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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 176 (17 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
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 104 (19 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.
The Method of Hypersequents in the Proof Theory of Propositional NonClassical Logics
 IN LOGIC: FROM FOUNDATIONS TO APPLICATIONS, EUROPEAN LOGIC COLLOQUIUM
, 1994
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Speeding Up Inferences Using Relevance Reasoning: A Formalism and Algorithms
 ARTIFICIAL INTELLIGENCE
, 1997
"... Irrelevance reasoning refers to the process in which a system reasons about which parts of its knowledge are relevant (or irrelevant) to a specific query. Aside from its importance in speeding up inferences from large knowledge bases, relevance reasoning is crucial in advanced applications such a ..."
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Cited by 14 (2 self)
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Irrelevance reasoning refers to the process in which a system reasons about which parts of its knowledge are relevant (or irrelevant) to a specific query. Aside from its importance in speeding up inferences from large knowledge bases, relevance reasoning is crucial in advanced applications such as modeling complex physical devices and information gathering in distributed heterogeneous systems. This article presents a novel framework for studying the various kinds of irrelevance that arise in inference and efficient algorithms for relevance reasoning. We present a
Multiplicative Conjunction as an Extensional Conjunction
 Journal of the IGPL
, 1997
"... We show that the rule that allows the inference of A from A\Omega B is admissible in many of the basic multiplicative (intensional) systems. By adding this rule to these systems we get, therefore, conservative extensions in which the tensor behaves as classical conjunction. Among the systems obtain ..."
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Cited by 4 (4 self)
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We show that the rule that allows the inference of A from A\Omega B is admissible in many of the basic multiplicative (intensional) systems. By adding this rule to these systems we get, therefore, conservative extensions in which the tensor behaves as classical conjunction. Among the systems obtained in this way the one derived from RMIm (= multiplicative linear logic together with contraction and its converse) has a particular interest. We show that this system has a simple infinitevalued semantics, relative to which it is strongly complete, and a nice cutfree Gentzentype formulation which employs hypersequents (= finite sequences of ordinary sequents). Moreover: classical logic has a simple, strong translation into this logic. This translation uses definable connectives and preserves the consequence relation of classical logic (not just the set of theorems). Similar results, but with a 3valued semantics, obtain if instead of RMIm we use RMm (the purely multiplicative fragment ...
Combining Classical Logic, Paraconsistency and Relevance
"... We present a logic with has both a simple semantics and a cutfree Gentzent ype system on one hand, and which combines relevance logics, da Costa's paraconsistent logics, and classical logic on the other. We further show that the logic has many other nice properties, and that its language is i ..."
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We present a logic with has both a simple semantics and a cutfree Gentzent ype system on one hand, and which combines relevance logics, da Costa's paraconsistent logics, and classical logic on the other. We further show that the logic has many other nice properties, and that its language is ideal from the semantic point of view. 1
Pertinence Construed Modally
, 2010
"... Capturing the notion of pertinence or relevance in logic is usually attempted at the metalevel. It can be induced either by specific extra information, or by general philosophical principles. In this paper we pay attention to both these origins. We present a semantic modal interpretation of the ide ..."
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Capturing the notion of pertinence or relevance in logic is usually attempted at the metalevel. It can be induced either by specific extra information, or by general philosophical principles. In this paper we pay attention to both these origins. We present a semantic modal interpretation of the idea that there are two distinct relationships between a premiss and a conclusion that are pertinent to each other: of semantic entailment in the forward direction from α to β, and of semantic constraint in the backward direction from β to α. Unpacking the notion of pertinence into these two semantic components yields a class of entailment relations with appealing properties. We define an entailment relation via a modal logic, and investigate its behaviour as a viable candidate for capturing the notion of pertinence. This approach allows us to deal with a number of paradoxes of material and strict implication (e.g. positive paradox), as well as some counterintuitive properties of classical (and modal) entailment (e.g. explosiveness and disjunctive syllogism), in a satisfactory way. Furthermore, the resulting logic is inframodal, nonmonotonic, and allows for nontrivial reasoning with inconsistencies.