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Automating Theories in Intuitionistic Logic
 in "7th International Symposium on Frontiers of Combining Systems FroCoS’09, Italie
"... Abstract. Deduction modulo consists in applying the inference rules of a deductive system modulo a rewrite system over terms and formulæ. This is equivalent to proving within a socalled compatible theory. Conversely, given a firstorder theory, one may want to internalize it into a rewrite system t ..."
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that can be used in deduction modulo, in order to get an analytic deductive system for that theory. In a recent paper, we have shown how this can be done in classical logic. In intuitionistic logic, however, we show here not only that this may be impossible, but also that the set of theories that can
Intuitionistic Logic Redisplayed
, 1995
"... We continue the study of Belnap's Display Logic. Specifically, we show that the booleantensemodal setting of Wansing and Kracht not only allows us to "redisplay" intuitionistic logic but also allows us to display superintuitionistic (intermediate) logics by using the underlying Krip ..."
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We continue the study of Belnap's Display Logic. Specifically, we show that the booleantensemodal setting of Wansing and Kracht not only allows us to "redisplay" intuitionistic logic but also allows us to display superintuitionistic (intermediate) logics by using the underlying
Hypothetical Reasoning with Intuitionistic Logic
 NonStandard Queries and Answers, Studies on Logic and Computation, chapter 8
, 1994
"... This paper addresses a limitation of most deductive database systems: They cannot reason hypothetically. Although they reason effectively about the world as it is, they are poor at tasks such as planning and design, where one must explore the consequences of hypothetical actions and possibilities. T ..."
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Cited by 5 (4 self)
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are interesting, not only because they extend the capabilities of database systems, but also because they fit neatly into a wellestablished logical framework, namely intuitionistic logic. This paper presents the proof theory for the logic, outlines its intuitionistic model theory, and summarizes results on its
Proof Nets for Intuitionistic Logic
 SAARBRÜCKEN, GERMANY
, 2006
"... Until the beginning of the 20th century, there was no way to reason formally about proofs. In particular, the question of proof equivalence had never been explored. When Hilbert asked in 1920 for an answer to this very question in his famous program, people started looking for proof formalizations.
..."
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proofs in intuitionistic and classical logic.
However, natural deduction only works well for intuitionistic logic. This is why Girard invented proof nets in 1986 as an analog to natural deduction for (the multiplicative fragment of) linear logic. Their universal structure made proof nets also interesting
Symmetric Normalisation for Intuitionistic Logic
"... We present two proof systems for implicationonly intuitionistic logic in the calculus of structures. The first is a direct adaptation of the standard sequent calculus to the deep inference setting, and we describe a procedure for cut elimination, similar to the one from the sequent calculus, but us ..."
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We present two proof systems for implicationonly intuitionistic logic in the calculus of structures. The first is a direct adaptation of the standard sequent calculus to the deep inference setting, and we describe a procedure for cut elimination, similar to the one from the sequent calculus
Intuitionistic Logic with Classical Atoms
"... In this paper, we define a Hilbertstyle axiom system IPCCA that conservatively extends intuitionistic propositional logic (IPC) by adding new classical atoms for which the law of excluded middle (LEM) holds. We establish completeness of IPCCA with respect to an appropriate class of Kripke models. W ..."
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In this paper, we define a Hilbertstyle axiom system IPCCA that conservatively extends intuitionistic propositional logic (IPC) by adding new classical atoms for which the law of excluded middle (LEM) holds. We establish completeness of IPCCA with respect to an appropriate class of Kripke models
ComplementTopoi and Dual Intuitionistic Logic
, 2010
"... Abstract: Mortensen in [11] studies dual intuitionistic logic by dualizing topos internal logic, but he did not study a sequent calculus. In this paper I present a sequent calculus for complementtopos logic, which throws some light on the problem of giving a dualization for LJ. 1 introductory remar ..."
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Abstract: Mortensen in [11] studies dual intuitionistic logic by dualizing topos internal logic, but he did not study a sequent calculus. In this paper I present a sequent calculus for complementtopos logic, which throws some light on the problem of giving a dualization for LJ. 1 introductory
THE INFORMATION IN INTUITIONISTIC LOGIC
 TO APPEAR IN SYNTHESE SPECIAL ISSUE ON ‘PHILOSOPHY OF INFORMATION’
, 2008
"... ..."
The Basic Intuitionistic Logic of Proofs
, 2005
"... The language of the basic logic of proofs extends the usual propositional language by forming sentences of the sort x is a proof of F for any sentence F. In this paper a complete axiomatization for the basic logic of proofs in Heyting Arithmetic HA was found. 1 Introduction. The classical logic of p ..."
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The language of the basic logic of proofs extends the usual propositional language by forming sentences of the sort x is a proof of F for any sentence F. In this paper a complete axiomatization for the basic logic of proofs in Heyting Arithmetic HA was found. 1 Introduction. The classical logic
Deep inference in Biintuitionistic logic
 In Int Workshop on Logic, Language, Information and Computation, WoLLIC 2009, LNAI 5514
, 2009
"... Abstract. Biintuitionistic logic is the extension of intuitionistic logic with exclusion, a connective dual to implication. Cutelimination in biintuitionistic logic is complicated due to the interaction between these two connectives, and various extended sequent calculi, including a display calcu ..."
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Abstract. Biintuitionistic logic is the extension of intuitionistic logic with exclusion, a connective dual to implication. Cutelimination in biintuitionistic logic is complicated due to the interaction between these two connectives, and various extended sequent calculi, including a display
Results 11  20
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12,836