The Logic of Sequences

• Authors: Norihiro Kamide
• Languages of publication: PL

Abstracts

PL

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.

Keywords

PL

• Publisher: [unknown2]
• Journal: Reports on Mathematical Logic
• Year: 2011
• Volume: 46

Dates

published

2011

online

07 - 07 - 2015

Contributors

author

Norihiro Kamide