Distributed Strategies and Managements based on State Constraint Logic with Predicate for Communication

From the views on cognitive management, this paper deals with state constraint and distributed systems, where communication between states is a key function of complexity. The primary purpose is concerned with logical analysis of complex, distributed system structure which contains strategies (procedures) designed in states. Between states, strategies may be communicative and transferrable, where the transferrability is supposed to be given by predicates for communication between states. The strategy as a procedure is assumed to be inductively constructed by other distributed strategies. The structure to represent the designed way of strategies takes an inductively defined form, on which some logical relation is characterized with respect to the compound construction of strategies (procedures). The logical relation is in accordance with possibly infinite set of propositional formulas constrained by states. As regards procedural executions, implementation, the undefined (implementation), and non-implementation may be considered for the remarked strategy. Based on the discussions of implementability for strategic constructions, a structural analysis of distributed strategies may be settled as 3-valued model theory of logical expressions. It is related to 3-valued model theory, where some fixed point theory is now examined, with respect to the mapping (which is in general monotonic) associated with a logical expression. The logical expression of this paper can be denoted as a propositional logic formula with default negation. As an application to logical system, logical formulas with both strong and default negations may be analyzed with 3-valued domain. This paper thus abstracts application of logical expressions to structural analysis of distributed strategies. Structure of strategies is complex owing to distribution of state constraint strategies, but effectiveness may be endowed with logical approach and abstraction of communication facility.