Abstract
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.
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Kamide, N. (2010). A Logic for Incomplete Sequential Information. In: Setchi, R., Jordanov, I., Howlett, R.J., Jain, L.C. (eds) Knowledge-Based and Intelligent Information and Engineering Systems. KES 2010. Lecture Notes in Computer Science(), vol 6277. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15390-7_16
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DOI: https://doi.org/10.1007/978-3-642-15390-7_16
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