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The admissibility of cut in the cutfree sequent calculus
, 2012
"... In the last lecture we saw cut elimination as the global version of cut reduction. In this lecture we begin with identity, which is the global version of identity expansion. Together, they provide the basis for understanding the left and right rules in the sequent calculus as meaning explanations of ..."
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of the logical connectives, a program with a long history [Dum91, ML83]. The cutfree sequent calculus is a good basis for proof search, but it still has too much nondeterminism. One way to reduce this nondeterminism is inversion, which we discuss in this lecture. Another is chaining, which will be subject
Completeness of CutFree Sequent Calculus Modulo
"... Abstract. Deduction modulo is a powerful way to replace axioms by rewrite rules and allows to integrate computation in deduction. But adding rewrite rules is not always safe for properties of the deduction system such as consistency or cut elimination. Proving completeness of the cutfree calculus w ..."
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Abstract. Deduction modulo is a powerful way to replace axioms by rewrite rules and allows to integrate computation in deduction. But adding rewrite rules is not always safe for properties of the deduction system such as consistency or cut elimination. Proving completeness of the cutfree calculus
Cutfree common knowledge
 Journal of Applied Logic
, 2007
"... Starting off from the infinitary system for common knowledge over multimodal epistemic logic presented in Alberucci and Jäger [1], we apply the finite model property to “finitize ” this deductive system. The result is a cutfree, sound and complete sequent calculus for common knowledge. 1 ..."
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Cited by 17 (9 self)
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Starting off from the infinitary system for common knowledge over multimodal epistemic logic presented in Alberucci and Jäger [1], we apply the finite model property to “finitize ” this deductive system. The result is a cutfree, sound and complete sequent calculus for common knowledge. 1
A CutFree and InvariantFree Sequent Calculus for PLTL ⋆
"... Abstract. Sequent calculi usually provide a general deductive setting that uniformly embeds other prooftheoretical approaches, such as tableaux methods, resolution techniques, goaldirected proofs, etc. Unfortunately, in temporal logic, existing sequent calculi make use of a kind of inference rules ..."
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Cited by 6 (2 self)
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, propositional linear temporal logic (PLTL). In this paper, we provide a complete finitary sequent calculus for PLTL, called FC, that not only is cutfree but also invariantfree. In particular, we introduce new rules which provide a new style of temporal deduction. We give a detailed proof of completeness. 1
Cutfree Sequent and Tableau Systems for Propositional Diodorean Modal Logics
"... We present sound, (weakly) complete and cutfree tableau systems for the propositional normal modal logics S4:3, S4:3:1 and S4:14. When the modality 2 is given a temporal interpretation, these logics respectively model time as a linear dense sequence of points; as a linear discrete sequence of po ..."
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Cited by 21 (3 self)
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We present sound, (weakly) complete and cutfree tableau systems for the propositional normal modal logics S4:3, S4:3:1 and S4:14. When the modality 2 is given a temporal interpretation, these logics respectively model time as a linear dense sequence of points; as a linear discrete sequence
A cutfree sequent calculus for biintuitionistic logic: extended version
, 2007
"... Abstract. Biintuitionistic logic is the extension of intuitionistic logic with a connective dual to implication. Biintuitionistic logic was introduced by Rauszer as a Hilbert calculus with algebraic and Kripke semantics. But her subsequent “cutfree ” sequent calculus for BiInt has recently been s ..."
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Cited by 6 (1 self)
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Abstract. Biintuitionistic logic is the extension of intuitionistic logic with a connective dual to implication. Biintuitionistic logic was introduced by Rauszer as a Hilbert calculus with algebraic and Kripke semantics. But her subsequent “cutfree ” sequent calculus for BiInt has recently been
Cutfree Sequent Calculi for Csystems with Generalized Finitevalued Semantics
"... In [5], a general method was developed for generating cutfree ordinary sequent calculi for logics that can be characterized by finitevalued semantics based on nondeterministic matrices (Nmatrices). In this paper, a substantial step towards automation of paraconsistent reasoning is made by applyin ..."
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Cited by 3 (0 self)
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In [5], a general method was developed for generating cutfree ordinary sequent calculi for logics that can be characterized by finitevalued semantics based on nondeterministic matrices (Nmatrices). In this paper, a substantial step towards automation of paraconsistent reasoning is made
A Cutfree Sequent Calculus for Elementary Situated Reasoning
, 1991
"... A rstorder language is interpreted in the following way: terms are regarded as referring to situations and the truth of formulae is relativized to a situation. The language is then extended to include formulae of the form t : (where t is a term and is a formula) meaning that is true in the s ..."
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Cited by 10 (3 self)
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in the situation referred to by t. Gentzen's sequent calculus for classical rstorder logic is extended with rules which capture this interpretation. Variants of the calculus and extensions of the language are discussed and the Cut rule is shown to be eliminable from some of the proposed calculi
Towards a Cutfree Sequent Calculus for Boolean BI
"... The logic of bunched implications (BI) of O’Hearn and Pym [5] is a substructural logic which freely combines additive connectives ⊃, ∧, ∨ from propositional logic and multiplicative connectives −⋆, ⋆ from linear logic. Because of its concise yet rich representation of states of resources, BI is reg ..."
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connectives intuitionistically and do not introduce multiplicative falsity or negation. Intuitionistic BI has a welldeveloped proof theory. It has a natural deduction system with the normalization property and also a cutfree sequent calculus. Because free combinations of additive connectives
Results 1  10
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