Computability in Europe 2008
Logic and Theory of Algorithms

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Regular Talk:
Notions of Bisimulation for Heyting-Valued Modal Languages

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Author(s): Pantelis Eleftheriou, Costas Koutras and Christos Nomikos
Slot: Wed, 17:30-17:50, Room 22 (col. 4)

Abstract

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.

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