The normalization theorem for extended natural deduction
نویسندگان
چکیده
منابع مشابه
The Normalization Theorem for Extended Natural Deduction
The normalization theorem for the system of extended natural deduction will be proved as a consequence of the cut-elimination theorem, by using the connections between the system of extended natural deduction and a standard system of sequents.
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 کاملA completeness theorem for strong normalization in minimal deduction modulo
Deduction modulo is an extension of first-order predicate logic where axioms are replaced by rewrite rules and where many theories, such as arithmetic, simple type theory and some variants of set theory, can be expressed. An important question in deduction modulo is to find a condition of the theories that have the strong normalization property. Dowek and Werner have given a semantic sufficient...
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 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Publications de l'Institut Mathematique
سال: 2017
ISSN: 0350-1302,1820-7405
DOI: 10.2298/pim1715075b