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We introduce the notion of strongly distributed structures and present a uniform approach to incremental automated reasoning on them. The approach is based on a systematic use of two logical reduction techniques: Feferman-Vaught reductions and syntactically defined translation schemes. The distributed systems are presented as logical structures A’s. We propose a uniform template for methods, which allow for a certain cost evaluation of formulae of logic L over A from values of formulae over its components and values of formulae over the index structure I. Given logic L, structure A as a composition of structures Ai, i ∈ I, index structure I and formula φ of the logic to be evaluated on A, the question is: what is the reduction sequence for φ if any. We show that if we may prove preservation theorems for L as well as if A is a strongly distributed composition of its components then the corresponding reduction sequence for A may be effectively computed. We show that the approach works for many extensions of FOL but not for all. The considered extensions of FOL are suitable candidates for modeling languages for components and services, used in incremental automated reasoning, data mining, decision making, planning and scheduling. A short complexity analysis of the method is also provided.

A Uniform Approach to Incremental Automated Reasoning on Strongly Distributed Structures