A normalization-procedure for the first order classical natural deduction with full logical symbols
نویسندگان
چکیده
منابع مشابه
Full classical S5 in natural deduction with weak normalization
Natural deduction systems for classical, intuitionistic and modal logics were deeply investigated by Prawitz [D. Prawitz, Natural Deduction: A Proof-theoretical Study, in: Stockholm Studies in Philosophy, vol. 3, Almqvist and Wiksell, Stockholm, 1965. Reprinted at: Dover Publications, Dover Books on Mathematics, 2006] from a proof-theoretical perspective. Prawitz proved weak normalization for c...
متن کاملA semantical proof of the strong normalization theorem for full propositional classical natural deduction
We give in this paper a short semantical proof of the strong normalization for full propositional classical natural deduction. This proof is an adaptation of reducibility candidates introduced by J.-Y. Girard and simplified to the classical case by M. Parigot.
متن کاملOn natural deduction in classical first-order logic: Curry-Howard correspondence, strong normalization and Herbrand's theorem
We present a new Curry-Howard correspondence for classical first-order natural deduction. We add to the lambda calculus an operator which represents, from the viewpoint of programming, a mechanism for raising and catching multiple exceptions, and from the viewpoint of logic, the excluded middle over arbitrary prenex formulas. The machinery will allow to extend the idea of learning – originally ...
متن کاملNatural Deduction for Full S5 Modal Logic with Weak Normalization
Natural deduction systems for classical, intuitionistic and modal logics were deeply investigated by Prawitz [10] from a proof-theoretical perspective. Prawitz proved weak normalization for classical logic just for a language without ∨, ∃ and with a restricted application of reduction ad absurdum. Reduction steps related to ∨, ∃ and classical negation brings about a lot of problems solved only ...
متن کاملCorrigendum to "Strong normalization proof with CPS-translation for second order classical natural deduction"
Our paper [1] contains a serious error. Proposition 4.6 of [1] is actually false and hence our strong normalization proof does not work for the Curry-style λμ-calculus. However, our method still can show that (1) the correction of Proposition 5.4 of [2], and (2) the correction of the proof of strong normalization of Church-style λμ-calculus by CPS-translation. Firstly, our method is still effec...
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ژورنال
عنوان ژورنال: Tsukuba Journal of Mathematics
سال: 1995
ISSN: 0387-4982
DOI: 10.21099/tkbjm/1496162804