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Frame constructions, truth invariance and validity preservation in many-valued modal logic

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2012

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Koutras, Costas D.

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https://doi.org/10.3166/jancl.15.367-388
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Journal of Applied Non-Classical Logics. Taylor & Francis. 2012, 15(4), pp. 367-388. ISSN 1166-3081. eISSN 1958-5780. Available under: doi: 10.3166/jancl.15.367-388

Zusammenfassung

In this paper we define and examine frame constructions for the family of manyvalued modal logics introduced by M. Fitting in the '90s. Every language of this family is built on an underlying space of truth values, a Heyting algebra H. We generalize Fitting's original work by considering complete Heyting algebras as truth spaces and proceed to define a suitable notion of H-indexed families of generated subframes, disjoint unions and bounded morphisms. Then, we provide an algebraic generalization of the canonical extension of a frame and model, and prove a preservation result inspired from Fitting's canonical model argument in [FIT 92a]. The analog of a complex algebra and of a principal ultrafilter is defined and the embedding of a frame into its canonical extension is presented.

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Fachgebiet (DDC)
510 Mathematik

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many-valued modal logic, frame/model theory, canonical extensions

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ISO 690ELEFTHERIOU, Pantelis E., Costas D. KOUTRAS, 2012. Frame constructions, truth invariance and validity preservation in many-valued modal logic. In: Journal of Applied Non-Classical Logics. Taylor & Francis. 2012, 15(4), pp. 367-388. ISSN 1166-3081. eISSN 1958-5780. Available under: doi: 10.3166/jancl.15.367-388
BibTex
@article{Eleftheriou2012-04-13Frame-49484,
  year={2012},
  doi={10.3166/jancl.15.367-388},
  title={Frame constructions, truth invariance and validity preservation in many-valued modal logic},
  number={4},
  volume={15},
  issn={1166-3081},
  journal={Journal of Applied Non-Classical Logics},
  pages={367--388},
  author={Eleftheriou, Pantelis E. and Koutras, Costas D.}
}
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