The Dynamics of Syntactic Knowledge

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 A˚ gotnes 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).

• Type: Journal
• Year: 2007
• Where: LOGCOM
• Authors: Thomas Ågotnes, Natasha Alechina
• Keywords: LOGCOM 2007, Logic, Syntactic Approach, Syntactic Epistemic Modalities