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Noncommutative logic III: focusing proofs
 Information and Computation
, 2000
"... We present a sequent calculus for noncommutative logic which enjoys the focalization property. In the multiplicative case, we give a focalized sequentialization theorem, and in the general case, we show that our focalized sequent calculus is equivalent to the original one by studying the permut ..."
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Cited by 5 (2 self)
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We present a sequent calculus for noncommutative logic which enjoys the focalization property. In the multiplicative case, we give a focalized sequentialization theorem, and in the general case, we show that our focalized sequent calculus is equivalent to the original one by studying
Basedon dependency Calculi for Noncommutative Logic
"... In this paper we propose new calculi for the multiplicative fragment of Noncommutative Logic (MNL) which is a linear logic that combines both commutative and noncommutative connectives. Both sequent and proof net calculi, that are new prooftheoretical formulations of MNL, are based on dependency r ..."
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Cited by 1 (0 self)
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In this paper we propose new calculi for the multiplicative fragment of Noncommutative Logic (MNL) which is a linear logic that combines both commutative and noncommutative connectives. Both sequent and proof net calculi, that are new prooftheoretical formulations of MNL, are based on dependency
Noncommutative logic III: focusing proofs \Lambda
, 2002
"... Abstract It is now wellestablished that the socalled focalization property plays a central role in the design of programming languages based on proof search, and more generally in the proof theory of linear logic. We present here a sequent calculus for noncommutative logic (NL) which enjoys the f ..."
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Abstract It is now wellestablished that the socalled focalization property plays a central role in the design of programming languages based on proof search, and more generally in the proof theory of linear logic. We present here a sequent calculus for noncommutative logic (NL) which enjoys
Noncommutative logic I : the multiplicative fragment
, 1998
"... INTRODUCTION Unrestricted exchange rules of Girard's linear logic [8] force the commutativity of the multiplicative connectives\Omega (times, conjunction) and & (par, disjunction) , and henceforth the commutativity of all logic. This a priori commutativity is not always desirable  it is ..."
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Cited by 41 (7 self)
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 it is quite problematic in applications like linguistics or computer science , and actually the desire of a noncommutative logic goes back to the very beginning of LL [9]. Previous works on noncommutativity deal essentially with noncommutative fragments of LL, obtained by removing the exchange rule
Focusing and ProofNets in Linear and NonCommutative Logic
 Proceedings of 6th International Conference on Logic Programming and Automated Reasoning
, 1999
"... Linear Logic [4] has raised a lot of interest in computer research, especially because of its resource sensitive nature. One line of research studies proof construction procedures and their interpretation as computational models, in the "Logic Programming" tradition. An efficient proof s ..."
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Cited by 16 (2 self)
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. This is, in particular, the case of the NonCommutative logic of [1], and all the computational exploitation of Focusing which has been performed in the commutative case can thus be revised and adapted to the non commutative case.
Hopf Algebras and Models of Noncommutative Logic
, 2000
"... We give a denition of categorical models for noncommutative logic, which we call entropic categories, and constructions thereof by means of partial bimonoids and modules over Hopf algebras. 1 Introduction Noncommutative logic, NL for short, has been introduced by Abrusci and the third author in [ ..."
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We give a denition of categorical models for noncommutative logic, which we call entropic categories, and constructions thereof by means of partial bimonoids and modules over Hopf algebras. 1 Introduction Noncommutative logic, NL for short, has been introduced by Abrusci and the third author
Quadratic correctness criterion for Non commutative Logic
 IN 15TH INT. WORKSHOP ON COMPUTER SCIENCE LOGIC, CSL 2001, LNCS 2142
, 2001
"... The multiplicative fragment of Non commutative Logic (MNL) has a proof nets theory [AR00] with a correctness criterion based on long trips for cutfree proof nets. Recently, R.Maieli has developed another criterion in the DanosRegnier style [Mai00]. Both are in exponential time. We give a quadratic ..."
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Cited by 3 (0 self)
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The multiplicative fragment of Non commutative Logic (MNL) has a proof nets theory [AR00] with a correctness criterion based on long trips for cutfree proof nets. Recently, R.Maieli has developed another criterion in the DanosRegnier style [Mai00]. Both are in exponential time. We give a
Noncommutative logic II: sequent calculus and phase semantics
, 1998
"... INTRODUCTION Noncommutative logic is a unication of :  commutative linear logic (Girard 1987) and  cyclic linear logic (Girard 1989; Yetter 1990), a classical conservative extension of the Lambek calculus (Lambek 1958). In a previous paper with Abrusci (Abrusci and Ruet 1999) we presented the mu ..."
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Cited by 27 (6 self)
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INTRODUCTION Noncommutative logic is a unication of :  commutative linear logic (Girard 1987) and  cyclic linear logic (Girard 1989; Yetter 1990), a classical conservative extension of the Lambek calculus (Lambek 1958). In a previous paper with Abrusci (Abrusci and Ruet 1999) we presented
Constraint Based Proof Construction in NonCommutative Logic
, 2001
"... This work presents a computational interpretation of the construction process for cyclic (CyLL) and noncommutative (NL) sequential proofs. We assume a proof construction paradigm, based on a normalization procedure, known as focussing which manages eciently the nondeterminism of the construction. ..."
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This work presents a computational interpretation of the construction process for cyclic (CyLL) and noncommutative (NL) sequential proofs. We assume a proof construction paradigm, based on a normalization procedure, known as focussing which manages eciently the nondeterminism of the construction
Results 1  10
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68,440