Representing Autoepistemic Logic in Modal Logic

The nonmonotonic logic called Autoepistemic Logic is shown to be representable in a monotonic Modal Quantificational Logic whose modal laws are stronger than S5. Specifically, it is proven that a set of sentences of First Order Logic is a fixed-point of the fixed-point equation of Autoepistemic Logic with an initial set of axioms if and only if the meaning or rather disquotation of that set of sentences is logically equivalent to a particular modal functor of the meaning of that initial set of sentences. This result is important because the modal representation allows the use of powerful automatic deduction systems for Modal Logic and unlike the original Autoepistemic Logic, it is easily generalized to the case where quantified variables may be shared across the scope of modal expressions thus allowing the derivation of quantified consequences. Furthermore, this generalization properly treats such quantifiers since both the Barcan formula and its converse hold.

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.

The Complex Unified Evolutionary Approach to the Creation of the Multilevel Distributed Control System of a Gas-transport Company

The objects of a large-scale gas-transport company (GTC) suggest a complex unified evolutionary approach, which covers basic building concepts, up-to-date technologies, models, methods and means that are used in the phases of design, adoption, maintenance and development of the multilevel automated distributed control systems (ADCS).. As a single methodological basis of the suggested approach three basic Concepts, which contain the basic methodological principles and conceptual provisions on the creation of distributed control systems, were worked out: systems of the lower level (ACS of the technological processes based on up-to-date SCADA), of the middle level (ACS of the operative-dispatch production control based on MES-systems) and of the high level (business process control on the basis of complex automated systems ERP).

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.

Method of Finding Hamilton Routes in Transport Network

This article discusses a solution method for Hamilton Problem, which either finds the task's solution, or indicates that the task is unsolvable. Offered method has significantly smaller requirements for computing resources than known algorithms.