Studia Logica 107 (2):313-349 (2019)

Dorota Leszczyńska-Jasion
Adam Mickiewicz University
This paper presents Rasiowa–Sikorski deduction systems for logics \, \, \ and \. For each of the logics two systems are developed: an R–S system that can be supplemented with admissible cut rule, and a \-version of R–S system in which the non-admissible rule of cut is the only branching rule. The systems are presented in a Smullyan-like uniform notation, extended and adjusted to the aims of this paper. Completeness is proved by the use of abstract refutability properties which are dual to consistency properties used by Fitting. Also the notion of admissibility of a rule in an R–S-system is analysed.
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DOI 10.1007/s11225-018-9795-7
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References found in this work BETA

First-Order Logic.William Craig - 1975 - Journal of Symbolic Logic 40 (2):237-238.
Proof Methods for Modal and Intuitionistic Logics.Melvin Fitting - 1985 - Journal of Symbolic Logic 50 (3):855-856.
Socratic Proofs.Andrzej Wiśniewski - 2004 - Journal of Philosophical Logic 33 (3):299-326.
Socratic Proofs for Quantifiers★.Andrzej Wiśniewski & Vasilyi Shangin - 2006 - Journal of Philosophical Logic 35 (2):147-178.
Don't Eliminate Cut.George Boolos - 1984 - Journal of Philosophical Logic 13 (4):373 - 378.

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