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Dual-Context Sequent Calculus and Strict Implication
MLQ, 2002Summary: We introduce a dual-context style sequent calculus which is complete with respect to Kripke semantics where implication is interpreted as strict implication in the modal logic K. The cut-elimination theorem for this calculus is proved by a variant of Gentzen's method.
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Herzberger’s Limit Rule with Labelled Sequent Calculus
Studia Logica, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Andreas Fjellstad
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[1990] Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science, 2002
An axiomatic approach that accounts for examples that come up in logic programming, symbolic computation, affine geometry, and elsewhere is presented. It is shown that if disjunction behaves in an intuitionistic fashion, notions of canonical form for positive constraints can be systematically extended to include negative constraints.
J.-L. Lassez, K. McAloon
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An axiomatic approach that accounts for examples that come up in logic programming, symbolic computation, affine geometry, and elsewhere is presented. It is shown that if disjunction behaves in an intuitionistic fashion, notions of canonical form for positive constraints can be systematically extended to include negative constraints.
J.-L. Lassez, K. McAloon
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1994
In Chapter I we discussed the way a mathematician proceeds to develop a particular mathematical theory: In order to obtain an overview of the theory, he tries to find out which propositions follow from its axioms. To show that a proposition follows from the axioms, he supplies a proof.
Heinz-Dieter Ebbinghaus +2 more
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In Chapter I we discussed the way a mathematician proceeds to develop a particular mathematical theory: In order to obtain an overview of the theory, he tries to find out which propositions follow from its axioms. To show that a proposition follows from the axioms, he supplies a proof.
Heinz-Dieter Ebbinghaus +2 more
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A desk-top sequent calculus machine
1993This paper presents an implementation of a sequent calculus to be used as a flexible tool for automated deduction. The proposed implementation represents a desk-top machine used in interactive mode to solve verification as well as generation and abduction problems.
Cioni G, Colagrossi A, MIOLA, Alfonso
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Purely Logical Sequent Calculus
2020In this chapter we consider a popular version of sequent calculus called G3. In sections 3.2 and 3.3 we focus on different strategies of proving admissibility of cut and some auxiliary results. Section 3.4 is devoted to additional topics connected with different ways of interpretation of sequents. As a by-product of these considerations we will provide
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2020
This chapter introduces the original sequent calculus of Gentzen, called LK (der Logistische Kalkul). In sections 2.2–2.3. we investigate some applications of cut concerning the equivalence of some forms of sequents and sequent rules and some invertibility results.
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This chapter introduces the original sequent calculus of Gentzen, called LK (der Logistische Kalkul). In sections 2.2–2.3. we investigate some applications of cut concerning the equivalence of some forms of sequents and sequent rules and some invertibility results.
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2-Sequent Calculus: Intuitionism and Natural Deduction
Journal of Logic and Computation, 1993The main idea of this cumbersome formalization can be traced to the first papers by Kripke on semantic treatment of modal and intuitionistic logic. The completeness proof given there used proof search trees for an elegant formulation in terms of indexed tableaux \(\sigma_ 1 S_ 1; \sigma_ 2 S_ 2; \dots; \sigma_ n S_ n\), where \(S_ i\) are sequents ...
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The Protological Sequent Calculus
1998Protologic is a system for elementary reasoning with constructions, as sketched in Chapter 8. See the following chapter for a detailed justification of the axioms and rules.
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