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Resource logics and minimalist grammars
 Proceedings ESSLLI’99 workshop (Special issue Language and Computation
, 2002
"... This ESSLLI workshop is devoted to connecting the linguistic use of resource logics and categorial grammar to minimalist grammars and related generative grammars. Minimalist grammars are relatively recent, and although they stem from a long tradition of work in transformational grammar, they are lar ..."
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This ESSLLI workshop is devoted to connecting the linguistic use of resource logics and categorial grammar to minimalist grammars and related generative grammars. Minimalist grammars are relatively recent, and although they stem from a long tradition of work in transformational grammar, they are largely informal apart from a few research papers. The study of resource logics, on the other hand, is formal and stems naturally from a long logical tradition. So although there appear to be promising connections between these traditions, there is at this point a rather thin intersection between them. The papers in this workshop are consequently rather diverse, some addressing general similarities between the two traditions, and others concentrating on a thorough study of a particular point. Nevertheless they succeed in convincing us of the continuing interest of studying and developing the relationship between the minimalist program and resource logics. This introduction reviews some of the basic issues and prior literature. 1 The interest of a convergence What would be the interest of a convergence between resource logical investigations of
Words as Modules: a Lexicalised Grammar in the framework of Linear Logic Proofnets
 Mathematical and Computational Analysis of Natural Language  selected papers from ICML`96, volume 45 of Studies in Functional and Structural Linguistics
, 1997
"... In this paper we describe the principles of a syntactic calculus whose building blocks are partial proofnets or modules. The main idea is to associate with each lexical item one or more modules which encode(s) its syntactic behaviour. The simplest of these modules are obtained by unfolding the comp ..."
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In this paper we describe the principles of a syntactic calculus whose building blocks are partial proofnets or modules. The main idea is to associate with each lexical item one or more modules which encode(s) its syntactic behaviour. The simplest of these modules are obtained by unfolding the components of formulae that would be the type(s) of the lexical items in a typelogical grammar a la Morrill (1994), while the more sophisticated ones really go beyond the usual typelogical approach. The syntactic analysis within such a paradigm consists in combining these modules into a complete proofnet by a uniform set of plugging rules. This approach is related to the Partial ProofTrees as building blocks of a categorial grammar of Joshi and Kulick (1995), the main difference being the emphasis put on the geometric notion of ProofNet as in our first attempt (Lecomte and Retore 1995). Our main motivation is to obtain a general logical model in which it would be possible to embed other calculi like Lambek grammars on one side and Lexicalised Tree Adjoining Grammars on the other side. The Lambek calculus is a very elegant syntactic calculus because it is a pure WORDS AS MODULES logical calculus enjoying all the properties one can expect: cutelimination, denotational semantics, truth valued semantics. This is also the reason why it allows a very simple interface with Montagovian semantics. Unfortunately, it suffers from many limitations when applied to linguistic descriptions: for instance it does not handle headwrapping, cross serial dependencies, right extraction, extraposition from a nonperipheral site etc. On the other side, the LTAG model provides us with a very efficient model which succeeds in many cases where the Lambek calculus fails. But, because some problems are...
Lexicalized ProofNets and TAGs
 Logical Aspects of Computational Linguistics, LACL‘98, selected papers’, number 2014 in ‘LNCS/LNAI
, 1998
"... Introduction First introduced by [Ret93], pomset linear logic can deal with linguistic aspects by inducing a partial order on words. [LR95] uses this property: it defines modules (or partial proofnets) which consist in entries for words, describing both the category of the word and its behavior wh ..."
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Introduction First introduced by [Ret93], pomset linear logic can deal with linguistic aspects by inducing a partial order on words. [LR95] uses this property: it defines modules (or partial proofnets) which consist in entries for words, describing both the category of the word and its behavior when interacting with other words. Then the natural question of comparing the generative power of such grammars with Tree Adjoining Grammars [JLT75], as [JK96] pointed some links out, arises. To answer this question, we propose a logical formalization of TAGs in the framework of linear logic proofnets. We aim to model trees and operations on these trees with a restricted part of proofnets (included in the intuitionistic ones), and we show how this kind of proofnets expresses equivalently TAGtrees. The first section presents all the definitions. Then, in the second section, we propose a fragment of proofnets allowing the tree encoding and the third section defines the way we mode
ProofNets, hybrid logics and minimalist representations
 In Mathematics of Language 6
, 1999
"... . In this paper, we aim at giving a logical account of the representationalist view on minimalist grammars by refering to the notion of ProofNet in Linear Logic. We propose at the same time a hybrid logic, which mixes one logic (Lambek calculus) for building up elementary proofs and another one for ..."
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. In this paper, we aim at giving a logical account of the representationalist view on minimalist grammars by refering to the notion of ProofNet in Linear Logic. We propose at the same time a hybrid logic, which mixes one logic (Lambek calculus) for building up elementary proofs and another one for combining the proofs so obtained. Because the first logic is non commutative and the second one is commutative, this brings us a way to combine commutativity and non commutativity in the same framework. The dynamic of cutelimination in proofnets is used to formalise the moveoperation. Otherwise, we advocate a proofnet formalism which allows us to consider formulae as nodes to which it is possible to assign weights which determine the final phonological interpretation. Keywords: generative grammar, typelogical grammar, linear logic, proofnets, hybrid logics 1. Introduction The basic idea concerning the use of Proofnets is to consider words and expressions as building blocks in the ...
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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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.
Abstract Derivations as Proofs a Logical Approach to Minimalism
"... The purpose of this paper is to show that we can work in the spirit of minimalist grammars by means of a labelled commutative (and associative) calculus (Oehrle’s Mon:LP), enriched with constraints on the use of assumptions. Lexical entries are considered proper axioms, some of which are coupled wit ..."
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The purpose of this paper is to show that we can work in the spirit of minimalist grammars by means of a labelled commutative (and associative) calculus (Oehrle’s Mon:LP), enriched with constraints on the use of assumptions. Lexical entries are considered proper axioms, some of which are coupled with (sequences of) hypotheses which must necessarily be introduced and discharged before the use of their associated axiom. Like similar proposals by P. de Groote or R. Muskens, our calculus has two interfaces. Each of them provides a homomorphism of types (from syntactic types to semantic ones, or �types, and from syntactic types to phonetic ones, or �types). Move is simply the link between a hypothesis A and its lifted type (A�X)�X when a �(or �)term of the later type applies to a piece of proof the last step of which consists in precisely discharging A. The ability for a phrase to overtly move is governed by the form of its �term. Moreover, the elimination rule for ª is used to simulate headmovements. An enrichment with the exponential of Linear Logic: ”! ” is also proposed in order to treat binding phenomena in the spirit of Kayne (2003). We see that this enrichment opens the field to new insights concerning ellipsis and coordination. Proximity with other formalisms like Lambda grammars and Abstract Categorial Grammars is discussed. Key words: minimalist grammars, typelogical grammars, logical form, CurryHoward, binding phenomena 1