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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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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 free starautonomous categories and full coherence
, 2005
"... This paper gives a simple presentation of the free starautonomous category over a category, based on EilenbergKellyMacLane graphs and Trimble rewiring, for full coherence. ..."
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Cited by 14 (0 self)
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This paper gives a simple presentation of the free starautonomous category over a category, based on EilenbergKellyMacLane graphs and Trimble rewiring, for full coherence.
On the Relation Between Coherence Semantics and Multiplicative Proof Nets
, 1994
"... It is known that (mix) proof nets admit a coherence semantics, computed as a set of experiments. We prove here the converse: a proof structure is shown to be a proof net whenever its set of experiments is a semantical object  a clique of the corresponding coherence space. Moreover the interpretat ..."
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Cited by 6 (4 self)
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It is known that (mix) proof nets admit a coherence semantics, computed as a set of experiments. We prove here the converse: a proof structure is shown to be a proof net whenever its set of experiments is a semantical object  a clique of the corresponding coherence space. Moreover the interpretation of atomic formulae can be restricted to a given coherent space with four tokens in its web. This is done by transforming cutlinks into tensorlinks. Dealing directly with noncutfree proof structure we characterise the deadlock freeness of the proof structure. These results are especially convenient for Abramsky 's proof expressions, and are extended to the pomset calculus.
Simple multiplicative proof nets with units
, 2005
"... Abstract. This paper presents a simple notion of proof net for multiplicative linear logic with units. Cut elimination is direct and strongly normalising, in contrast to previous approaches which resorted to moving jumps (attachments) of par units during normalisation. Composition ..."
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Cited by 4 (1 self)
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Abstract. This paper presents a simple notion of proof net for multiplicative linear logic with units. Cut elimination is direct and strongly normalising, in contrast to previous approaches which resorted to moving jumps (attachments) of par units during normalisation. Composition
Incremental Parsing Of Lambek Calculus Using ProofNet Interfaces
, 2003
"... The paper describes an incremental parsing algorithm for natural languages that uses normalized interfaces of modules of proofnets. This algorithm produces at each step the dierent possible partial syntactical analyses of the rst words of a sentence. Thus, it can analyze texts on the y leaving part ..."
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Cited by 1 (0 self)
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The paper describes an incremental parsing algorithm for natural languages that uses normalized interfaces of modules of proofnets. This algorithm produces at each step the dierent possible partial syntactical analyses of the rst words of a sentence. Thus, it can analyze texts on the y leaving partially analyzed sentences.
École Polytechnique Thèse
, 2014
"... Automated reasoning techniques as proofsearch in sequent calculus Thèse présentée par ..."
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Automated reasoning techniques as proofsearch in sequent calculus Thèse présentée par
Digital Equipment Corporation 1991
"... The purpose of this paper is to give an exposition of material dealing with constructive logics, typed calculi, and linear logic. The first part of this paper gives an exposition of background material (with the exception of the Girardtranslation of classical logic into intuitionistic logic, which ..."
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The purpose of this paper is to give an exposition of material dealing with constructive logics, typed calculi, and linear logic. The first part of this paper gives an exposition of background material (with the exception of the Girardtranslation of classical logic into intuitionistic logic, which is new). This second part is devoted to linear logic and proof nets. Particular attention is given to the algebraic semantics (in Girard's terminology, phase semantics) of linear logic. We show how phase spaces arise as an instance of a Galois connection. We also give a direct proof of the correctness of the DanosRegnier criterion for proof nets. This proof is based on a purely graphtheoretic decomposition lemma. As a corollary, we give an O(n 2 )time algorithm for testing whether a proof net is correct. Although the existence of such an algorithm has been announced by Girard, our algorithm appears to be original. R esum e Le but de cet article est de donner une presentation d'elements...