Logical operations research
by
Inna Davydova
St.-Petersburg State University
Coauthors: Gennady Davydov (Russian Academy of Sciences)

The model of operations research as the join of following interpretations of true formulas in predicate calculus is presented. In propositional case we use

true as stable non-negative solvability of linear homogeneous systems [1];

true as preservation of measure of configurational space of elemental events [2, 3];

true as deadlockless infinite evolution of dynamic system without restriction on the sequence of evolution steps [1]. Some constraints on the sequence of evolution steps are added in predicate case.

Circulation of resources has been going on the work of a production system. On the one hand, this circulation makes it possible to execute needed jobs, service or functions. On the other hand, it yields a renewal of system ability to execute new jobs. Every such complex circulation is represented by combination of sufficiently visible aggregate of circulations of elemental resources units and every complex job is represented by combination of elemental jobs - operations.

Predicate variables are interpreted by elemental resources circulations and conjunctions of literals are interpreted by sets of conditions for operations executing in presented model. If the model is described by true formula then stable solvability causes solvability of balance equations between available elemental resources and demand for them. Preservation of measure involves full using of potential of elemental resources circulations and allows to estimate the contribution of every operation in the workability of the system.

Propositional case corresponds with cash case in which every elemental resource is available fully in any needed amount. Predicate case corresponds with stack structure of elemental resources. In this case for balance and workability of the system to be accessible it is necessary to stratify elemental resources and to specify operations like theorem Herbrand.

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. G. Davydov, I. Davydova Tautologies and positive solvability of homogeneous systems - Annals of Pure and Applied Logic, 57 (1992), No.1, 27-43

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. Kazuo Iwama CNF satisfiability test by counting and polynomial average time - SIAM J. Comput., Vol.18, (1989), No.2, 385-391

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. G.V.Davydov, I.M.Davydova Measure of formulas: calculation and polynomial class for satisfiability (Russian) - Vestnik St.-Petersburg University, Math., (1997), No.3, 27-33

Date received: March 1, 1999