Natural Deduction Systems of Normal Modal Logics
Abstract
Most normal modal logics have been constructed as axiomatic systems rather than natural deduction. However, a lot of them have Gentzen-style or Kalish-Montague-style counterparts. Unfortunately, very few systems have Słupecki-Borkowski-style natural deduction counterparts. To fill in the gap is an aim of the present paper.
The system K is developed as a Leśniewski-Borkowski-style natural deduction system in two ways. Equivalence of the systems is proved. A way is described to develop other normal systems beginning with the given system K.
References
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Borkowski L.: O pewnym systemie logicznym opartym na regułach i jego zastosowaniu przy nauczaniu logiki matematycznej, rozdz. III: Nieklasyczne rachunki logiczne, [w:] tenże, Studia logiczne. Wybór, Lublin: TN KUL 1990, s. 174-183.
Borkowski L.: Wprowadzenie do logiki i teorii mnogości, Lublin: TN KUL 1991.
Hughes G. E., Cresswell M. J.: A New Introduction to Modal Logic, London and New York: Routledge 1996.
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