Logical Paradoxes in Non-Classical Logic Systems

It is shown that well-known logical paradoxes such as Barber paradox can be interpreted differently in non-classical logic systems such as multi-valued, continuous and quantum logic with possibility of solutions of the paradox. The results of this research can have applications in investigations of completeness of logic systems.

New FMEA Risks Ranking Approach Utilizing Four Fuzzy Logic Systems

Process equipment and plant maintenance problems are complex in the oil refinery business, since effective maintenance needs to ensure the reliability and availability of the plant. Failure Mode and Effects Analysis (FMEA) is a risk assessment tool that aims to determine possible failure modes, and to reduce the ratio of unknown failure modes, by identifying business-critical systems and the risks of their failures. For the identified failure modes, FMEA determines risk mitigation action(s). The goal is to prevent failure and keep assets and plants running at peak performance by providing fully integrated operations, maintenance, turnarounds, modifications, and asset integrity solutions, during all phases of the asset life cycle. This research was based on FMEA use/application in refineries’ units, and proposes the new fuzzy FMEA risk quantification approach method: “four fuzzy logic system”. The model included a pre-assessment, by sets of fuzzy logic systems, that examined the input parameters that affected the variables of severity, occurrence, and detectability. The proposed model prioritized risks better and addressed the drawbacks of the conventional FMEA method.

Evaluation of the Level of Prognostic Competence with Fuzzy Logic Systems

The chapter deals with main components are part of the prognostic competence. The chapter discusses possibility of using intelligent systems to model the predictive competence of a civil engineer. The analysis of the study of the problem was carried out using content analysis A model of the development of prognostic competence of a civil engineer using the Matlab software package with the Fuzzy Logic Toolbox module has been developed. A step-by-step forecasting technology, as well as possible errors in creating a forecast by an expert and ways of solving them, are proposed. In conclusion the chapter says most of all the level of formation of predictive competence depends on activity component.

Functions-as-constructors higher-order unification: extended pattern unification

Unification is a central operation in constructing a range of computational logic systems based on first-order and higher-order logics. First-order unification has several properties that guide its incorporation in such systems. In particular, first-order unification is decidable, unary, and can be performed on untyped term structures. None of these three properties hold for full higher-order unification: unification is undecidable, unifiers can be incomparable, and term-level typing can dominate the search for unifiers. The so-called pattern subset of higher-order unification was designed to be a small extension to first-order unification that respects the laws governing λ-binding (i.e., the equalities for α, β, and η-conversion) but which also satisfied those three properties. While the pattern fragment of higher-order unification has been used in numerous implemented systems and in various theoretical settings, it is too weak for many applications. This paper defines an extension of pattern unification that should make it more generally applicable, especially in proof assistants that allow for higher-order functions. This extension’s main idea is that the arguments to a higher-order, free variable can be more than just distinct bound variables. In particular, such arguments can be terms constructed from (sufficient numbers of) such bound variables using term constructors and where no argument is a subterm of any other argument. We show that this extension to pattern unification satisfies the three properties mentioned above.