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A Judgmental Analysis of Linear Logic
, 2003
"... We reexamine the foundations of linear logic, developing a system of natural deduction following MartinL of's separation of judgments from propositions. Our construction yields a clean and elegant formulation that accounts for a rich set of multiplicative, additive, and exponential connectives, ext ..."
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Cited by 49 (27 self)
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We reexamine the foundations of linear logic, developing a system of natural deduction following MartinL of's separation of judgments from propositions. Our construction yields a clean and elegant formulation that accounts for a rich set of multiplicative, additive, and exponential connectives, extending dual intuitionistic linear logic but differing from both classical linear logic and Hyland and de Paiva's full intuitionistic linear logic. We also provide a corresponding sequent calculus that admits a simple proof of the admissibility of cut by a single structural induction. Finally, we show how to interpret classical linear logic (with or without the MIX rule) in our system, employing a form of doublenegation translation.
Linear lambdaCalculus and Categorical Models Revisited
, 1992
"... this paper we shall consider multiplicative exponential linear logic (MELL), i.e. the fragment which has multiplicative conjunction or tensor,\Omega , linear implication, \Gammaffi, and the logical operator "exponential", !. We recall the rules for MELL in a sequent calculus system in Fig. 1. We us ..."
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Cited by 22 (0 self)
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this paper we shall consider multiplicative exponential linear logic (MELL), i.e. the fragment which has multiplicative conjunction or tensor,\Omega , linear implication, \Gammaffi, and the logical operator "exponential", !. We recall the rules for MELL in a sequent calculus system in Fig. 1. We use capital Greek letters \Gamma; \Delta for sequences of formulae and A; B for single formulae. The Exchange rule simply allows the permutation of assumptions. The `! rules' have been given names by other authors. ! L\Gamma1 is called Weakening , ! L\Gamma2 Contraction, ! L\Gamma3 Dereliction and (! R ) Promotion
From proof nets to the free * autonomous category
 Logical Methods in Computer Science, 2(4:3):1–44, 2006. Available from: http://arxiv.org/abs/cs/0605054. [McK05] Richard McKinley. Classical categories and deep inference. In Structures and Deduction 2005 (Satellite Workshop of ICALP’05
, 2005
"... Vol. 2 (4:3) 2006, pp. 1–44 www.lmcsonline.org ..."
On the axiomatisation of Boolean categories with and without medial, 2005. Preprint, available at http://arxiv.org/abs/cs.LO/0512086
"... Abstract. In its most general meaning, a Boolean category is to categories what a Boolean algebraic structure underlying the proofs in Boolean Logic, in the same sense as a ..."
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Cited by 15 (8 self)
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Abstract. In its most general meaning, a Boolean category is to categories what a Boolean algebraic structure underlying the proofs in Boolean Logic, in the same sense as a
ON THE AXIOMATISATION OF BOOLEAN CATEGORIES WITH AND WITHOUT MEDIAL
"... should be used for describing an object that ..."
FROM PROOF NETS TO THE FREE *AUTONOMOUS CATEGORY FRANÇOIS LAMARCHE AND LUTZ STRASSBURGER
, 2006
"... Abstract. In the first part of this paper we present a theory of proof nets for full multiplicative linear logic, including the two units. It naturally extends the wellknown theory of unitfree multiplicative proof nets. A linking is no longer a set of axiom links but a tree in which the axiom link ..."
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Abstract. In the first part of this paper we present a theory of proof nets for full multiplicative linear logic, including the two units. It naturally extends the wellknown theory of unitfree multiplicative proof nets. A linking is no longer a set of axiom links but a tree in which the axiom links are subtrees. These trees will be identified according to an equivalence relation based on a simple form of graph rewriting. We show the standard results of sequentialization and strong normalization of cut elimination. In the second part of the paper we show that the identifications enforced on proofs are such that the class of twoconclusion proof nets defines the free *autonomous category.
FROM PROOF NETS TO THE FREE *AUTONOMOUS CATEGORY FRANÇOIS LAMARCHE AND LUTZ STRASSBURGER
, 2006
"... Abstract. In the first part of this paper we present a theory of proof nets for full multiplicative linear logic, including the two units. It naturally extends the wellknown theory of unitfree multiplicative proof nets. A linking is no longer a set of axiom links but a tree in which the axiom link ..."
Abstract
 Add to MetaCart
Abstract. In the first part of this paper we present a theory of proof nets for full multiplicative linear logic, including the two units. It naturally extends the wellknown theory of unitfree multiplicative proof nets. A linking is no longer a set of axiom links but a tree in which the axiom links are subtrees. These trees will be identified according to an equivalence relation based on a simple form of graph rewriting. We show the standard results of sequentialization and strong normalization of cut elimination. In the second part of the paper we show that the identifications enforced on proofs are such that the class of twoconclusion proof nets defines the free *autonomous category.