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Natural Deduction
, 1999
"... This paper presents a theoretical analysis of natural deduction. First, a brief description will be given of a natural deduction system for sentential logic (i.e., no quantifiers or variables). Then it will be shown how to extend it to firstorder logic using skolemization and unification. ..."
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This paper presents a theoretical analysis of natural deduction. First, a brief description will be given of a natural deduction system for sentential logic (i.e., no quantifiers or variables). Then it will be shown how to extend it to firstorder logic using skolemization and unification.
Natural deduction
, 1999
"... Most automated theorem provers are clausalform provers based on variants of resolutionrefutation. In my [1990], I described the theorem prover OSCAR that was based instead on natural deduction. Some limited evidence was given suggesting that OSCAR was suprisingly efficient. The evidence consisted o ..."
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Cited by 6 (0 self)
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Most automated theorem provers are clausalform provers based on variants of resolutionrefutation. In my [1990], I described the theorem prover OSCAR that was based instead on natural deduction. Some limited evidence was given suggesting that OSCAR was suprisingly efficient. The evidence consisted
Skolemization and Unification in Natural Deduction
"... This paper presents a theoretical analysis of natural deduction. First, a brief description will be given of a natural deduction system for sentential logic (i.e., no quantifiers or variables). Then it will be shown how to extend it to firstorder logic using skolemization and unification. Skolemiza ..."
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This paper presents a theoretical analysis of natural deduction. First, a brief description will be given of a natural deduction system for sentential logic (i.e., no quantifiers or variables). Then it will be shown how to extend it to firstorder logic using skolemization and unification
B.: Contextual natural deduction
 In: LFCS
, 2013
"... Abstract. This paper defines the contextual natural deduction calculus NDc for the implicational fragment of intuitionistic logic. NDc extends the usual natural deduction calculus (here called ND) by allowing the implication introduction and elimination rules to operate on formulas that occur inside ..."
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Abstract. This paper defines the contextual natural deduction calculus NDc for the implicational fragment of intuitionistic logic. NDc extends the usual natural deduction calculus (here called ND) by allowing the implication introduction and elimination rules to operate on formulas that occur
Natural Deduction for Belief at Most
"... We present a new approach to the logic of at most, introducing the notion of parametric propositions to modal natural deduction proofs. We apply the method with a natural deduction formulation of the doxastic logic N , a new system in the "only knowing" family. Using parametric proo ..."
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We present a new approach to the logic of at most, introducing the notion of parametric propositions to modal natural deduction proofs. We apply the method with a natural deduction formulation of the doxastic logic N , a new system in the "only knowing" family. Using parametric
Natural Deduction in Connectionist Systems
, 1994
"... The relation between logic and thought has long been controversial, but has recently influenced theorizing about the nature of mental processes in cognitive science. One prominent tradition argues that to explain the systematicity of thought we must posit syntactically structured representations ins ..."
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Cited by 2 (0 self)
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inside the cognitive system which can be operated upon by structure sensitive rules similar to those employed in systems of natural deduction. I have argued elsewhere that the systematicity of human thought might better be explained as resulting from the fact that we have learned natural languages which
An Explicit Natural Deduction
, 1998
"... The typed calculus and the natural deduction are isomorph. There is a mapping (the CurryHoward's isomorphism) between each others. This paper shows that the typed calculi with explicit substitutions are isomorph to a logical deduction system which is equivalent to the natural deduction. This ..."
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The typed calculus and the natural deduction are isomorph. There is a mapping (the CurryHoward's isomorphism) between each others. This paper shows that the typed calculi with explicit substitutions are isomorph to a logical deduction system which is equivalent to the natural deduction
Bidirectional Natural Deduction
 AI*IA Notizie
, 1993
"... The goal of this paper is to present a theorem prover able to perform both forward and backward reasoning supported by a well defined formal system. This system for bidirectional reasoning has been proved equivalent to Gentzen's classical system of propositional natural deduction. Thi ..."
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Cited by 4 (2 self)
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The goal of this paper is to present a theorem prover able to perform both forward and backward reasoning supported by a well defined formal system. This system for bidirectional reasoning has been proved equivalent to Gentzen's classical system of propositional natural deduction
Natural deduction environment for Matita
"... Abstract. Matita is a proof assistant characterised by a rich, user extensible, output facility based on a widget for the rendering of MathML Presentation, and by the automatic handling of overloading by means of a flexible disambiguation mechanism. We show how to use these features to obtain a simp ..."
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simple learning environment for natural deduction, without modifying the source code or Matita. 1
Natural Deduction and Arbitrary Objects
 Journal of Philosophical Logic
, 1985
"... This paper is an abridged and simplified version of my monograph Reasoning with Arbitrary Objects [4]. It may be read by the diligent as a preparation for the longer work or by the indolent as a substitute for it. But the reader, in either case, may find it helpful to consult the paper, A Defence of ..."
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Cited by 20 (0 self)
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of Arbitrary Objects [3], for general philosophical orientation. This paper deals with certain problems in understanding natural deduction and ordinary reasoning. As is well known, there exist in ordinary reasoning certain procedures for arguing to a universal conclusion and from an existential premiss. We
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