A Useful Four-Valued Logic
01 Jan 1977-pp 5-37
TL;DR: It is argued that a sophisticated question-answering machine that has the capability of making inferences from its data base should employ a certain four-valued logic, the motivating consideration being that minor inconsistencies in its data should not be allowed to lead to irrelevant conclusions.
Abstract: It is argued that a sophisticated question-answering machine that has the capability of making inferences from its data base should employ a certain four-valued logic, the motivating consideration being that minor inconsistencies in its data should not be allowed to lead (as in classical logic) to irrelevant conclusions. The actual form of the four-valued logic is ‘deduced’ from an interplay of this motivating consideration with certain ideas of Dana Scott concerning ‘approximation lattices.’
Citations
More filters
Book•
01 Jan 2004TL;DR: This landmark text takes the central concepts of knowledge representation developed over the last 50 years and illustrates them in a lucid and compelling way, and offers the first true synthesis of the field in over a decade.
Abstract: Knowledge representation is at the very core of a radical idea for understanding intelligence. Instead of trying to understand or build brains from the bottom up, its goal is to understand and build intelligent behavior from the top down, putting the focus on what an agent needs to know in order to behave intelligently, how this knowledge can be represented symbolically, and how automated reasoning procedures can make this knowledge available as needed.
This landmark text takes the central concepts of knowledge representation developed over the last 50 years and illustrates them in a lucid and compelling way. Each of the various styles of representation is presented in a simple and intuitive form, and the basics of reasoning with that representation are explained in detail. This approach gives readers a solid foundation for understanding the more advanced work found in the research literature. The presentation is clear enough to be accessible to a broad audience, including researchers and practitioners in database management, information retrieval, and object-oriented systems as well as artificial intelligence. This book provides the foundation in knowledge representation and reasoning that every AI practitioner needs.
*Authors are well-recognized experts in the field who have applied the techniques to real-world problems
* Presents the core ideas of KR&R in a simple straight forward approach, independent of the quirks of research systems
*Offers the first true synthesis of the field in over a decade
Table of Contents
1 Introduction * 2 The Language of First-Order Logic *3 Expressing Knowledge * 4 Resolution * 5 Horn Logic * 6 Procedural Control of Reasoning * 7 Rules in Production Systems * 8 Object-Oriented Representation * 9 Structured Descriptions * 10 Inheritance * 11 Numerical Uncertainty *12 Defaults *13 Abductive Reasoning *14 Actions * 15 Planning *16 A Knowledge Representation Tradeoff * Bibliography * Index
938 citations
Book•
23 Nov 2007TL;DR: This work defines the set-theoretic operators on an instance of a neutrosophic set, and calls it an Interval Neutrosophics Set (INS), and introduces a new logic system based on interval neutrosophile sets and proposed data model based on the extension of fuzzy data model and paraconsistent data model.
Abstract: 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.
643 citations
Cites background from "A Useful Four-Valued Logic"
...de Costa’s Cw logic [46] and Belnap’s four-valued logic [33] are two well-known paraconsistent logics....
[...]
Proceedings Article•
06 Aug 1984TL;DR: This paper point out deficiencies in current semantic treatments of knowledge and belief and suggest a new analysis in the form of a logic that avoids these shortcomings and is also more viable computationally.
Abstract: As part of an on-going project to understand the foundations of Knowledge Representation, we are attempting to characterize a kind of belief that forms a more appropriate basis for Knowledge Representation systems than that captured by the usual possible-world formalizations begun by Hintikka. In this paper, we point out deficiencies in current semantic treatments of knowledge and belief (including recent syntactic approaches) and suggest a new analysis in the form of a logic that avoids these shortcomings and is also more viable computationally.
637 citations
01 Jan 2010
TL;DR: The authors generalizes the intuitionistic fuzzy set (IFSFS), paraconsistent set, and intuitionistic set to the neutrosophic set (NS), and distinguishes between NS and IFS.
Abstract: In this paper one generalizes the intuitionistic fuzzy set (IFS), paraconsistent set, and intuitionistic set to the neutrosophic set (NS). Many examples are presented. Distinctions between NS and IFS are underlined.
551 citations
TL;DR: A new semantics for multivalued logic programming is introduced: a model theory for Fitting's bilattice-based logic programming, which until now has not been characterized model-theoretically.
Abstract: Annotated logics were introduced in [43] and later studied in [5, 7, 31, 32]. In [32], annotations were extended to allow variables and functions, and it was argued that such logics can be used to provide a formal semantics for rule-based expert systems with uncertainty. In this paper, we continue to investigate the power of this approach. First, we introduce a new semantics for such programs based on ideals of lattices. Subsequently, some proposals for multivalued logic programming [5, 7, 18, 32, 40, 47] as well as some formalisms for temporal reasoning [1, 3, 41] are shown to fit into this framework. As an interesting byproduct of the investigation, we obtain a new result concerning multivalued logic programming: a model theory for Fitting's bilattice-based logic programming, which until now has not been characterized model-theoretically. This is accompanied by a corresponding proof theory.
498 citations
References
More filters
Book•
01 Jan 1975
TL;DR: The Description for this book, Entailment: The Logic of Relevance and Necessity, will be forthcoming.
Abstract: The Description for this book, Entailment: The Logic of Relevance and Necessity Vol I, will be forthcoming
1,187 citations
TL;DR: In this article, a semantical analysis of modal logic ii and non-normal modal propositional calculi is presented, and the tableaux that leads to a decision procedure for the propositional calculus is considered.
Abstract: Publisher Summary This chapter discusses semantical analysis of modal logic ii and non-normal modal propositional calculi. The proof of sufficiency, which is omitted by many, proceeds by constructing a normal characteristic matrix by Lindenbaum's method. The tableaux that leads to a decision procedure for the propositional calculi is considered.
1,174 citations
881 citations
Book•
01 Nov 1970
TL;DR: However, Scott does realize that the approach argued for above is simply an argument for an approach that accomodates human understanding of computation and that the operational approach must not be ignored because the machines that the programs of study run on are not capable of dealing with such an abstract level of understanding.
Abstract: However, Scott does realize that the approach argued for above is simply an argument for an approach that accomodates human understanding of computation and that the operational approach must not be ignored because, as he points out, the machines that the programs of study run on are not capable of dealing with such an abstract level of understanding. That is, the computaional approach should not be abandoned because the machines that we build operate on that lower level.
746 citations