Speaker
Marta Bílková

Title
Epistemic logic for sceptical agents

Abstract
We present an epistemic logic for a notion of knowledge confirmed by a reliable source of information. Such notion of knowledge can be modelled as a diamond modality over a substructural logic. As the weakest propositional background logic we choose distributive non-associative full Lambek calculus with a negation and work with its relational semantics, interpreting the elements of a relational frame as information states consisting of collections of data which may be incomplete or even inconsistent. The principal epistemic relation between the states is the one of being a reliable source of information. From this point of view it is natural to define the epistemic operator existentially as a (backward-looking) diamond modality. The resulting knowledge modality satisfies axioms of factivity and consistency, admits a weak form of logical omniscience (the monotonicity rule for the modality), but avoids stronger ones (an analogue of necessitation rule and the K-axiom) as well as some closure properties discussed in normal epistemic logics (like the positive and negative introspection). For these properties we can provided characteristic frame conditions, so that they can be present in the system if they are considered to be appropriate for some specific epistemic context. The system is modular in the sense that the axiomatization sound and complete with respect to a wide class of background propositional logics, for the weakest system we can also prove decidability using a filtration method. The system can be extended with a reasonable belief modality in a similar manner, and we can provide a display style proof theory for the resulting logic.

The talk is based on a joint work with Ondrej Majer and on the previous paper:

M. Bilkova, O. Majer, M. Pelis, Epistemic logics for sceptical agents, JLC, online first March 2015.
http://logcom.oxfordjournals.org/content/early/2015/03/18/logcom.exv009.abstract
(preprint version available at: http://web.ff.cuni.cz/~bilkmaff/soubory/JA1_JLC2014.pdf )