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Inexact Knowledge with Introspection

Abstract : Standard Kripke models are inadequate to model situations of inexact knowledge with introspection, since positive and negative introspection force the relation of epistemic indiscernibility to be transitive and euclidean. Correlatively, Williamson's margin for error semantics for inexact knowledge invalidates axioms 4 and 5. We present a new semantics for modal logic which is shown to be complete for K45, without constraining the accessibility relation to be transitive or euclidean. The semantics corresponds to a system of modular knowledge, in which iterated modalities and simple modalities are not on a par. We show how the semantics helps to solve Williamson's luminosity paradox, and argue that it corresponds to an integrated model of perceptual and introspective knowledge that is psychologically more plausible than the one defended by Williamson. We formulate a generalized version of the semantics, called token semantics, in which modalities are iteration-sensitive up to degree n and insensitive beyond n. The multi-agent version of the semantics yields a resourcesensitive logic with implications for the representation of common knowledge in situations of bounded rationality
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Contributor : Paul Égré <>
Submitted on : Friday, March 7, 2008 - 10:58:09 PM
Last modification on : Friday, July 2, 2021 - 9:58:02 AM
Long-term archiving on: : Friday, September 28, 2012 - 10:55:28 AM


  • HAL Id : ijn_00261673, version 1


Denis Bonnay, Paul Egré. Inexact Knowledge with Introspection. Journal of Philosophical Logic, Springer Verlag, 2008, pp.00. ⟨ijn_00261673⟩



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