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Notions of Bisimulation for Heyting-Valued Modal Languages

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2012

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Koutras, Costas D.
Nomikos, Christos

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https://doi.org/10.1093/logcom/exq005
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Journal of Logic and Computation. Oxford University Press. 2012, 22(2), pp. 213-235. ISSN 0955-792X. eISSN 1465-363X. Available under: doi: 10.1093/logcom/exq005

Zusammenfassung

We examine the notion of bisimulation and its ramifications, in the context of the family of Heyting-valued modal languagesintroduced by M. Fitting. Each modal language in this family is built on an underlying space of truth values, a HeytingalgebraH. All the truth values are directly represented in the language, which is interpreted on relational frames with an H-valued accessibility relation. We define two notions of bisimulation that allow us to obtain truth invariance results. Weprovide game semantics and, for the more interesting and complicated notion, we are able to provide characteristic formulaeand prove a Hennessy–Milner-type theorem. If the underlying algebraHis finite, Heyting-valued modal models can beequivalently reformulated to a form relevant to epistemic situations with many interrelated experts. Our definitions and resultsdraw inspiration from this formulation, which is of independent interest to Knowledge Representation applications.

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510 Mathematik

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Many-valued Modal Logic, bisimulation

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ISO 690ELEFTHERIOU, Pantelis E., Costas D. KOUTRAS, Christos NOMIKOS, 2012. Notions of Bisimulation for Heyting-Valued Modal Languages. In: Journal of Logic and Computation. Oxford University Press. 2012, 22(2), pp. 213-235. ISSN 0955-792X. eISSN 1465-363X. Available under: doi: 10.1093/logcom/exq005
BibTex
@article{Eleftheriou2012-04-01Notio-49536,
  year={2012},
  doi={10.1093/logcom/exq005},
  title={Notions of Bisimulation for Heyting-Valued Modal Languages},
  number={2},
  volume={22},
  issn={0955-792X},
  journal={Journal of Logic and Computation},
  pages={213--235},
  author={Eleftheriou, Pantelis E. and Koutras, Costas D. and Nomikos, Christos}
}
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