The Logic of Sequences
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RIS BIB ENDNOTEThe Logic of Sequences
Publication date: 15.12.2011
Reports on Mathematical Logic, 2011, Number 46, pp. 29-57
https://doi.org/10.4467/20842589RM.11.003.0281Authors
The Logic of Sequences
The notion of “sequences” is fundamental to practical reasoning in computer science, because it can appropriately represent “data (information) sequences”, “program (execution) sequences”, “action sequences”, “time sequences”, “trees”, “orders” etc. The aim of this paper is thus to provide a basic logic for reasoning with sequences. A propositional modal logic LS of sequences is introduced as a Gentzen-type sequent calculus by extending Gentzen’s LK for classical propositional logic. The completeness theorem with respect to a sequence-indexed semantics for LS is proved, and the cut-elimination theorem for LS is shown. Moreover, a first-order modal logic FLS of sequences, which is a first-order extension of LS, is introduced. The completeness theorem with respect to a first-order sequence-indexed semantics for FLS is proved, and the cut-elimination theorem for FLS is shown. LS and the monadic fragment of FLS are shown to be decidable.
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Information: Reports on Mathematical Logic, 2011, Number 46, pp. 29-57
Article type: Original article
Teikyo University, Faculty of Science and Engineering, Department of Human Information Systems, Toyosatodai 1-1, Utsunomiya-shi, Tochigi 320-8551, Japan
Published at: 15.12.2011
Article status: Open
Licence: None
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English