Extended Continuous Logic and the Theory of Complex Criteria *

Proposed in this paper is extended continuous logic (ECL), a generalization of continuous logic based on the introduction of variable degree of conjunction and disjunction in complex conjunctive and disjunctive statements. The properties of ECL, as an algebraic structure, are analysed and various ECL functions are defined and classified. The apparatus of sentential algebra in ECL is defined with the objective to develop a theory of complex criteria as a separate branch of continuous logic. The basic concept was that the central problem of criteria theory is the simulation and formalisation of the human reasoning process in the intuitive synthesis of complex criteria. Possible applications of criteria theory are numerous, but of special interest is the solution to the problem of evaluation and comparison of various complex systems. For this purpose an algorithm for synthesizing effectiveness criteria of complex systems is proposed. The algorithm represents a general theoretical model of arbitrary complex criterion.