On Some Problems of Efficient Inference Search in First-Order Cut-Free Modal Sequent Calculi

A unified approach is developed for constructing first-order cut-free sequent calculi without equality representing two classes of modal logics in dependence of whether classical logic or intuitionistic one is taken as a basis. It uses the original notions of admissibility and compatibility, which,...

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Vydané v:Symbolic and Numeric Algorithms for Scientific Computing, Proceedings s. 39 - 46
Hlavný autor: Lyaletski, A.
Médium: Konferenčný príspevok..
Jazyk:English
Vydavateľské údaje: IEEE 01.09.2008
Predmet:
Application software
Calculus
classical logic
coextensivity
Cybernetics
first-order sequent calculi
Inference algorithms
intuitionistic logic
Logic
modal logics
Scientific computing
Search methods
ISBN:0769535232, 9780769535234
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Popis
Shrnutí:A unified approach is developed for constructing first-order cut-free sequent calculi without equality representing two classes of modal logics in dependence of whether classical logic or intuitionistic one is taken as a basis. It uses the original notions of admissibility and compatibility, which, in general, permits to avoid skolemization being a forbidden operation for the logics under consideration.Additionally, it requires the modal sequent calculi to satisfy a so-called principle-subformula condition. Following the approach, cut-free sequent modal calculi avoiding the dependence of inference search on different orders of quantifier rules applications are described. Results relating to the co-extensivity of various modal sequent calculi are given. The research gives a possibility to construct sound and complete methods for enough high efficient inference search in certain first-order modal logics if efficient technique for the handling of their propositional parts is available.
ISBN:0769535232
9780769535234
DOI:10.1109/SYNASC.2008.92