Results 1  10
of
43
An introduction to substructural logics
, 2000
"... Abstract: This is a history of relevant and substructural logics, written for the Handbook of the History and Philosophy of Logic, edited by Dov Gabbay and John Woods. 1 1 ..."
Abstract

Cited by 139 (16 self)
 Add to MetaCart
Abstract: This is a history of relevant and substructural logics, written for the Handbook of the History and Philosophy of Logic, edited by Dov Gabbay and John Woods. 1 1
Tractable Reasoning via Approximation
 Artificial Intelligence
, 1995
"... Problems in logic are wellknown to be hard to solve in the worst case. Two different strategies for dealing with this aspect are known from the literature: language restriction and theory approximation. In this paper we are concerned with the second strategy. Our main goal is to define a semantical ..."
Abstract

Cited by 92 (0 self)
 Add to MetaCart
Problems in logic are wellknown to be hard to solve in the worst case. Two different strategies for dealing with this aspect are known from the literature: language restriction and theory approximation. In this paper we are concerned with the second strategy. Our main goal is to define a semantically wellfounded logic for approximate reasoning, which is justifiable from the intuitive point of view, and to provide fast algorithms for dealing with it even when using expressive languages. We also want our logic to be useful to perform approximate reasoning in different contexts. We define a method for the approximation of decision reasoning problems based on multivalued logics. Our work expands and generalizes in several directions ideas presented by other researchers. The major features of our technique are: 1) approximate answers give semantically clear information about the problem at hand; 2) approximate answers are easier to compute than answers to the original problem; 3) approxim...
A UNIFYING FIELD IN LOGICS: NEUTROSOPHIC LOGIC. NEUTROSOPHY, NEUTROSOPHIC SET, NEUTROSOPHIC PROBABILITY AND STATISTICS (fourth edition)
, 2005
"... ..."
The Family of Stable Models
, 1993
"... The family of all stable models for a logic program has a surprisingly simple overall structure, once two naturally occurring orderings are made explicit. In a socalled knowledge ordering based on degree of definedness, every logic program P has a smallest stable model, s k P it is the well ..."
Abstract

Cited by 54 (4 self)
 Add to MetaCart
The family of all stable models for a logic program has a surprisingly simple overall structure, once two naturally occurring orderings are made explicit. In a socalled knowledge ordering based on degree of definedness, every logic program P has a smallest stable model, s k P it is the wellfounded model. There is also a dual largest stable model, S k P , which has not been considered before. There is another ordering based on degree of truth. Taking the meet and the join, in the truth ordering, of the two extreme stable models s k P and S k P just mentioned, yields the alternating fixed points of [29], denoted s t P and S t P here. From s t P and S t P in turn, s k P and S k P can be produced again, using the meet and join of the knowledge ordering. All stable models are bounded by these four valuations. Further, the methods of proof apply not just to logic programs considered classically, but to logic programs over any bilattice meeting certain co...
A Treatise on ManyValued Logics
 Studies in Logic and Computation
, 2001
"... The paper considers the fundamental notions of many valued logic together with some of the main trends of the recent development of infinite valued systems, often called mathematical fuzzy logics. Besides this logical approach also a more algebraic approach is discussed. And the paper ends with som ..."
Abstract

Cited by 52 (3 self)
 Add to MetaCart
The paper considers the fundamental notions of many valued logic together with some of the main trends of the recent development of infinite valued systems, often called mathematical fuzzy logics. Besides this logical approach also a more algebraic approach is discussed. And the paper ends with some hints toward applications which are based upon actual theoretical considerations about infinite valued logics. Key words: mathematical fuzzy logic, algebraic semantics, continuous tnorms, leftcontinuous tnorms, Pavelkastyle fuzzy logic, fuzzy set theory, nonmonotonic fuzzy reasoning 1 Basic ideas 1.1 From classical to manyvalued logic Logical systems in general are based on some formalized language which includes a notion of well formed formula, and then are determined either semantically or syntactically. That a logical system is semantically determined means that one has a notion of interpretation or model 1 in the sense that w.r.t. each such interpretation every well formed formula has some (truth) value or represents a function into
A Relevance Terminological Logic for Information Retrieval
 IN PROCEEDINGS OF SIGIR96, 19TH INTERNATIONAL CONFERENCE ON RESEARCH AND DEVELOPMENT IN INFORMATION RETRIEVAL
, 1996
"... A Terminological Logic is presented as an information retrieval model, with a fourvalued semantics that gives to its inference relation the flavour of relevance, that is a strict connection in meaning between the premises and the conclusion of the arguments licensed by the logic. The logic also per ..."
Abstract

