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Journal of Logic and Computation Advance Access published online on October 10, 2006
Journal of Logic and Computation, doi:10.1093/logcom/exl019
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© The Author, 2006. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org
Received September 26, 2005

Original Papers

The Dynamics of Syntactic Knowledge

Thomas Ågotnes 1 * and Natasha Alechina 2 *

1 Department of Informatics, University of Bergen, P.B. 7800,N-5020 Bergen, Norway.
2 School of Computer Science and IT, University of Nottingham, Nottingham, UK.

* To whom correspondence should be addressed.
Thomas Ågotnes, E-mail: agotnes{at}ii.uib.no
Natasha Alechina, E-mail: nza{at}cs.nott.ac.uk


  Abstract

The syntactic approach to epistemic logic avoids the logical omniscience problem by taking knowledge as primary rather than as defined in terms of possible worlds. In this study, we combine the syntactic approach with modal logic, using transition systems to model reasoning. We use two syntactic epistemic modalities: `knowing at least' a set of formulae and `knowing at most' a set of formulae. We are particularly interested in models restricting the set of formulae known by an agent at a point in time to be finite. The resulting systems are investigated from the point of view of axiomatization and complexity. We show how these logics can be used to formalise non-omniscient agents who know some inference rules, and study their relationship to other systems of syntactic epistemic logics, such as Ågotnes and Walicki (2004, Proc. 2nd EUMAS, pp. 1-10), Alechina et al. (2004, Proc. 3rd AAMAS, pp. 601-613), Duc (1997, J. Logic Comput., 7, 633-648).

Keywords: Modal logic; epistemic logic; logical omniscience.
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