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

From paraconsistent three-valued logics to multiple-source epistemic logic

National audienceSeveral interpretations can be given to the third truth value in three-valued logics. Here, we consider the case when it refers to the epistemic notion of contradictory, or both true and false at the same time. We study several paraconsistent three-valued logics that carry this concern and show that they can be translated into a fragment of a simple epistemic logic where modalities can only appear in front of literals. This logic is unusual in the sense that necessity modalities distribute over disjunctions instead of conjunctions. An equivalent translation into a fragment of KD modal logic can be obtained by exchanging the role of possibility and necessity modalities, highlighting the perfect symmetry between three-valued logics of contradiction and three-valued logics of incomplete information

Cognitive context and arguments from ontologies for learning

The deployment of learning resources on the web by different experts has resulted in the accessibility of multiple viewpoints about the same topics. In this work we assume that learning resources are underpinned by ontologies. Different formalizations of domains may result from different contexts, different use of terminology, incomplete knowledge or conflicting knowledge. We define the notion of cognitive learning context which describes the cognitive context of an agent who refers to multiple and possibly inconsistent ontologies to determine the truth of a proposition. In particular we describe the cognitive states of ambiguity and inconsistency resulting from incomplete and conflicting ontologies respectively. Conflicts between ontologies can be identified through the derivation of conflicting arguments about a particular point of view. Arguments can be used to detect inconsistencies between ontologies. They can also be used in a dialogue between a human learner and a software tutor in order to enable the learner to justify her views and detect inconsistencies between her beliefs and the tutor’s own. Two types of arguments are discussed, namely: arguments inferred directly from taxonomic relations between concepts, and arguments about the necessary an

On the Satisfiability of Quasi-Classical Description Logics

Though quasi-classical description logic (QCDL) can tolerate the inconsistency of description logic in reasoning, a knowledge base in QCDL possibly has no model. In this paper, we investigate the satisfiability of QCDL, namely, QC-coherency and QC-consistency and develop a tableau calculus, as a formal proof, to determine whether a knowledge base in QCDL is QC-consistent. To do so, we repair the standard tableau for DL by introducing several new expansion rules and defining a new closeness condition. Finally, we prove that this calculus is sound and complete. Based on this calculus, we implement an OWL paraconsistent reasoner called QC-OWL. Preliminary experiments show that QC-OWL is highly efficient in checking QC-consistency

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

Controlled Natural Languages for Knowledge Representation and Reasoning

Controlled natural languages (CNLs) are effective languages for knowledge representation and reasoning. They are designed based on certain natural languages with restricted lexicon and grammar. CNLs are unambiguous and simple as opposed to their base languages. They preserve the expressiveness and coherence of natural languages. In this paper, it mainly focuses on a class of CNLs, called machine-oriented CNLs, which have well-defined semantics that can be deterministically translated into formal languages to do logical reasoning. Although a number of machine-oriented CNLs emerged and have been used in many application domains for problem solving and question answering, there are still many limitations: First, CNLs cannot handle inconsistencies in the knowledge base. Second, CNLs are not powerful enough to identify different variations of a sentence and therefore might not return the expected inference results. Third, CNLs do not have a good mechanism for defeasible reasoning. This paper addresses these three problems and proposes a research plan for solving these problems. It also shows the current state of research: a paraconsistent logical framework from which six principles that guide the user to encode CNL sentences were created. Experiment results show this paraconsistent logical framework and these six principles can consistently and effectively solve word puzzles with injections of inconsistencies

Towards Large-scale Inconsistency Measurement

We investigate the problem of inconsistency measurement on large knowledge bases by considering stream-based inconsistency measurement, i.e., we investigate inconsistency measures that cannot consider a knowledge base as a whole but process it within a stream. For that, we present, first, a novel inconsistency measure that is apt to be applied to the streaming case and, second, stream-based approximations for the new and some existing inconsistency measures. We conduct an extensive empirical analysis on the behavior of these inconsistency measures on large knowledge bases, in terms of runtime, accuracy, and scalability. We conclude that for two of these measures, the approximation of the new inconsistency measure and an approximation of the contension inconsistency measure, large-scale inconsistency measurement is feasible.Comment: International Workshop on Reactive Concepts in Knowledge Representation (ReactKnow 2014), co-located with the 21st European Conference on Artificial Intelligence (ECAI 2014). Proceedings of the International Workshop on Reactive Concepts in Knowledge Representation (ReactKnow 2014), pages 63-70, technical report, ISSN 1430-3701, Leipzig University, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-15056