Parallelization of Logical Inference for Confluent Rule-based System

* This paper was made according to the program № 14 of fundamental scientific research of the Presidium of the Russian Academy of Sciences, the project 06-I-П14-052

Mixed Theories

In the present paper we investigate the life cycles of formalized theories that appear in decision making instruments and science. In few words mixed theories are build in the following steps: Initially a small collection of facts is the kernel of the theory. To express these facts we make a special formalized language. When the collection grows we add some inference rules and thus some axioms to compress the knowledge. The next step is to generalize these rules to all expressions in the formalized language. For these rules we introduce some conclusion procedure. In such a way we make small theories for restricted fields of the knowledge. The most important procedure is the mixing of these partial knowledge systems. In that step we glue the theories together and eliminate the contradictions. The last operation is the most complicated one and some simplifying procedures are proposed.

The Development of Parallel Resolution Algorithms Using the Graph Representation

The parallel resolution procedures based on graph structures method are presented. OR-, AND- and DCDP- parallel inference on connection graph representation is explored and modifications to these algorithms using heuristic estimation are proposed. The principles for designing these heuristic functions are thoroughly discussed. The colored clause graphs resolution principle is presented. The comparison of efficiency (on the Steamroller problem) is carried out and the results are presented. The parallel unification algorithm used in the parallel inference procedure is briefly outlined in the final part of the paper.

Admissible Substitutions in Sequent Calculi

For first-order classical logic a new notion of admissible substitution is defined. This notion allows optimizing the procedure of the application of quantifier rules when logical inference search is made in sequent calculi. Our objective is to show that such a computer-oriented sequent technique may be created that does not require a preliminary skolemization of initial formulas and that is efficiently comparable with methods exploiting the skolemization. Some results on its soundness and completeness are given.

Conditions of Effectiveness of Pattern Recognition Problem Solution Using Logical Level Descriptions of Classes

Earlier the authors have suggested a logical level description of classes which allows to reduce a solution of various pattern recognition problems to solution of a sequence of one-type problems with the less dimension. Here conditions of the effectiveness of the use of such a level descriptions are proposed.

Detection of Logical-and-Probabilistic Correlation in Time Series

An application of the heterogeneous variables system prediction method to solving the time series analysis problem with respect to the sample size is considered in this work. It is created a logical-and-probabilistic correlation from the logical decision function class. Two ways is considered. When the information about event is kept safe in the process, and when it is kept safe in depending process.

Simulation-based Approach to Verification of Logical Descriptions with Functional Indeterminacy

A verification task of proving the equivalence of two descriptions of the same device is examined for the case, when one of the descriptions is partially defined. In this case, the verification task is reduced to checking out whether logical descriptions are equivalent on the domain of the incompletely defined one. Simulation-based approach to solving this task for different vector forms of description representations is proposed. Fast Boolean computations over Boolean and ternary vectors having big sizes underlie the offered methods.

Hierarchical Logical Description and Neural Recognition of Complex Patterns

Authors suggested earlier hierarchical method for definition of class description at pattern recognition problems solution. In this paper development and use of such hierarchical descriptions for parallel representation of complex patterns on the base of multi-core computers or neural networks is proposed.

Measure Refutations and Metrics on Statements of Experts (Logical Formulas) in the Models for Some Theory

* This work was financially supported by the Russian Foundation for Basic Research, project no. 04-01-00858a.

On Logical Correction of Neural Network Algorithms for Pattern Recognition

The paper is devoted to the description of hybrid pattern recognition method developed by research groups from Russia, Armenia and Spain. The method is based upon logical correction over the set of conventional neural networks. Output matrices of neural networks are processed according to the potentiality principle which allows increasing of recognition reliability.

INFRAWEBS Axiom Editor – A Graphical Ontology-Driven Tool for Creating Complex Logical Expressions

The current INFRAWEBS European research project aims at developing ICT framework enabling software and service providers to generate and establish open and extensible development platforms for Web Service applications. One of the concrete project objectives is developing a full-life-cycle software toolset for creating and maintaining Semantic Web Services (SWSs) supporting specific applications based on Web Service Modelling Ontology (WSMO) framework. According to WSMO, functional and behavioural descriptions of a SWS may be represented by means of complex logical expressions (axioms). The paper describes a specialized userfriendly tool for constructing and editing such axioms – INFRAWEBS Axiom Editor. After discussing the main design principles of the Editor, its functional architecture is briefly presented. The tool is implemented in Eclipse Graphical Environment Framework and Eclipse Rich Client Platform.

Extreme Situations Prediction by MultidimenSional Heterogeneous Time Series Using Logical Decision Functions

* The work is supported by RFBR, grant 04-01-00858-a

DIAGaRa: An Incremental Algorithm for Inferring Implicative Rules from Examples

An approach is proposed for inferring implicative logical rules from examples. The concept of a good diagnostic test for a given set of positive examples lies in the basis of this approach. The process of inferring good diagnostic tests is considered as a process of inductive common sense reasoning. The incremental approach to learning algorithms is implemented in an algorithm DIAGaRa for inferring implicative rules from examples.

Logical Models of Composite Dynamic Objects Control

The questions of designing multicriteria control systems on the basis of logic models of composite dynamic objects are considered.

A Mathematical Apparatus for Domain Ontology Simulation. Logical Relationship Systems

* This paper was made according to the program of fundamental scientific research of the Presidium of the Russian Academy of Sciences «Mathematical simulation and intellectual systems», the project "Theoretical foundation of the intellectual systems based on ontologies for intellectual support of scientific researches".