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 Author

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.

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

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

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

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

[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.

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

[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).

[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.

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

[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.

[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.

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

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

[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.

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