Interpolation Property on Visser's Formal Propositional Logic

Authors

  • Majid Alizadeh University of Tehran, College of Science School of Mathematics, Statistics and Computer Science, 14155-6455 Tehran, Iran image/svg+xml https://orcid.org/0000-0003-2644-5959
  • Masoud Memarzadeh University of Tehran, College of Science School of Mathematics, Statistics and Computer Science, 14155-6455 Tehran, Iran image/svg+xml

DOI:

https://doi.org/10.18778/0138-0680.2022.18

Keywords:

basic propositional logic, formal propositional logic, layered bisimulation, interpolation

Abstract

 In this paper by using a model-theoretic approach, we prove Craig interpolation property for Formal Propositional Logic, FPL, Basic propositional logic, BPL and the uniform left-interpolation property for FPL. We also show that there are countably infinite extensions of FPL with the uniform interpolation property.

References

M. Alizadeh, M. Ardeshir, On Löb algebras, Mathematical Logic Quarterly, vol. 52(1) (2006), pp. 95–105, DOI: https://doi.org/10.1002/malq.200510016
Google Scholar DOI: https://doi.org/10.1002/malq.200510016

M. Ardeshir, B. Hesaam, An introduction to basic arithmetic, Logic Journal of the IGPL, vol. 16(1) (2008), pp. 1–13, DOI: https://doi.org/10.1093/jigpal/jzm013
Google Scholar DOI: https://doi.org/10.1093/jigpal/jzm013

M. Ardeshir, W. Ruitenburg, Basic propositional calculus I, Mathematical Logic Quarterly, vol. 44(3) (1998), pp. 317–343, DOI: https://doi.org/10.1002/malq.19980440304
Google Scholar DOI: https://doi.org/10.1002/malq.19980440304

M. Ardeshir, W. Ruitenburg, Basic propositional calculus II. Interpolation, Archive for Mathematical Logic, vol. 40(5) (2001), pp. 349–364, DOI: https://doi.org/10.1007/PL00003844
Google Scholar DOI: https://doi.org/10.1007/PL00003844

S. Ghilardi, M. Zawadowski, A sheaf representation and duality for finitely presented Heyting algebras, Journal of Symbolic Logic, (1995), pp. 911–939, DOI: https://doi.org/10.2307/2275765
Google Scholar DOI: https://doi.org/10.2307/2275765

A. M. Pitts, On an interpretation of second order quantification in first order intuitionistic propositional logic, The Journal of Symbolic Logic, (1992), pp. 33–52.
Google Scholar DOI: https://doi.org/10.2307/2275175

A. Visser, A propositional logic with explicit fixed points, Studia Logica, vol. 40(2) (1981), pp. 155–175, DOI: https://doi.org/10.1007/BF01874706
Google Scholar DOI: https://doi.org/10.1007/BF01874706

A. Visser, et al., Uniform interpolation and layered bisimulation, [in:] P. Hájek (ed.), Gödel’96: Logical foundations of mathematics, computer science and physics—Kurt Gödel’s legacy, Brno, Czech Republic, August 1996, proceedings, vol. 6 of Lecture Notes in Logic, Springer-Verlag, Berlin (1996), pp. 139–164, DOI: https://doi.org/10.1007/978-3-662-21963-8_9
Google Scholar DOI: https://doi.org/10.1017/9781316716939.010

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Published

2022-09-20

How to Cite

Alizadeh, M., & Memarzadeh, M. (2022). Interpolation Property on Visser’s Formal Propositional Logic. Bulletin of the Section of Logic, 51(3), 297–316. https://doi.org/10.18778/0138-0680.2022.18

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Section

Research Article