Dynamical Systems in Description of Nonlinear Recursive Regression Transformers

The task of approximation-forecasting for a function, represented by empirical data was investigated. Certain class of the functions as forecasting tools: so called RFT-transformers, – was proposed. Least Square Method and superposition are the principal composing means for the function generating. Besides, the special classes of beam dynamics with delay were introduced and investigated to get classical results regarding gradients. These results were applied to optimize the RFT-transformers. The effectiveness of the forecast was demonstrated on the empirical data from the Forex market.

New Knowledge Obtaining in Structural-predicate Models of Knowledge

An effective mathematical method of new knowledge obtaining on the structure of complex objects with required properties is developed. The method comprehensively takes into account information on the properties and relations of primary objects, composing the complex objects. It is based on measurement of distances between the predicate groups with some interpretation of them. The optimal measure for measurement of these distances with the maximal discernibleness of different groups of predicates is constructed. The method is tested on solution of the problem of obtaining of new compound with electro-optical properties.

On the Relationships Among Quantified Autoepistemic Logic, its Kernel, and Quantified Reflective Logic

A Quantified Autoepistemic Logic is axiomatized in a monotonic Modal Quantificational Logic whose modal laws are slightly stronger than S5. This Quantified Autoepistemic Logic obeys all the laws of First Order Logic and its L predicate obeys the laws of S5 Modal Logic in every fixed-point. It is proven that this Logic has a kernel not containing L such that L holds for a sentence if and only if that sentence is in the kernel. This result is important because it shows that L is superfluous thereby allowing the ori ginal equivalence to be simplified by eliminating L from it. It is also shown that the Kernel of Quantified Autoepistemic Logic is a generalization of Quantified Reflective Logic, which coincides with it in the propositional case.

Distances between Predicates in By-Analogy Reasoning Systems

The purpose is to develop expert systems where by-analogy reasoning is used. Knowledge “closeness” problems are known to frequently emerge in such systems if knowledge is represented by different production rules. To determine a degree of closeness for production rules a distance between predicates is introduced. Different types of distances between two predicate value distribution functions are considered when predicates are “true”. Asymptotic features and interrelations of distances are studied. Predicate value distribution functions are found by empirical distribution functions, and a procedure is proposed for this purpose. An adequacy of obtained distribution functions is tested on the basis of the statistical 2 χ –criterion and a testing mechanism is discussed. A theorem, by which a simple procedure of measurement of Euclidean distances between distribution function parameters is substituted for a predicate closeness determination one, is proved for parametric distribution function families. The proposed distance measurement apparatus may be applied in expert systems when reasoning is created by analogy.