Results 261 to 270 of about 17,292 (295)
Some of the next articles are maybe not open access.
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 ...
openaire +2 more sources
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 ...
openaire +2 more sources
Natural Deduction for 'Generally'
Logic Journal of IGPL, 2007Logics for ‘generally’ (LG’s) were introduced for handling assertions with vague notions (e.g. ‘generally’, ‘most’, ‘several’), which occur often in ordinary language and in science. LG’s provide a framework for distinct notions of ‘generally’: one builds a specific logic for the notion one has in mind.
Leonardo B. Vana +2 more
openaire +1 more source
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.
openaire +1 more source
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
openaire +1 more source
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
openaire +1 more source
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
openaire +1 more source
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
openaire +1 more source
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
openaire +1 more source
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
openaire +1 more source
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
openaire +1 more source
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.
openaire +2 more sources
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 ...
openaire +3 more sources
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 ...
openaire +1 more source
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 ...
openaire +1 more source