Results 241 to 250 of about 4,442,858 (282)
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2021
AbstractNatural deduction is a philosophically as well as pedagogically important logical proof system. This chapter introduces Gerhard Gentzen’s original system of natural deduction for minimal, intuitionistic, and classical predicate logic. Natural deduction reflects the ways we reason under assumption in mathematics and ordinary life.
Paolo Mancosu +2 more
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AbstractNatural deduction is a philosophically as well as pedagogically important logical proof system. This chapter introduces Gerhard Gentzen’s original system of natural deduction for minimal, intuitionistic, and classical predicate logic. Natural deduction reflects the ways we reason under assumption in mathematics and ordinary life.
Paolo Mancosu +2 more
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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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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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&: Automated natural deduction
1992In this paper we describe a sequent calculus-based theorem prover called −5. The underlying logic of & is that of Zermelo set theory. In addition to the usual rules of first-order sequent based systems, the logic contains inference rules to handle set abstraction terms, including the ability to unify formulae involving such terms, and the ability to ...
Dave Barker-Plummer +2 more
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Automated Natural Deduction in Thinker
Studia Logica, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Natural Deduction and Curry's Paradox
Journal of Philosophical Logic, 2006Following Fitch, the author presents a natural deduction version of Curry's paradox, a well-known set-theoretic paradox that does not involve negation. She then discusses various restrictions proposed independently by Fitch and Prawitz to prevent the derivation of the paradox.
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Natural Deduction for Hybrid Logic
Journal of Logic and Computation, 2004In this paper, the author studies a natural deduction calculus for hybrid logic. The underlying language contains satisfaction operators \(\forall_a\) as well as binders \(\forall a\) and \(\downarrow a\), where \(a\) is any nominal. It turns out that certain first-order properties of the involved accessibility relation, originating from so-called ...
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2013
This paper defines the contextual natural deduction calculus \(\textbf{ND}^\textbf{c}\) for the implicational fragment of intuitionistic logic. \(\textbf{ND}^\textbf{c}\) extends the usual natural deduction calculus (here called \(\textbf{ND}\)) by allowing the implication introduction and elimination rules to operate on formulas that occur inside ...
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This paper defines the contextual natural deduction calculus \(\textbf{ND}^\textbf{c}\) for the implicational fragment of intuitionistic logic. \(\textbf{ND}^\textbf{c}\) extends the usual natural deduction calculus (here called \(\textbf{ND}\)) by allowing the implication introduction and elimination rules to operate on formulas that occur inside ...
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Lambek Calculus in Natural Deduction
Journal of Logic and Computation, 2007A formulation of Lambek calculus in natural deduction is given. New rules for Lambek's multiplicative, non-commutative conjunction are proposed, rules for Lambek's two implications are standard. Rules for Lambek's conjunction are variants of general elimination rules: a symmetric elimination rule and its specializations, left elimination rule and right
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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.
openaire +1 more source