A Formal System for the Logical Analysis of Temporal Relationships Between Intervals of Time.

by R. Mattison

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A formal deduction system for the logical analysis of chronological data (such as before, after, and during relationships). The development of the system was motivated by the requirements of current data-retrieval projects, one of which is Rand's Cybernetics Data-Research Project. A mathematical model of intervals of time is constructed. Twenty basic configurations are used to express all possible time relationships, in which the smallest unit is one calendar day. Axioms are given for making inferences using the Tarski first-order predicate calculus with identity (=), one binary predicate constant meaning [wholly before], and two unary operations: min, [the beginning of], and max, [the end of]. Every sentence in this formal language is such that either it or its negation is deducible from the given axioms. Each proper expression is uniquely readable. Semantic and syntactic completeness are demonstrated, the latter by mathematical logic using Kochen's theorems on ultraproducts of models. An appendix gives more general axioms that have both the finite intervals of rationals and the finite intervals of reals as models. 40 pp. Ref.

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