Strong Normalization for Truth Table Natural Deduction
نویسندگان
چکیده
منابع مشابه
Strong normalization of classical natural deduction with disjunctions
This paper proves strong normalization of classical natural deduction with disjunction and permutative conversions, by using CPS-translation and augmentations. By them, this paper also proves strong normalization of classical natural deduction with general elimination rules for implication and conjunction, and their permutative conversions. This paper also proves natural deduction can be embedd...
متن کاملA note on strong normalization in classical natural deduction
In the context of natural deduction for propositional classical logic, with classicality given by the inference rule reductio ad absurdum, we investigate the De Morgan translation of disjunction in terms of negation and conjunction. Once the translation is extended to proofs, it obtains a reduction of provability to provability in the disjunction-free subsystem. It is natural to ask whether a r...
متن کاملStrong Normalization of Classical Natural Deduction with Disjunction
We introduce λμ→∧∨⊥, an extension of Parigot’s λμ-calculus where disjunction is taken as a primitive. The associated reduction relation, which includes the permutative conversions related to disjunction, is Church-Rosser, strongly normalizing, and such that the normal deductions satisfy the subformula property. From a computer science point of view, λμ→∧∨⊥ may be seen as the core of a typed cbn...
متن کاملThe 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 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: Fundamenta Informaticae
سال: 2019
ISSN: 0169-2968,1875-8681
DOI: 10.3233/fi-2019-1858