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Published in:
2010 | OriginalPaper | Chapter
A Logic for Incomplete Sequential Information
Author : Norihiro Kamide
Published in: Knowledge-Based and Intelligent Information and Engineering Systems
Publisher: Springer Berlin Heidelberg
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Describing incomplete sequential information is of growing importance in Knowledge Representation in Artificial Intelligence and Computer Science. To obtain logical foundations for representing incomplete sequential information, a new logic, called sequence-indexed constructive propositional logic (SLJ), is introduced as a Gentzen-type sequent calculus by extending Gentzen’s LJ for intuitionistic logic. The system LJ is known as useful for representing incomplete information, and SLJ is obtained from LJ by adding a sequence modal operator which can represent sequential information. The cut-elimination and decidability theorems for SLJ are proved. A sequence-indexed Kripke semantics is introduced for SLJ, and the completeness theorem with respect to this semantics is proved. A logic programming framework can be developed based on SLJ.