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INTUITIONISTIC LOGIC AND COMPUTATION
"... My first encounter with the theory of computation was the basic course on this subject by Dick de Jongh in the spring of 1991. For years to follow, Dick would be one of my teachers in mathematical logic. Close colleagues of Dick will know that this did not actually involve a lot of teaching, but rat ..."
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My first encounter with the theory of computation was the basic course on this subject by Dick de Jongh in the spring of 1991. For years to follow, Dick would be one of my teachers in mathematical logic. Close colleagues of Dick will know that this did not actually involve a lot of teaching
Intuitionistic Logic of Proofs
, 2009
"... The logic of proofs LP was introduced in [3] and thoroughly studied in [1]. LP is a natural extension of the propositional calculus in the language representing proofs as formal objects. Proof expressing terms are constructed using constants, variables, and symbols of natural operations on derivatio ..."
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The logic of proofs LP was introduced in [3] and thoroughly studied in [1]. LP is a natural extension of the propositional calculus in the language representing proofs as formal objects. Proof expressing terms are constructed using constants, variables, and symbols of natural operations
An Interactive Prover for Biintuitionistic Logic
"... Abstract. In this paper we present an interactive prover for deciding formulas in propositional biintuitionistic logic (BiInt). This tool is based on a recent connectionbased characterization of biintuitionistic validity through biintuitionistic resource graphs (biRG). After giving the main conc ..."
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Abstract. In this paper we present an interactive prover for deciding formulas in propositional biintuitionistic logic (BiInt). This tool is based on a recent connectionbased characterization of biintuitionistic validity through biintuitionistic resource graphs (biRG). After giving the main
A local system for intuitionistic logic
 of Lecture Notes in Artificial Intelligence
, 2006
"... Abstract. This paper presents systems for firstorder intuitionistic logic and several of its extensions in which all the propositional rules are local, in the sense that, in applying the rules of the system, one needs only a fixed amount of information about the logical expressions involved. The ma ..."
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Cited by 13 (1 self)
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Abstract. This paper presents systems for firstorder intuitionistic logic and several of its extensions in which all the propositional rules are local, in the sense that, in applying the rules of the system, one needs only a fixed amount of information about the logical expressions involved
A lower bound for intuitionistic logic
, 2007
"... We give an exponential lower bound on number of prooflines in intuitionistic propositional logic, IL, axiomatised in the usual Fregestyle fashion; i.e., we give an example of ILtautologies A1, A2,... s.t. every ILproof of Ai must have a number of prooflines exponential in terms of the size of A ..."
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We give an exponential lower bound on number of prooflines in intuitionistic propositional logic, IL, axiomatised in the usual Fregestyle fashion; i.e., we give an example of ILtautologies A1, A2,... s.t. every ILproof of Ai must have a number of prooflines exponential in terms of the size
Encoding Dependent Types in an Intuitionistic Logic
 LOGICAL FRAMEWORKS
, 1991
"... Various languages have been proposed as specification languages for representing a wide variety of logics. The development of typed calculi has been one approach toward this goal. The logical framework (LF), a calculus with dependent types is one example of such a language. A small subset of intui ..."
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Cited by 22 (6 self)
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of intuitionistic logic with quantification over the simply typed calculus has also been proposed as a framework for specifying general logics. The logic of hereditary Harrop formulas with quantification at all nonpredicate types, denoted here as hh ! , is such a metalogic. In this paper, we show how
GIL: A Generalization of Intuitionistic Logic
"... We introduce GIL, a new logic inspired by linear logic and recent results on focusing and polarization in sequent calculus proof systems. GIL is a unified logic in which connectives from intuitionistic, classical and linear logic can mix with few restrictions. Systems that resemble it include Girard ..."
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We introduce GIL, a new logic inspired by linear logic and recent results on focusing and polarization in sequent calculus proof systems. GIL is a unified logic in which connectives from intuitionistic, classical and linear logic can mix with few restrictions. Systems that resemble it include
A Resolution Theorem Prover for Intuitionistic Logic
 Proceedings of CADE13
, 1996
"... We use the general scheme of building resolution calculi (also called the inverse method) originating from S.Maslov and G.Mints to design and implement a resolution theorem prover for intuitionistic logic. A number of search strategies is introduced and proved complete. The resolution method is show ..."
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Cited by 44 (4 self)
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We use the general scheme of building resolution calculi (also called the inverse method) originating from S.Maslov and G.Mints to design and implement a resolution theorem prover for intuitionistic logic. A number of search strategies is introduced and proved complete. The resolution method
Search Calculi for Classical and Intuitionistic Logic
"... Abstract. It is wellknown that inference rules in the sequent calculus can be interpreted as both proof construction rules (i.e. constructing proofs from the leaves towards the root of the tree) and proof search rules (i.e. finding proofs by starting at the (supposed) root and working towards the l ..."
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. In this paper we explore a variation of the sequent calculus in which search information, in the form of Boolean constraints, is added to each sequent. In particular, we show how this can be done for the sequent calculus LK for classical logic and the multipleconclusioned sequent LM for intuitionistic logic
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