Interpolation in Normal Extensions of the Brouwer Logic

Zofia Kostrzycka

doi:10.18778/0138-0680.45.3.4.03

Authors

Zofia Kostrzycka Opole University of Technology

DOI:

https://doi.org/10.18778/0138-0680.45.3.4.03

Keywords:

normal extensions of the Brouwer logics, Kripke frames, interpolation property, amalgamation property

Abstract

The Craig interpolation property and interpolation property for deducibility are considered for special kind of normal extensions of the Brouwer logic.

References

[1] J. F. A. K. van Benthem, I. I. Humberstone, Halldén-completeness by Gluing of Kripke Frames, Notre Dame Journal of Formal Logic 24, No 4 (1983), pp. 426–430.
Google Scholar

[2] M. Byrd, D. Ullrich,The extensions of BAlt3, Journal of Philosophical Logic 6 (1977), pp. 109–117.
Google Scholar

[3] M. Byrd, The extensions of BAlt3-revisited, Journal of Philosophical Logic 7 (1978), pp. 407–413.
Google Scholar

[4] A. Chagrov, M. Zakharyaschev, Modal Logic, Oxford Logic Guides 35, (1997).
Google Scholar

[5] J. Czelakowski, Logical matrices and the amalgamation property, SL 41 (4), (1981), pp. 329–341.
Google Scholar

[6] D. M. Gabbay, Craig’s interpolation theorem for modal logics, [in:] W. Hodges, editor, Proceedings of logic conference, London 1970, Vol. 255 of Lecture Notes in Mathematics, Springer-Verlag, Berlin, (1972), pp. 111–127.
Google Scholar

[7] S. Halldén, On the semantic non-completeness of certain Lewis calculi, The Journal of Symbolic Logic 16 (1951), pp. 127–129.
Google Scholar

[8] Z. Kostrzycka, On Modal Systems in the Neighbourhood of the Brouwer Logic, Acta Universitatis Wratislaviensis No 3238, Logika 25, Wydawnictwo Uniwersytetu Wrocławskiego, Wrocław (2010).
Google Scholar

[9] Z. Kostrzycka, On interpolation and Halld´en-completeness in NEXT(KTB), Bulletin of the Section of Logic 41:1/2 (2012), pp. 23–32.
Google Scholar

[10] Z. Kostrzycka, Y. Miyazaki, Normal modal logics determined by aligned clusters, Studia Logica (2017), pp. 105–111.
Google Scholar

[11] Z. Kostrzycka, On Hallden completeness of modal logics determined by homogeneous Kripke frames, Bulletin of the Section of Logic 44:3/4 (2015), pp. 1–20.
Google Scholar

[12] Z. Kostrzycka, All splitting logics in the lattice NEXT(KTB.3'), Scientific Issues Jan D lugosz University in Częstochowa, Mathematics XXI (2016), pp. 31–61.
Google Scholar

[13] E. J. Lemmon, A note on Halld´en-incompleteness, Notre Dame Journal of Formal Logic, VII, No 4, (1966), pp. 296–300.
Google Scholar

[14] L. Maksimowa, Amalgamation and Interpolation in Normal Modal Logics, Studia Logica, Vol. 50 (3/4), (1991), pp. 457–471.
Google Scholar

[15] J. C. C. McKinsey, Systems of modal logics which are not unreasonable in the sense of Hallden, Journal of Symbolic Logic 18 (1953), pp. 109–113.
Google Scholar

[16] G. F. Schumm, Some failures of interpolatin in modal logic, Notre Dame Journal of Formal Logic 27 (1), (1986), pp. 108–110.
Google Scholar