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

Computing The Well-Founded Model Of Deductive Databases

this paper, we show how paraconsistent relations can be used to capture a partial model of a general deductive database and how the associated algebra can be used to compute the well-founded model of the database. The central idea in arriving at this model is to associate paraconsistent relations with the predicate symbols of the given general deductive database. Our method for constructing the well-founded model involves two steps. In the first step, the database clauses are converted into paraconsistent relation definitions involving the operators on them. In the second step, these definitions are used to iteratively construct the model. Computing the Well-founded Model of Deductive Databases 3 The approach presented in this paper lays an algebraic foundation for query processing and optimization for general deductive databases. Query processing will proceed in a bottom-up manner and will use popular rewriting strategies, such as Magic Sets [15], to focus the search for answers. Query optimization can also be achieved at the level of the paraconsistent relational algebra by making use of the laws of equalities. The rest of this paper is organized as follows. Section 2 provides a brief overview of the well-founded model. Section 3 gives a quick introduction to paraconsistent relations and some algebraic operators over them. Section 4 presents the first part of the model construction method, namely an algorithm to convert the database clauses into algebraic equations defining paraconsistent relations. Section 5 presents the second part of the method, namely an algorithm to incrementally construct the paraconsistent relations using the equations constructed earlier. Finally, Section 6 contains some concluding remarks and comparisons with related work

Multispace & Multistructure. Neutrosophic Transdisciplinarity (100 Collected Papers of Sciences), Vol. IV

The fourth volume, in my book series of “Collected Papers”, includes 100 published and unpublished articles, notes, (preliminary) drafts containing just ideas to be further investigated, scientific souvenirs, scientific blogs, project proposals, small experiments, solved and unsolved problems and conjectures, updated or alternative versions of previous papers, short or long humanistic essays, letters to the editors - all collected in the previous three decades (1980-2010) – but most of them are from the last decade (2000-2010), some of them being lost and found, yet others are extended, diversified, improved versions. This is an eclectic tome of 800 pages with papers in various fields of sciences, alphabetically listed, such as: astronomy, biology, calculus, chemistry, computer programming codification, economics and business and politics, education and administration, game theory, geometry, graph theory, information fusion, neutrosophic logic and set, non-Euclidean geometry, number theory, paradoxes, philosophy of science, psychology, quantum physics, scientific research methods, and statistics. It was my preoccupation and collaboration as author, co-author, translator, or cotranslator, and editor with many scientists from around the world for long time. Many topics from this book are incipient and need to be expanded in future explorations