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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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Cited by 138 (16 self)
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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
A clash of intuitions: The current state of nonmonotonic multiple inheritance systems
 IJCAI87
, 1987
"... Abstract: Early attempts at combining multiple inheritance with nonmonotonic reasoning were based on straight forward extensions of treestructured inheritance systems, and were theoretically unsound. In The Mathematics of Inheritance Systems, or TMOIS, Touretzky described two problems these systems ..."
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Cited by 128 (15 self)
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Abstract: Early attempts at combining multiple inheritance with nonmonotonic reasoning were based on straight forward extensions of treestructured inheritance systems, and were theoretically unsound. In The Mathematics of Inheritance Systems, or TMOIS, Touretzky described two problems these systems cannot handle: reasoning in the presence of true but redundant assertions, and coping with ambiguity. TMOIS provided a definition and analysis of a theoretically sound multiple inheritance system, accompanied by inference algorithms. Other definitions for inheritance have since been proposed that are equally sound and intuitive, but do not always agree with TMOIS. At the heart of the controversy is a clash of intuitions about certain fundamental issues such as skepticism versus credulity, the direction in which inheritance paths are extended, and classical versus intuitive notions of consistency. Just as there are alternative logics, there may be no single "best" approach to nonmonotonic multiple inheritance. 1.
A Skeptical Theory of Inheritance in Nonmonotonic Semantic Networks
 ARTIFICIAL INTELLIGENCE
, 1990
"... This paper describes a new approach to inheritance reasoning in semantic networks allowing for multiple inheritance with exceptions. The approach leads to an analysis of defeasible inheritance which is both welldefined and intuitively attractive: it yields unambiguous results applied to any acyclic ..."
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Cited by 107 (12 self)
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This paper describes a new approach to inheritance reasoning in semantic networks allowing for multiple inheritance with exceptions. The approach leads to an analysis of defeasible inheritance which is both welldefined and intuitively attractive: it yields unambiguous results applied to any acyclic semantic network, and the results conform to our intuitions in those cases in which the intuitions themselves are firm and unambiguous. Since the definition provided here is based on an alternative, skeptical view of inheritance reasoning, however, it does not always agree with previous definitions when it is applied to nets about which our intuitions are unsettled, or in which different reasoning strategies could naturally be expected to yield distinct results. After exploring certain features of the definition presented here, we describe also a hybrid (parallelserial) algorithm that implements the definition in a parallel markerpassing architecture.
Simple Consequence Relations
 Information and Computation
, 1991
"... We provide a general investigation of Logic in which the notion of a simple consequence relation is taken to be fundamental. Our notion is more general than the usual one since we give up monotonicity and use multisets rather than sets. We use our notion for characterizing several known logics (incl ..."
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Cited by 100 (18 self)
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We provide a general investigation of Logic in which the notion of a simple consequence relation is taken to be fundamental. Our notion is more general than the usual one since we give up monotonicity and use multisets rather than sets. We use our notion for characterizing several known logics (including Linear Logic and nonmonotonic logics) and for a general, semanticsindependent classification of standard connectives via equations on consequence relations (these include Girard's "multiplicatives" and "additives"). We next investigate the standard methods for uniformly representing consequence relations: Hilbert type, Natural Deduction and Gentzen type. The advantages and disadvantages of using each system and what should be taken as good representations in each case (especially from the implementation point of view) are explained. We end by briefly outlining (with examples) some methods for developing nonuniform, but still efficient, representations of consequence relations.
SemiStable Semantics
, 2003
"... In this paper, we examine an argumentbased semantics called semistable semantics. Semistable semantics is quite close to traditional stable semantics in the sense that every stable extension is also a semistable extension. One of the advantages of semistable semantics is that there exists at le ..."
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Cited by 56 (13 self)
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In this paper, we examine an argumentbased semantics called semistable semantics. Semistable semantics is quite close to traditional stable semantics in the sense that every stable extension is also a semistable extension. One of the advantages of semistable semantics is that there exists at least one semistable extension. Furthermore, if there also exists at least one stable extension, then the semistable extensions coincide with the stable extensions. This, and other properties, make semistable semantics an attractive alternative for the more traditional stable semantics, which until now has been widely used in fields such as logic programming and answer set programming.
Multivalued Logics: A Uniform Approach to Inference in Artificial Intelligence
 Computational Intelligence
, 1988
"... This paper describes a uniform formalization of much of the current work in AI on inference systems. We show that many of these systems, including firstorder theorem provers, assumptionbased truth maintenance systems (atms's) and unimplemented formal systems such as default logic or circumscr ..."
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Cited by 56 (0 self)
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This paper describes a uniform formalization of much of the current work in AI on inference systems. We show that many of these systems, including firstorder theorem provers, assumptionbased truth maintenance systems (atms's) and unimplemented formal systems such as default logic or circumscription can be subsumed under a single general framework. We begin by defining this framework, which is based on a mathematical structure known as a bilattice. We present a formal definition of inference using this structure, and show that this definition generalizes work involving atms's and some simple nonmonotonic logics. Following the theoretical description, we describe a constructive approach to inference in this setting; the resulting generalization of both conventional inference and atms's is achieved without incurring any substantial computational overhead. We show that our approach can also be used to implement a default reasoner, and discuss a combination of default and atms methods th...
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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Cited by 53 (3 self)
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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
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 50 (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
Natural 3valued logics : characterization and proof theory. The Journal of Symbolic Logic
 Contemporary Aspects of Philosophy
, 1991
"... ..."
Deontic Logic as Founded on Nonmonotonic Logic
 Annals of Mathematics and Artificial Intelligence
, 1993
"... this paper, however, that the techniques of nonmonotonic logic may provide a better theoretical frameworkat least for the formalization of commonsense normative reasoningthan the usual modal treatment. After reviewing some standard approaches to deontic logic, I focus on two areas in which non ..."
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Cited by 36 (3 self)
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this paper, however, that the techniques of nonmonotonic logic may provide a better theoretical frameworkat least for the formalization of commonsense normative reasoningthan the usual modal treatment. After reviewing some standard approaches to deontic logic, I focus on two areas in which nonmonotonic techniques promise improved understanding: reasoning in the presence of conflicting obligations, and reasoning with conditional obligations. 2 Modal techniques in deontic logic