox of the perfect believer’, which is not a theorem of . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Non-Classical Logics Taylor & Francis

Knowledge means ‘all’, belief means ‘most’

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Knowledge means ‘all’, belief means ‘most’

Abstract

We introduce a bimodal epistemic logic intended to capture knowledge as truth in all epistemically alternative states and belief as a generalised ‘majority’ quantifier, interpreted as truth in most (i.e. a ‘majority’) of the epistemically alternative states. This doxastic interpretation is of interest in knowledge-representation applications and it also holds an independent philosophical and technical appeal. The logic comprises an epistemic modal operator, a...
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Publisher
Taylor & Francis
Copyright
© 2016 Informa UK Limited, trading as Taylor & Francis Group
ISSN
1958-5780
eISSN
1166-3081
DOI
10.1080/11663081.2016.1214804
Publisher site
See Article on Publisher Site

Abstract

We introduce a bimodal epistemic logic intended to capture knowledge as truth in all epistemically alternative states and belief as a generalised ‘majority’ quantifier, interpreted as truth in most (i.e. a ‘majority’) of the epistemically alternative states. This doxastic interpretation is of interest in knowledge-representation applications and it also holds an independent philosophical and technical appeal. The logic comprises an epistemic modal operator, a doxastic modal operator of consistent and complete belief and ‘bridge’ axioms which relate knowledge to belief. To capture the notion of a ‘majority’ we use the ‘large sets’ introduced independently by K. Schlechta and V. Jauregui, augmented with a requirement of completeness, which furnishes a ‘weak ultrafilter’ concept. We provide semantics in the form of possible-worlds frames, properly blending relational semantics with a version of general Scott–Montague (neighbourhood) frames and we obtain soundness and completeness results. We examine the validity of certain epistemic principles discussed in the literature, in particular some of the ‘bridge’ axioms discussed by W. Lenzen and R. Stalnaker, as well as the ‘paradox of the perfect believer’, which is not a theorem of .

Journal

Journal of Applied Non-Classical Logics – Taylor & Francis

Published: Jul 2, 2016

Keywords: Logics of knowledge and belief; modal logic; majority spaces

References

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  • Is justified true belief knowledge?
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  • On logics of knowledge and belief