منابع مشابه
A 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 کاملA Natural Extension of Natural Deduction
One of the main ideas of calculi of natural deduction, as introduced by Jaskowski and Gentzen, is that assumptions may be discharged in the course of a derivation. As regards sentential logic, this conception will be extended in so far as not only formulas but also rules may serve as assumptions which can be discharged. The resulting calculi and derivations with rules of any finite level are in...
متن کاملA Deficiency of Natural Deduction
Natural languages are ill-suited to express mathematical reasoning. The purpose of an artificial language-predicate logic-with a deduction system is to enable us to express reasoning clearly and concisely. In this article we give two examples illustrating how Gentzen's system of 'natural de-duction' [2] fails to meet the case. In [1], the following problem is stated and solved: Given two casket...
متن کاملA Note on Deduction Rules with Negative Premises
The so called frame axioms problem or frame problem is well-known to anybody who is interested in automatic problem solving.Some information concerning this problem can be found in (1) or (2).In (2) the author proposes to eliminate the frame axioms in such a way that they are replaced by a new deduction rule denoted as UNLESS-operator.In fact,this operator is a rule enabling to derive that some...
متن کاملBidirectional Natural Deduction
The goal of this paper is to present a theorem prover able to perform both forward and backward reasoning supported by a well deened formal system. This system for bidirectional reasoning has been proved equivalent to Gentzen's classical system of propositional natural deduction. This paper, primarily aimed at developing a deeper theoretical understanding of bidirectional reasoning, provides ba...
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ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 1966
ISSN: 0029-4527
DOI: 10.1305/ndjfl/1093958561