Accession Number : AD0651122

Title :   A FORMAL SYSTEM FOR THE LOGICAL ANALYSIS OF TEMPORAL RELATIONSHIPS BETWEEN INTERVALS OF TIME,

Corporate Author : RAND CORP SANTA MONICA CALIF

Personal Author(s) : Mattison,Robert

Report Date : APR 1967

Pagination or Media Count : 41

Abstract : A formal deduction system is presented 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, meaning 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 ultra-products of models. An appendix gives more general axioms that have both the finite intervals of rationals and the finite intervals of reals as models.

Descriptors :   (*MATHEMATICAL LOGIC, TIME), (*DATA STORAGE SYSTEMS, *INFORMATION RETRIEVAL), MINIMAX TECHNIQUE, COMPUTER PROGRAMMING, LANGUAGE, LINGUISTICS, SEMANTICS, SYNTAX, THEOREMS, MATHEMATICAL MODELS, CYBERNETICS

Subject Categories : Theoretical Mathematics
      Computer Programming and Software
      Computer Hardware

Distribution Statement : APPROVED FOR PUBLIC RELEASE