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Logic of temporal attribute implications. (English) Zbl 1409.68283
Summary: We study logic for reasoning with if-then formulas describing dependencies between attributes of objects which are observed in consecutive points in time. We introduce semantic entailment of the formulas, show its fixed-point characterization, investigate closure properties of model classes, present an axiomatization and prove its completeness, and investigate alternative axiomatizations and normalized proofs. We investigate decidability and complexity issues of the logic and prove that the entailment problem is NP-hard and belongs to EXPSPACE. We show that by restricting to predictive formulas, the entailment problem is decidable in pseudo-linear time.

MSC:
68T27 Logic in artificial intelligence
68Q25 Analysis of algorithms and problem complexity
68T30 Knowledge representation
Software:
PDDL
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