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122
Partial Proof Trees as Building Blocks for a Categorial Grammar
 Linguistics and Philosophy
, 1997
"... We describe a categorial system (PPTS) based on partial proof trees (PPTs) as the building blocks of the system. The PPTs are obtained by unfolding the arguments of the type that would be associated with a lexical item in a simple categorial grammar. The PPTs are the basic types in the system and a ..."
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Cited by 38 (10 self)
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We describe a categorial system (PPTS) based on partial proof trees (PPTs) as the building blocks of the system. The PPTs are obtained by unfolding the arguments of the type that would be associated with a lexical item in a simple categorial grammar. The PPTs are the basic types in the system and a derivation proceeds by combining PPTs together. We describe the construction of the finite set of basic PPTs and the operations for combining them. PPTS can be viewed as a categorial system incorporating some of the key insights of lexicalized tree adjoining grammar, namely the notion of an extended domain of locality and the consequent factoring of recursion from the domain of dependencies. PPTS therefore inherits the linguistic and computational properties of that system, and so can be viewed as a `middle ground' between a categorial grammar and a phrase structure grammar. We also discuss the relationship between PPTS, natural deduction, and linear logic proofnets, and argue that natural ...
Once Upon a Polymorphic Type
, 1998
"... We present a sound typebased `usage analysis' for a realistic lazy functional language. Accurate information on the usage of program subexpressions in a lazy functional language permits a compiler to perform a number of useful optimisations. However, existing analyses are either adhoc and approxim ..."
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Cited by 38 (5 self)
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We present a sound typebased `usage analysis' for a realistic lazy functional language. Accurate information on the usage of program subexpressions in a lazy functional language permits a compiler to perform a number of useful optimisations. However, existing analyses are either adhoc and approximate, or defined over restricted languages. Our work extends the Once Upon A Type system of Turner, Mossin, and Wadler (FPCA'95). Firstly, we add type polymorphism, an essential feature of typed functional programming languages. Secondly, we include general Haskellstyle userdefined algebraic data types. Thirdly, we explain and solve the `poisoning problem', which causes the earlier analysis to yield poor results. Interesting design choices turn up in each of these areas. Our analysis is sound with respect to a Launchburystyle operational semantics, and it is straightforward to implement. Good results have been obtained from a prototype implementation, and we are currently integrating the system into the Glasgow Haskell Compiler.
Pomset Logic: A NonCommutative Extension of Classical Linear Logic
, 1997
"... We extend the multiplicative fragment of linear logic with a noncommutative connective (called before), which, roughly speaking, corresponds to sequential composition. This lead us to a calculus where the conclusion of a proof is a Partially Ordered MultiSET of formulae. We firstly examine coherenc ..."
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Cited by 37 (8 self)
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We extend the multiplicative fragment of linear logic with a noncommutative connective (called before), which, roughly speaking, corresponds to sequential composition. This lead us to a calculus where the conclusion of a proof is a Partially Ordered MultiSET of formulae. We firstly examine coherence semantics, where we introduce the before connective, and ordered products of formulae. Secondly we extend the syntax of multiplicative proof nets to these new operations. We then prove strong normalisation, and confluence. Coming back to the denotational semantics that we started with, we establish in an unusual way the soundness of this calculus with respect to the semantics. The converse, i.e. a kind of completeness result, is simply stated: we refer to a report for its lengthy proof. We conclude by mentioning more results, including a sequent calculus which is interpreted by both the semantics and the proof net syntax, although we are not sure that it takes all proof nets into account...
Interaction Combinators
 Information and Computation
, 1995
"... This paper is the continuation of the author 's work on interaction nets, inspired by Girard's proof nets for linear logic, but no preliminary knowledge of these topics is required for its reading. Introduction ..."
