Logical Approaches to Computational Barriers

Notions of Bisimulation for Heyting-Valued Modal Languages

Author(s): |
Pantelis Eleftheriou, Costas Koutras and Christos Nomikos |

Slot: |
Array, 17:30-17:50, col. 4 |

We define notions of bisimulation for the family of Heyting-valued modal logics introduced by M. Fitting. In this family of logics, each modal language is built on an underlying space of truth values, a Heyting algebra $H$. All the truth values are directly represented in the language which is interpreted on relational frames with an $H$-valued accessibility relation. We investigate the correct notion of bisimulation in this context: we define two variants of bisimulation relations and derive relative (to a truth value) modal equivalence results for bisimilar states. We further investigate game semantics for our bisimulation, Hennessy-Milner classes and other relevant properties. If the underlying algebra $H$ is finite, Heyting-valued modal models can be equivalently reformulated to a form relevant to epistemic situations with many interrelated experts. Our definitions and results draw from this formulation, which is of independent interest to Knowledge Representation applications.

websites: Arnold Beckmann | 2008-05-19 |