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Sequents, Frames, and Completeness
2000Entailment relations, originated from Scott, have been used for describing mathematical concepts constructively and for representing categories of domains. This paper gives an analysis of the freely generated frames from entailment relations. This way, we obtain completeness results under the unifying principle of the spatiality of coherence logic.
Thierry Coquand, Guo-Qiang Zhang 0001
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Linear Nested Sequents, 2-Sequents and Hypersequents
2015We introduce the framework of linear nested sequent calculi by restricting nested sequents to linear structures. We show the close connection between this framework and that of 2-sequents, and provide linear nested sequent calculi for a number of modal logics as well as for intuitionistic logic.
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A sequent calculus for circumscription
1997In this paper, we introduce a sequent calculus CIRC for propositional Circumscription. This work is part of a larger project, aiming at a uniform proof-theoretic reconstruction of the major families of non-monotonic logics. Among the novelties of the calculus, we mention that CIRC is analytic and comprises an axiomatic rejection method, which allows ...
BONATTI, PIERO ANDREA, Nicola Olivetti
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2021
Considers the methodology and techniques of sequent calculus to illustrate its use in proving a wide range of metatheoretical results Includes many results and their proofs that are often not well known or easily accessible Examines important and nonstandard generalized sequent calculi, like hypersequent and structured sequent calculi.
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Considers the methodology and techniques of sequent calculus to illustrate its use in proving a wide range of metatheoretical results Includes many results and their proofs that are often not well known or easily accessible Examines important and nonstandard generalized sequent calculi, like hypersequent and structured sequent calculi.
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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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Sequent calculi and quasivarieties
Reports Math. Log., 2000Summary: We discuss relatively point-regular quasivarieties related in some special sense to sequent calculi. We show that the free algebra in such a quasivariety is Fregean iff in the sequent calculus the so-called symmetric contraction rules are admissible. In the presence of the fusion connective this is equivalent to having contraction.
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Falsification-Aware Semantics and Sequent Calculi for Classical Logic
Journal of Philosophical Logic, 2021Norihiro Kamide, Kamide Norihiro
exaly
1997
Abstract Let us think, in a general way, about what happens in a natural deduction proof. As a whole the proof is an array of formulae, which we say establishes some sequent (namely the sequent which has on its left all the formulae which are undischarged assumptions in the proof, and on its right the single formula proved at the bottom ...
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Abstract Let us think, in a general way, about what happens in a natural deduction proof. As a whole the proof is an array of formulae, which we say establishes some sequent (namely the sequent which has on its left all the formulae which are undischarged assumptions in the proof, and on its right the single formula proved at the bottom ...
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... pro vacante professione rhetorica speciminis loco eruditorum examini submittit M. Iohan. Tonjola coetus italici qui Basil. colligitur minister respondente ornatissimo iuvene Davide Bazino Rossiniensi ad d. ... Ian. 1669.
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