Interval Neutrosophic Sets and Logic: Theory and Applications in Computing

A neutrosophic set is a part of neutrosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. The neutrosophic set is a powerful general formal framework that has been recently proposed. However, the neutrosophic set needs to be specified from a technical point of view. Here, we define the set-theoretic operators on an instance of a neutrosophic set, and call it an Interval Neutrosophic Set (INS). We prove various properties of INS, which are connected to operations and relations over INS. We also introduce a new logic system based on interval neutrosophic sets. We study the interval neutrosophic propositional calculus and interval neutrosophic predicate calculus. We also create a neutrosophic logic inference system based on interval neutrosophic logic. Under the framework of the interval neutrosophic set, we propose a data model based on the special case of the interval neutrosophic sets called Neutrosophic Data Model. This data model is the extension of fuzzy data model and paraconsistent data model. We generalize the set-theoretic operators and relation-theoretic operators of fuzzy relations and paraconsistent relations to neutrosophic relations. We propose the generalized SQL query constructs and tuple-relational calculus for Neutrosophic Data Model. We also design an architecture of Semantic Web Services agent based on the interval neutrosophic logic and do the simulation study

Handling Inconsistency in Knowledge Bases

Real-world automated reasoning systems, based on classical logic, face logically inconsistent information, and they must cope with it. It is onerous to develop such systems because classical logic is explosive. Recently, progress has been made towards semantics that deal with logical inconsistency. However, such semantics was never analyzed in the aspect of inconsistency tolerant relational model. In our research work, we use an inconsistency and incompleteness tolerant relational model called Paraconsistent Relational Model. The paraconsistent relational model is an extension of the ordinary relational model that can store, not only positive information but also negative information. Therefore, a piece of information in the paraconsistent relational model has four truth values: true, false, both, and unknown. However, the paraconsistent relational model cannot represent disjunctive information (disjunctive tuples). We then introduce an extended paraconsistent relational model called disjunctive paraconsistent relational model. By using both the models, we handle inconsistency - similar to the notion of quasi-classic logic or four-valued logic -- in deductive databases (logic programs with no functional symbols). In addition to handling inconsistencies in extended databases, we also apply inconsistent tolerant reasoning technique in semantic web knowledge bases. Specifically, we handle inconsistency assosciated with closed predicates in semantic web. We use again the paraconsistent approach to handle inconsistency. We further extend the same idea to description logic programs (combination of semantic web and logic programs) and introduce dl-relation to represent inconsistency associated with description logic programs

An Entailment Relation for Reasoning on the Web

Reasoning on the Web is receiving an increasing attention because of emerging fields such as Web adaption and Semantic Web. Indeed, the advanced functionalities striven for in these fields call for reasoning capabilities. Reasoning on the Web, however, is usually done using existing techniques rarely fitting the Web. As a consequence, additional data processing like data conversion from Web formats (e.g. XML or HTML) into some other formats (e.g. classical logic terms and formulas) is often needed and aspects of the Web (e.g. its inherent inconsistency) are neglected. This article first gives requirements for an entailment tuned to reasoning on the Web. Then, it describes how classical logic’s entailment can be modified so as to enforce these requirements. Finally, it discusses how the proposed entailment can be used in applying logic programming to reasoning on the Web

Inconsistency and Incompleteness in Relational Databases and Logic Programs

The aim of this thesis is to study the role played by negation in databases and to develop data models that can handle inconsistent and incomplete information. We develop models that also allow incompleteness through disjunctive information under both the CWA and the OWA in relational databases. In the area of logic programming, extended logic programs allow explicit representation of negative information. As a result, a number of extended logic programs have an inconsistent semantics. We present a translation of extended logic programs to normal logic programs that is more tolerant to inconsistencies. Extended logic programs have also been used widely in order to compute the repairs of an inconsistent database. We present some preliminary ideas on how source information can be incorporated into the repair program in order to produce a subset of the set of all repairs based on a preference for certain sources over others

Living with inconsistencies in a multidatabase system

Integration of autonomous sources of information is one of the most important problems in implementation of the global information systems. This paper considers multidatabase systems as one of the typical architectures of global information services and addresses a problem of storing and processing inconsistent information in such systems. A new data model proposed in the paper separates sure from inconsistent information and introduces a system of elementary operations on the containers with sure and inconsistent information. A review of the implementation aspects in an environment of a typical relational database management system concludes the paper

Kiel Declarative Programming Days 2013

This report contains the papers presented at the Kiel Declarative Programming Days 2013, held in Kiel (Germany) during September 11-13, 2013. The Kiel Declarative Programming Days 2013 unified the following events: * 20th International Conference on Applications of Declarative Programming and Knowledge Management (INAP 2013) * 22nd International Workshop on Functional and (Constraint) Logic Programming (WFLP 2013) * 27th Workshop on Logic Programming (WLP 2013) All these events are centered around declarative programming, an advanced paradigm for the modeling and solving of complex problems. These specification and implementation methods attracted increasing attention over the last decades, e.g., in the domains of databases and natural language processing, for modeling and processing combinatorial problems, and for high-level programming of complex, in particular, knowledge-based systems

Paraconsistência em lógica híbrida

Mestrado em Matemática e AplicaçõesThe use of hybrid logics allows the description of relational structures, at the same time that allows establishing accessibility relations between states and, furthermore, nominating and making mention to what happens at speci c states. However, the information we collect is subject to inconsistencies, namely, the search for di erent information sources can lead us to pick up contradictions. Nowadays, by having so many means of dissemination available, that happens frequently. The aim of this work is to develop tools capable of dealing with contradictory information that can be described as hybrid logics' formulas. To build models, to compare inconsistency in di erent databases, and to see the applicability of this method in day-to-day life are the basis for the development of this dissertation.O uso de lógicas híbridas permite a descrição de estruturas relacionais, ao mesmo tempo que permite estabelecer relações de acessibilidade entre estados, e, para além disso, nomear e fazer referência ao que acontece em estados específicos. No entanto, a informação que recolhemos está sujeita a inconsistências, isto é, a procura de diferentes fontes de informação pode levar a recolha de contradições. O que nos dias de hoje, com tantos meios de divulgação disponíveis, acontece frequentemente. O objetivo deste trabalho e desenvolver ferramentas capazes de lidar com informação contraditória que possa ser descrita através de fórmulas de lógicas híbridas. Construir modelos e comparar a inconsistência de diferentes bases de dados e ver a aplicabilidade deste método no dia-a-dia são a base para o desenvolvimento desta dissertação

Propositional and predicate logics of incomplete information

International audienceOne of the most common scenarios of handling incomplete information occurs in relational databases. They describe in-complete knowledge with three truth values, using Kleene’s logic for propositional formulae and a rather peculiar exten-sion to predicate calculus. This design by a committee from several decades ago is now part of the standard adopted by vendors of database management systems. But is it really the right way to handle incompleteness in propositional and pred-icate logics?Our goal is to answer this question. Using an epistemic ap-proach, we first characterize possible levels of partial knowl-edge about propositions, which leads to six truth values. We impose rationality conditions on the semantics of the connec-tives of the propositional logic, and prove that Kleene’s logic is the maximal sublogic to which the standard optimization rules apply, thereby justifying this design choice. For exten-sions to predicate logic, however, we show that the additional truth values are not necessary: every many-valued extension of first-order logic over databases with incomplete informa-tion represented by null values is no more powerful than the usual two-valued logic with the standard Boolean interpreta-tion of the connectives. We use this observation to analyze the logic underlying SQL query evaluation, and conclude that the many-valued extension for handling incompleteness does not add any expressiveness to it