A Mathematical Apparatus for Domain Ontology Simulation. An Extendable Language of Applied Logic

* 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".

A Mathematical Apparatus for Ontology Simulation. Specialized Extensions of the Extendable Language of Applied Logic

* 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".

Mathematical Models of Domain Ontologies

* This paper was made according to the program No 14 of fundamental scientific research of the Presidium of the Russian Academy of Sciences, the project "Intellectual Systems Based on Multilevel Domain Models".

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".

A Metaontology for Medical Diagnostics of Acute Diseases. Part 1. An Informal Description and Definitions of Basic Terms

The aim of this article is to describe formally a metaontology for medical diagnostics of acute diseases in the language of applied logic. The article includes an informal description of the metaontology, and the part of its model which contains the definitions for basic terms of knowledge and situations and also their integrity restrictions in the form of ontological agreements.

A Metaontology for Medical Diagnostics of Acute Diseases. Part 2. A Formal Description of Cause-and-effect Relations

This article is the continuation of the formal description of the metaontology for medical diagnostics in the language of applied logic. It contains a description of interrelations between terms of knowledge and reality in the form of ontological agreements.

A Metaontology for Medical Diagnostics of Acute Diseases. Part 3. A Formal Description of the Causes of Signs’ Values and of Diseases

This article is the final part of the formal description of the metaontology for medical diagnostics in the language of applied logic. It contains a description of the causes of signs’ values and of the causes of diseases.

Applications of Nonclassical Logic Methods for Purposes of Knowledge Discovery and Data Mining

* The work is partially supported by Grant no. NIP917 of the Ministry of Science and Education – Republic of Bulgaria.

Application of Fuzzy Logic on Image Edge Detection

In this paper a novel method for an application of digital image processing, Edge Detection is developed. The contemporary Fuzzy logic, a key concept of artificial intelligence helps to implement the fuzzy relative pixel value algorithms and helps to find and highlight all the edges associated with an image by checking the relative pixel values and thus provides an algorithm to abridge the concepts of digital image processing and artificial intelligence. Exhaustive scanning of an image using the windowing technique takes place which is subjected to a set of fuzzy conditions for the comparison of pixel values with adjacent pixels to check the pixel magnitude gradient in the window. After the testing of fuzzy conditions the appropriate values are allocated to the pixels in the window under testing to provide an image highlighted with all the associated edges.

On the Range and the Kernel of Derivations

2000 Mathematics Subject Classification: Primary 47B47, 47B10; Secondary 47A30.

Integration Principles of Russian and Japanese Databases on Inorganic Materials

The methods and software for integration of databases (DBs) on inorganic material and substance properties have been developed. The information systems integration is based on known approaches combination: EII (Enterprise Information Integration) and EAI (Enterprise Application Integration). The metabase - special database that stores data on integrated DBs contents is an integrated system kernel. Proposed methods have been applied for DBs integrated system creation in the field of inorganic chemistry and materials science. Important developed integrated system feature is ability to include DBs that have been created by means of different DBMS using essentially various computer platforms: Sun (DB "Diagram") and Intel (other DBs) and diverse operating systems: Sun Solaris (DB "Diagram") and Microsoft Windows Server (other DBs).

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.

Non-Linear Network-Flow Model of Lukasiewicz’s Multivalue Logic

The paper presents a new network-flow interpretation of Łukasiewicz’s logic based on models with an increased effectiveness. The obtained results show that the presented network-flow models principally may work for multivalue logics with more than three states of the variables i.e. with a finite set of states in the interval from 0 to 1. The described models give the opportunity to formulate various logical functions. If the results from a given model that are contained in the obtained values of the arc flow functions are used as input data for other models then it is possible in Łukasiewicz’s logic to interpret successfully other sophisticated logical structures. The obtained models allow a research of Łukasiewicz’s logic with specific effective methods of the network-flow programming. It is possible successfully to use the specific peculiarities and the results pertaining to the function ‘traffic capacity of the network arcs’. Based on the introduced network-flow approach it is possible to interpret other multivalue logics – of E.Post, of L.Brauer, of Kolmogorov, etc.