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.

Unpicking Priest's Bootstraps

Date of Acceptance: 13/07/2015

Unpicking Priest's Bootstraps

Date of Acceptance: 13/07/2015

Automatic Indexing and Information Visualization: A Study Based on Paraconsistent Logic

This paper reports a research to evaluate the potential and the effects of use of annotated Paraconsistent logic in automatic indexing. This logic attempts to deal with contradictions, concerned with studying and developing inconsistency-tolerant systems of logic. This logic, being flexible and containing logical states that go beyond the dichotomies yes and no, permits to advance the hypothesis that the results of indexing could be better than those obtained by traditional methods. Interactions between different disciplines, as information retrieval, automatic indexing, information visualization, and nonclassical logics were considered in this research. From the methodological point of view, an algorithm for treatment of uncertainty and imprecision, developed under the Paraconsistent logic, was used to modify the values of the weights assigned to indexing terms of the text collections. The tests were performed on an information visualization system named Projection Explorer (PEx), created at Institute of Mathematics and Computer Science (ICMC - USP Sao Carlos), with available source code. PEx uses traditional vector space model to represent documents of a collection. The results were evaluated by criteria built in the information visualization system itself, and demonstrated measurable gains in the quality of the displays, confirming the hypothesis that the use of the para-analyser under the conditions of the experiment has the ability to generate more effective clusters of similar documents. This is a point that draws attention, since the constitution of more significant clusters can be used to enhance information indexing and retrieval. It can be argued that the adoption of non-dichotomous (non-exclusive) parameters provides new possibilities to relate similar information.

The logic of ADHD : a brief review of fallacious reasoning

This paper has two central purposes: the first is to survey some of the more important examples of fallacious argument, and the second is to examine the frequent use of these fallacies in support of the psychological construct: Attention Deficit Hyperactivity Disorder (ADHD). The paper divides 12 familiar fallacies into three different categories—material, psychological and logical—and contends that advocates of ADHD often seem to employ these fallacies to support their position. It is suggested that all researchers, whether into ADHD or otherwise, need to pay much closer attention to the construction of their arguments if they are not to make truth claims unsupported by satisfactory evidence, form or logic.

Some applications of logic to feasibility in higher types

While it is commonly accepted that computability on a Turing machine in polynomial time represents a correct formalization of the notion of a feasibly computable function, there is no similar agreement on how to extend this notion on functionals, that is, what functionals should be considered feasible. One possible paradigm was introduced by Mehlhorn, who extended Cobham's definition of feasible functions to type 2 functionals. Subsequently, this class of functionals (with inessential changes of the definition) was studied by Townsend who calls this class POLY, and by Kapron and Cook who call the same class basic feasible functionals. Kapron and Cook gave an oracle Turing machine model characterisation of this class. In this article, we demonstrate that the class of basic feasible functionals has recursion theoretic properties which naturally generalise the corresponding properties of the class of feasible functions, thus giving further evidence that the notion of feasibility of functionals mentioned above is correctly chosen. We also improve the Kapron and Cook result on machine representation.Our proofs are based on essential applications of logic. We introduce a weak fragment of second order arithmetic with second order variables ranging over functions from NN which suitably characterises basic feasible functionals, and show that it is a useful tool for investigating the properties of basic feasible functionals. In particular, we provide an example how one can extract feasible programs from mathematical proofs that use nonfeasible functions.

Mind change complexity of learning logic programs

The present paper motivates the study of mind change complexity for learning minimal models of length-bounded logic programs. It establishes ordinal mind change complexity bounds for learnability of these classes both from positive facts and from positive and negative facts. Building on Angluin’s notion of finite thickness and Wright’s work on finite elasticity, Shinohara defined the property of bounded finite thickness to give a sufficient condition for learnability of indexed families of computable languages from positive data. This paper shows that an effective version of Shinohara’s notion of bounded finite thickness gives sufficient conditions for learnability with ordinal mind change bound, both in the context of learnability from positive data and for learnability from complete (both positive and negative) data. Let Omega be a notation for the first limit ordinal. Then, it is shown that if a language defining framework yields a uniformly decidable family of languages and has effective bounded finite thickness, then for each natural number m >0, the class of languages defined by formal systems of length <= m: • is identifiable in the limit from positive data with a mind change bound of Omega (power)m; • is identifiable in the limit from both positive and negative data with an ordinal mind change bound of Omega × m. The above sufficient conditions are employed to give an ordinal mind change bound for learnability of minimal models of various classes of length-bounded Prolog programs, including Shapiro’s linear programs, Arimura and Shinohara’s depth-bounded linearly covering programs, and Krishna Rao’s depth-bounded linearly moded programs. It is also noted that the bound for learning from positive data is tight for the example classes considered.

Fuzzy logic power system stabilizer in multimachine stability studies

Power system stabilizers (PSS) work well at the particular network configuration and steady state conditions for which they were designed. Once conditions change, their performance degrades. This can be overcome by an intelligent nonlinear PSS based on fuzzy logic. Such a fuzzy logic power system stabilizer (FLPSS) is developed, using speed and power deviation as inputs, and provides an auxiliary signal for the excitation system of a synchronous motor in a multimachine power system environment. The FLPSS's effect on the system damping is then compared with a conventional power system stabilizer's (CPSS) effect on the system. The results demonstrate an improved system performance with the FLPSS and also that the FLPSS is robust

Fuzzy logic traffic control at a road junction with time-varying flow rates

Fuzzy logic has been applied to control traffic at road junctions. A simple controller with one fixed rule-set is inadequate to minimise delays when traffic flow rate is time-varying and likely to span a wide range. To achieve better control, fuzzy rules adapted to the current traffic conditions are used.