Cited by 35 (9 self)
 Add to MetaCart
A Terminological Logic is presented as an information retrieval model, with a fourvalued semantics that gives to its inference relation the flavour of relevance, that is a strict connection in meaning between the premises and the conclusion of the arguments licensed by the logic. The logic also permits the expression of metaknowledge enforcing a closedworld reading of the knowledge concerning specified individuals and primitive concepts. A Gentzenstyle, sound and complete calculus for reasoning in the logic is given, thus establishing the basis for an information retrieval engine.
Kleene’s threevalued logics and their children
 Fundamenta Informaticae
, 1994
"... Abstract. Kleene’s strong threevalued logic extends naturally to a fourvalued logic proposed by Belnap. We introduce a guard connective into Belnap’s logic and consider a few of its properties. Then we show that by using it fourvalued analogs of Kleene’s weak threevalued logic, and the asymmetri ..."
Abstract

Cited by 25 (4 self)
 Add to MetaCart
Abstract. Kleene’s strong threevalued logic extends naturally to a fourvalued logic proposed by Belnap. We introduce a guard connective into Belnap’s logic and consider a few of its properties. Then we show that by using it fourvalued analogs of Kleene’s weak threevalued logic, and the asymmetric logic of Lisp are also available. We propose an extension of these ideas to the family of distributive bilattices. Finally we show that for bilinear bilattices the extensions do not produce any new equivalences. 1
FourValued Semantics For Relevant Logics (and Some Of Their Rivals)
 Journal of Philosophical Logic
, 1995
"... This paper gives an outline of three different approaches to the fourvalued semantics for relevant logics (and other nonclassical logics in their vicinity). The first approach borrows from the `Australian Plan' semantics, which uses a unary operator `' for the evaluation of negation. This appro ..."
Abstract

Cited by 18 (6 self)
 Add to MetaCart
This paper gives an outline of three different approaches to the fourvalued semantics for relevant logics (and other nonclassical logics in their vicinity). The first approach borrows from the `Australian Plan' semantics, which uses a unary operator `' for the evaluation of negation. This approach can model anything that the twovalued account can, but at the cost of relying on insights from the Australian Plan. The second approach is natural, well motivated, independent of the Australian Plan, and it provides a semantics for the contractionfree relevant logic C (or RW). Unfortunately, its approach seems to model little else. The third approach seems to capture a wide range of formal systems, but at the time of writing, lacks a completeness proof. 1 Definitions In their paper `Simplified Semantics for Basic Relevant Logics' (hereafter `SS1'), Priest and Sylvan gave a simplification of the usual ternaryrelational frame semantics for relevant logics. The original semantics, ...
EvaluationBased Reasoning with Disjunctive Information in FirstOrder Knowledge Bases
 In Proc. of KR02
, 2002
"... In previous work, Levesque proposed an evaluationbased reasoning procedure for socalled proper KBs, equivalent to a possibly incomplete possibly infinite set of functionfree ground literals. The procedure, called V; preserved the efficiency and logical soundness of database query evaluation ..."
Abstract

Cited by 13 (6 self)
 Add to MetaCart
In previous work, Levesque proposed an evaluationbased reasoning procedure for socalled proper KBs, equivalent to a possibly incomplete possibly infinite set of functionfree ground literals. The procedure, called V; preserved the efficiency and logical soundness of database query evaluation. Moreover, if the query was constrained to be in a special normal form, V was also logically complete. In this paper, we propose an extension to this work to handle disjunctive information in a KB. We define a query evaluation procedure X that generalizes V to deal with KBs that are equivalent to a possibly infinite set of functionfree ground clauses.