Results 281 to 290 of about 205,593 (312)
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Mathematical Logic Quarterly, 1990
Many authors have proposed several systems of ``fuzzy logic'' as formal counterparts of approximate reasoning and these systems are obtained via suitable ``fuzzyfications'' of the ordinary Hilbert-type logical systems. In this paper the possibility of a fuzzyfication of natural deduction is explored and a very general notion of fuzzy natural deduction ...
G. GERLA, TORTORA, ROBERTO
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Many authors have proposed several systems of ``fuzzy logic'' as formal counterparts of approximate reasoning and these systems are obtained via suitable ``fuzzyfications'' of the ordinary Hilbert-type logical systems. In this paper the possibility of a fuzzyfication of natural deduction is explored and a very general notion of fuzzy natural deduction ...
G. GERLA, TORTORA, ROBERTO
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Naturalizing Natural Deduction
2016A simplified and improved system of natural deduction for classical predicate logic is presented. The inference rules of existential instantiation EI, existential elimination (\(\exists\) E), and universal generalization UG (\(\forall\) I) are not employed in this system.
David DeVidi, Herbert Korté
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A Many‐Sorted Natural Deduction
Computational Intelligence, 1998The goal of this paper is to motivate and define yet another sorted logic, called SND. All the previous sorted logics that can be found in the Artificial Intelligence literature have been designed to be used in (completely) automated deduction. SND has been designed to be used in interactive theorem proving. Because of this shift of focus, SND has been
A. Cimatti +2 more
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Natural Deduction for Quantum Logic
Logica Universalis, 2022This paper presents a natural deduction system for orthomodular quantum logic. The system is shown to be provably equivalent to Nishimura’s quantum sequent calculus. Through the Curry-Howard isomorphism, quantum λ-calculus is also introduced for which strong normalization property is established.
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1999
The functional interpretation of logical connectives is concerned with a certain harmony between, on the one hand, a indexfunctional! calculus functional calculus on the expressions built up from the recording of the deduction steps (the labels), and, on the other hand, a logical calculus on the formulae.
Ruy J. G. B. De Queiroz, Dov M. Gabbay
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The functional interpretation of logical connectives is concerned with a certain harmony between, on the one hand, a indexfunctional! calculus functional calculus on the expressions built up from the recording of the deduction steps (the labels), and, on the other hand, a logical calculus on the formulae.
Ruy J. G. B. De Queiroz, Dov M. Gabbay
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Journal of Symbolic Logic, 1965
We consider some natural deduction systems for quantification theory whose only quantificational rules involve elimination of quantifiers. By imposing certain restrictions on the rules, we obtain a system which we term Analytic Natural Deduction; it has the property that the only formulas used in the proof of a given formula X are either subformulas of
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We consider some natural deduction systems for quantification theory whose only quantificational rules involve elimination of quantifiers. By imposing certain restrictions on the rules, we obtain a system which we term Analytic Natural Deduction; it has the property that the only formulas used in the proof of a given formula X are either subformulas of
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1997
Abstract Axiomatic proofs are hard to construct, and often very lengthy. So in practice one does not actually construct such proofs; rather, one proves that there is a proof, as originally defined. One way in which we make use of this technique is when we allow ourselves to use, in a proof, any theorem that has been proved already.
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Abstract Axiomatic proofs are hard to construct, and often very lengthy. So in practice one does not actually construct such proofs; rather, one proves that there is a proof, as originally defined. One way in which we make use of this technique is when we allow ourselves to use, in a proof, any theorem that has been proved already.
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2007
Abstract In this course we shall study some ways of proving statements. Of course not every statement can be proved; so we need to analyse the statements before we prove them. Within propositional logic we analyse complex statements down into shorter statements. Later chapters will analyse statements into smaller expressions too, but the
Ian Chiswell, Wilfrid Hodges
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Abstract In this course we shall study some ways of proving statements. Of course not every statement can be proved; so we need to analyse the statements before we prove them. Within propositional logic we analyse complex statements down into shorter statements. Later chapters will analyse statements into smaller expressions too, but the
Ian Chiswell, Wilfrid Hodges
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Journal of Symbolic Logic, 1950
For Gentzen's natural deduction, a formalized method of deduction in quantification theory dating from 1934, these important advantages may be claimed: it corresponds more closely than other methods of formalized quantification theory to habitual unformalized modes of reasoning, and it consequently tends to minimize the false moves involved in seeking ...
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For Gentzen's natural deduction, a formalized method of deduction in quantification theory dating from 1934, these important advantages may be claimed: it corresponds more closely than other methods of formalized quantification theory to habitual unformalized modes of reasoning, and it consequently tends to minimize the false moves involved in seeking ...
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2010
Natural deduction for intuitionistic linear logic is known to be full of non-deterministic choices. In order to control these choices, we combine ideas from intercalation and focusing to arrive at the calculus of focused natural deduction. The calculus is shown to be sound and complete with respect to first-order intuitionistic linear natural deduction
Brock-Nannestad, Taus +1 more
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Natural deduction for intuitionistic linear logic is known to be full of non-deterministic choices. In order to control these choices, we combine ideas from intercalation and focusing to arrive at the calculus of focused natural deduction. The calculus is shown to be sound and complete with respect to first-order intuitionistic linear natural deduction
Brock-Nannestad, Taus +1 more
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