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Cited by 31 (2 self)
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This paper is the continuation of the author 's work on interaction nets, inspired by Girard's proof nets for linear logic, but no preliminary knowledge of these topics is required for its reading. Introduction
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 25 (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 the multiplicative fragment of noncommutative logic, with proof nets and a sequent calculus based on the structure of order varieties, and a sequentialization theorem. Here we consider full propositional noncommutative logic. Noncommutative logic. Let us rst review the basic ideas. Consider the purely noncommutative fragment of linear logic, obtained by removing the exchange rule entirely : ` ; ; ; , ` ; ; ; y This work has been partly carried out at LIENSCNRS, Ecole Normale Superieure (Paris), at McGill University
The Finite Model Property For Various Fragments Of Linear Logic
, 1997
"... B stand for formulas. The connectives of propositional linear logic are: ffl the multiplicatives A & B, A\Omega B, ?, 1; ffl the additives A&B, A \Phi B, ?, 0; ffl the exponentials ?A, !A. Linear negation A ? is only given for positive atoms. It is extended to all formulas by A ?? = A and by ..."
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Cited by 25 (0 self)
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B stand for formulas. The connectives of propositional linear logic are: ffl the multiplicatives A & B, A\Omega B, ?, 1; ffl the additives A&B, A \Phi B, ?, 0; ffl the exponentials ?A, !A. Linear negation A ? is only given for positive atoms. It is extended to all formulas by A ?? = A and by (A & B) ? = A ?\Omega B ? ; ? ? = 1; (A &B) ? = A ? \Phi B ?
Frühwirth: A LinearLogic Semantics For Constraint Handling Rules
 Proceedings of CP 2005
, 2005
"... Abstract. We motivate and develop a linear logic declarative semantics for CHR ∨ , an extension of the CHR programming language that integrates concurrent committed choice with backtrack search and a predefined underlying constraint handler. We show that our semantics maps each of these aspects of t ..."
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Cited by 23 (10 self)
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Abstract. We motivate and develop a linear logic declarative semantics for CHR ∨ , an extension of the CHR programming language that integrates concurrent committed choice with backtrack search and a predefined underlying constraint handler. We show that our semantics maps each of these aspects of the language to a distinct aspect of linear logic. We show how we can use this semantics to reason about derivations in CHR ∨ and we present strong theorems concerning its soundness and completeness. 1
Proof nets and the complexity of processing centerembedded constructions
 Journal of Logic, Language and Information
, 1998
"... Abstract. This paper shows how proof nets can be used to formalize the notion of “incomplete dependency ” used in psycholinguistic theories of the unacceptability of centerembedded constructions. Such theories of human language processing can usually be restated in terms of geometrical constraints ..."
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Cited by 18 (0 self)
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Abstract. This paper shows how proof nets can be used to formalize the notion of “incomplete dependency ” used in psycholinguistic theories of the unacceptability of centerembedded constructions. Such theories of human language processing can usually be restated in terms of geometrical constraints on proof nets. The paper ends with a discussion of the relationship between these constraints and incremental semantic interpretation. 1.
Coherent Banach spaces: a continuous denotational semantics
 Theoretical Computer Science
, 1999
"... We present a denotational semantics based on Banach spaces; it is inspired from the familiar coherent semantics of linear logic, the role of coherence being played by the norm: coherence is rendered by a supremum, whereas incoherence is rendered by a sum, and cliques are rendered by vectors of norm ..."
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Cited by 18 (3 self)
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We present a denotational semantics based on Banach spaces; it is inspired from the familiar coherent semantics of linear logic, the role of coherence being played by the norm: coherence is rendered by a supremum, whereas incoherence is rendered by a sum, and cliques are rendered by vectors of norm at most 1. The basic constructs of linear (and therefore intuitionistic) logic are implemented in this framework: positive connectives yield ℓ 1like norms and negative connectives yield ℓ ∞like norms. The problem of nonreflexivity of Banach spaces is handled by specifying the dual in ¡ advance, whereas the exponential connectives (i.e. intuitionistic implication) are handled by means of analytical functions on the open unit ball. The fact that this ball is open (and not closed) explains the absence of a simple solution to the question of a topological cartesian closed