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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 ..."
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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 ..."
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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
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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 ..."
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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
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 ..."
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Cited by 64 (4 self)
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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 Nonstandard Approach to the Logical Omniscience Problem
 Artificial Intelligence
, 1990
"... We introduce a new approach to dealing with the wellknown logical omniscience problem in epistemic logic. Instead of taking possible worlds where each world is a model of classical propositional logic, we take possible worlds which are models of a nonstandard propositional logic we call NPL, which ..."
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Cited by 53 (4 self)
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We introduce a new approach to dealing with the wellknown logical omniscience problem in epistemic logic. Instead of taking possible worlds where each world is a model of classical propositional logic, we take possible worlds which are models of a nonstandard propositional logic we call NPL, which is somewhat related to relevance logic. This approach gives new insights into the logic of implicit and explicit'belief considered by Levesque and Lakemeyer. In particular, we show that in a precise sense agents in the structures considered by Levesque and Lakemeyer are perfect reasoners in NPL. 1
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 ..."
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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
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 ..."
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Cited by 37 (9 self)
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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.
Logical Pluralism
 To appear, Special Logic issue of the Australasian Journal of Philosophy
, 2000
"... Abstract: A widespread assumption in contemporary philosophy of logic is that there is one true logic, that there is one and only one correct answer as to whether a given argument is deductively valid. In this paper we propose an alternative view, logical pluralism. According to logical pluralism th ..."
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Cited by 29 (6 self)
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Abstract: A widespread assumption in contemporary philosophy of logic is that there is one true logic, that there is one and only one correct answer as to whether a given argument is deductively valid. In this paper we propose an alternative view, logical pluralism. According to logical pluralism there is not one true logic; there are many. There is not always a single answer to the question “is this argument valid?” 1 Logic, Logics and Consequence Anyone acquainted with contemporary Logic knows that there are many socalled logics. 1 But are these logics rightly socalled? Are any of the menagerie of nonclassical logics, such as relevant logics, intuitionistic logic, paraconsistent logics or quantum logics, as deserving of the title ‘logic ’ as classical logic? On the other hand, is classical logic really as deserving of the title ‘logic ’ as relevant logic (or any of the other nonclassical logics)? If so, why so? If not, why not? Logic has a chief subject matter: Logical Consequence. The chief aim of