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SUBSTRUCTURAL LOGICS ∗
"... A b s t r a c t. The present paper is concerned with the cut eliminability for some sequent systems of noncommutative substructural logics, i.e. substructural logics without exchange rule. Sequent systems of several extensions of noncommutative logics FL and LBB ′ I, which is sometimes called T → − ..."
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A b s t r a c t. The present paper is concerned with the cut eliminability for some sequent systems of noncommutative substructural logics, i.e. substructural logics without exchange rule. Sequent systems of several extensions of noncommutative logics FL and LBB ′ I, which is sometimes called
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 182 (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
Substructural Logics and Residuated Lattices  An Introduction
, 2003
"... This is an introductory survey of substructural logics and of residuated lattices which are algebraic structures for substructural logics. Our survey starts from sequent systems for basic substructural logics and develops the proof theory of them. Then, residuated lattices are introduced as algebra ..."
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Cited by 31 (3 self)
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This is an introductory survey of substructural logics and of residuated lattices which are algebraic structures for substructural logics. Our survey starts from sequent systems for basic substructural logics and develops the proof theory of them. Then, residuated lattices are introduced
Categorial Grammars and Substructural Logics
"... Substructural logics are formal logics whose Gentzenstyle sequent systems abandon some/all structural rules (Weakening, Contraction, Exchange, Associativity). They have extensively been studied in current literature on nonclassical logics from different points of view: as sequent axiomatizations of ..."
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Substructural logics are formal logics whose Gentzenstyle sequent systems abandon some/all structural rules (Weakening, Contraction, Exchange, Associativity). They have extensively been studied in current literature on nonclassical logics from different points of view: as sequent axiomatizations
Meeting strength in substructural logics
 Logic Group Preprint Series 38, Dept. of
, 1993
"... This paper contributes to the theory of hybrid substructural logics, i.e. weak logics given by a Gentzenstyle proof theory in which there is only a limited possibility to use structural rules. Following the literature, we use an operator to mark formulas to which the extra structural rules may be a ..."
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Cited by 4 (0 self)
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This paper contributes to the theory of hybrid substructural logics, i.e. weak logics given by a Gentzenstyle proof theory in which there is only a limited possibility to use structural rules. Following the literature, we use an operator to mark formulas to which the extra structural rules may
Substructural Logics on Display
, 1998
"... Substructural logics are traditionally obtained by dropping some or all of the structural rules from Gentzen's sequent calculi LK or LJ. It is well known that the usual logical connectives then split into more than one connective. Alternatively, one can start with the (intuitionistic) Lambek ca ..."
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Cited by 49 (16 self)
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Substructural logics are traditionally obtained by dropping some or all of the structural rules from Gentzen's sequent calculi LK or LJ. It is well known that the usual logical connectives then split into more than one connective. Alternatively, one can start with the (intuitionistic) Lambek
Substructural Logical Specifications
, 2012
"... Any opinions, findings, conclusions or recommendations expressed in this publication are those of the author and A logical framework and its implementation should serve as a flexible tool for specifying, simulating, and reasoning about formal systems. When the formal systems we are interested in exh ..."
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Cited by 6 (2 self)
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in exhibit state and concurrency, however, existing logical frameworks fall short of this goal. Logical frameworks based on a rewriting interpretation of substructural logics, ordered and linear logic in particular, can help. To this end, this dissertation introduces and demonstrates four methodologies
Modalities In Substructural Logics
, 1994
"... This paper generalises Girard's results which embed intuitionistic logic into linear logic by showing how arbitrary substructural logics can be embedded into weaker substructural logics, using a single modality which `encodes' the new structural rules. Logics 1 1. Logics Logic is abou ..."
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This paper generalises Girard's results which embed intuitionistic logic into linear logic by showing how arbitrary substructural logics can be embedded into weaker substructural logics, using a single modality which `encodes' the new structural rules. Logics 1 1. Logics Logic
Glueing of Algebras for Substructural Logics
, 1995
"... $\dot{\mathrm{W}}\mathrm{e} $ will introduce the notion of the glueing of algebras for substructural logics and prove the disjunction and existence properties for them, by using the glueing. First, we will introduce the glueing of algebras for intuitionistic substructural propositional logics and pr ..."
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$\dot{\mathrm{W}}\mathrm{e} $ will introduce the notion of the glueing of algebras for substructural logics and prove the disjunction and existence properties for them, by using the glueing. First, we will introduce the glueing of algebras for intuitionistic substructural propositional logics
A Useful Substructure! Logic
"... Formal systems seem to come in two general kinds: useful and useless. This is painting things starkly, but the point is important. Formal structures can either be used in interesting and important ways, or they can languish unused and irrelevant. Lewis' modal logics are good examples. The syste ..."
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in different ways, while the structures described by SI to S3 are not so important. In this paper, we will see another formal system with a number of different uses. We will examine a substructural logic which is important in a number of different ways. The logic of Peirce monoids, inspired by the logic
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