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Norihiro Kamide 《Studia Logica》2009,91(2):217-238
New propositional and first-order paraconsistent logics (called L
ω
and FL
ω
, respectively) are introduced as Gentzen-type sequent calculi with classical and paraconsistent negations. The embedding
theorems of L
ω
and FL
ω
into propositional (first-order, respectively) classical logic are shown, and the completeness theorems with respect to simple
semantics for L
ω
and FL
ω
are proved. The cut-elimination theorems for L
ω
and FL
ω
are shown using both syntactical ways via the embedding theorems and semantical ways via the completeness theorems.
Presented by Yaroslav Shramko and Heinrich Wansing 相似文献
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We introduce necessary and sufficient conditions for a (single-conclusion) sequent calculus to admit (reductive) cut-elimination.
Our conditions are formulated both syntactically and semantically. 相似文献
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Cut-free double sequent calculus for S5 总被引:2,自引:0,他引:2
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Michael Tiomkin 《Journal of Applied Logic》2013,11(4):530-535
We introduce a sequent calculus that is sound and complete with respect to propositional contingencies, i.e., formulas which are neither provable nor refutable. Like many other sequent and natural deduction proof systems, this calculus possesses cut elimination and the subformula property and has a simple proof search mechanism. 相似文献
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We introduce various sequent systems for propositional logicshaving strict implication, and prove the completeness theoremsand the finite model properties of these systems.The cut-eliminationtheorems or the (modified) subformula properties are provedsemantically. 相似文献
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Norihiro Kamide 《Studia Logica》2005,80(2-3):265-289
A general Gentzen-style framework for handling both bilattice (or strong) negation and usual negation is introduced based
on the characterization of negation by a modal-like operator. This framework is regarded as an extension, generalization or
re- finement of not only bilattice logics and logics with strong negation, but also traditional logics including classical
logic LK, classical modal logic S4 and classical linear logic CL. Cut-elimination theorems are proved for a variety of proposed
sequent calculi including CLS (a conservative extension of CL) and CLScw (a conservative extension of some bilattice logics, LK and S4). Completeness theorems are given for these calculi with respect
to phase semantics, for SLK (a conservative extension and fragment of LK and CLScw, respectively) with respect to a classical-like semantics, and for SS4 (a conservative extension and fragment of S4 and CLScw,
respectively) with respect to a Kripke-type semantics. The proposed framework allows for an embedding of the proposed calculi
into LK, S4 and CL. 相似文献
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The paper discusses the relationship between normal natural deductions and cutfree proofs in Gentzen (sequent) calculi in the absence of term labeling. For Gentzen calculi this is the usual version; for natural deduction this is the version under the complete discharge convention, where open assumptions are always discharged as soon as possible. The paper supplements work by Mints, Pinto, Dyckhoff, and Schwichtenberg on the labeled calculi. 相似文献
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We introduce Gentzen calculi for intuitionistic logic extended with an existence predicate. Such a logic was first introduced
by Dana Scott, who provided a proof system for it in Hilbert style. We prove that the Gentzen calculus has cut elimination
in so far that all cuts can be restricted to very simple ones. Applications of this logic to Skolemization, truth value logics
and linear frames are also discussed. 相似文献
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An analysis of (linear) exponentials based on extended sequents 总被引:1,自引:0,他引:1
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We investigate sequent calculi for the weak modal (propositional) system reduced to the equivalence rule and extensions of it up to the full Kripke system containing monotonicity, conjunction and necessitation rules. The calculi have cut elimination and we concentrate on the inversion of rules to give in each case an effective procedure which for every sequent either furnishes a proof or a finite countermodel of it. Applications to the cardinality of countermodels, the inversion of rules and the derivability of Löb rules are given. 相似文献