Consistency in Fuzzy Description Logics over Residuated De Morgan Lattices

Fuzzy description logics can be used to model vague knowledge in application domains. This paper analyses the consistency and satisfiability problems in the description logic SHI with semantics based on a complete residuated De Morgan lattice. The problems are undecidable in the general case, but can be decided by a tableau algorithm when restricted to finite lattices. For some sublogics of SHI, we provide upper complexity bounds that match the complexity of crisp reasoning

Undecidability of Fuzzy Description Logics

Fuzzy description logics (DLs) have been investigated for over two decades, due to their capacity to formalize and reason with imprecise concepts. Very recently, it has been shown that for several fuzzy DLs, reasoning becomes undecidable. Although the proofs of these results differ in the details of each specific logic considered, they are all based on the same basic idea. In this report, we formalize this idea and provide sufficient conditions for proving undecidability of a fuzzy DL. We demonstrate the effectiveness of our approach by strengthening all previously-known undecidability results and providing new ones. In particular, we show that undecidability may arise even if only crisp axioms are considered

Fuzzy Description Logics with General Concept Inclusions

Description logics (DLs) are used to represent knowledge of an application domain and provide standard reasoning services to infer consequences of this knowledge. However, classical DLs are not suited to represent vagueness in the description of the knowledge. We consider a combination of DLs and Fuzzy Logics to address this task. In particular, we consider the t-norm-based semantics for fuzzy DLs introduced by Hájek in 2005. Since then, many tableau algorithms have been developed for reasoning in fuzzy DLs. Another popular approach is to reduce fuzzy ontologies to classical ones and use existing highly optimized classical reasoners to deal with them. However, a systematic study of the computational complexity of the different reasoning problems is so far missing from the literature on fuzzy DLs. Recently, some of the developed tableau algorithms have been shown to be incorrect in the presence of general concept inclusion axioms (GCIs). In some fuzzy DLs, reasoning with GCIs has even turned out to be undecidable. This work provides a rigorous analysis of the boundary between decidable and undecidable reasoning problems in t-norm-based fuzzy DLs, in particular for GCIs. Existing undecidability proofs are extended to cover large classes of fuzzy DLs, and decidability is shown for most of the remaining logics considered here. Additionally, the computational complexity of reasoning in fuzzy DLs with semantics based on finite lattices is analyzed. For most decidability results, tight complexity bounds can be derived

Foundations of Fuzzy Logic and Semantic Web Languages

This book is the first to combine coverage of fuzzy logic and Semantic Web languages. It provides in-depth insight into fuzzy Semantic Web languages for non-fuzzy set theory and fuzzy logic experts. It also helps researchers of non-Semantic Web languages get a better understanding of the theoretical fundamentals of Semantic Web languages. The first part of the book covers all the theoretical and logical aspects of classical (two-valued) Semantic Web languages. The second part explains how to generalize these languages to cope with fuzzy set theory and fuzzy logic

Foundations of Fuzzy Logic and Semantic Web Languages

This book is the first to combine coverage of fuzzy logic and Semantic Web languages. It provides in-depth insight into fuzzy Semantic Web languages for non-fuzzy set theory and fuzzy logic experts. It also helps researchers of non-Semantic Web languages get a better understanding of the theoretical fundamentals of Semantic Web languages. The first part of the book covers all the theoretical and logical aspects of classical (two-valued) Semantic Web languages. The second part explains how to generalize these languages to cope with fuzzy set theory and fuzzy logic

Integration of Reciprocal Teaching-ICT Model To Improve Students’Mathematics Critical Thinking Ability

This research examines the effectiveness on how mathematics teachers have begun to integrate information and communication technology (ICT) with reciprocal teaching model to improve students’ mathematics critical thinking ability into seventh junior high school classroom practice. This study was experimental research with a quasi-experimental design. The samples of the study are 36 students for classroom experiments and 36 students for classroom control. The instruments employed in this study were pre-test and post-test. All the instruments are made in essays forms. The data were analyzed by using descriptive statistics. Based on the research findings, it was gotten that (1) the development of teaching instructional multimedia of the seven grade students of junior high school; (2) the improvement of students’ mathematics critical thinking ability in experimental class; (3) the aspect of attractiveness shows that the developed instructional multimedia was very interesting; and (4) reciprocal learning has good impact on students’ mathematics critical thinking ability