An Algebraic Formulation of Temporal Knowledge for Reasoning about Recurring Events

We formulate an algebra of binary temporal relations between events the number of occurrences of which is unknown, but which are known to recur in time. Ontologically, we view the temporal domain of recurring events as a set of (convex) intervals of unknown cardinality. Thus, an explicit, declarative representation of time adequate to solve reasoning problems involvingrecurring events indicates aformof higher-order reasoning about relations between collections, or sequences ofintervals. The relations de ned here are each formed out of convex interval relations by applying an operator like \always" or \sometimes". An operator of this kind imposes a mappingbetween subintervals of one set of intervals and subintervals of another. Although in general higher order reasoning problems are undecidable, a restricted system for reasoning about binary relations between collections of intervals is demonstrably tractable. The means to achieving this desirable result is to impose restrict...

• Type: Conference
• Year: 1994
• Where: TIME
• Authors: Robert A. Morris, William D. Shoaff, Lina Khatib
• Keywords: Automated Reasoning, Binary Temporal Relations, Reasoning Problem, Speci Cation, TIME 1994