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Are Types needed for Natural Language?
, 1996
"... Logic, due to the paradoxes, is absent from the type free calculus. This makes such a calculus an unsuitable device for Natural Language Semantics. Moreover, the problems that arise from mixing the type free calculus with logic lead to type theory and hence formalisations of Natural Language were ..."
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Logic, due to the paradoxes, is absent from the type free calculus. This makes such a calculus an unsuitable device for Natural Language Semantics. Moreover, the problems that arise from mixing the type free calculus with logic lead to type theory and hence formalisations of Natural Language were carried out in a strictly typed framework. It was shown however, that strict type theory cannot capture the selfreferential nature of language ([Parsons 79], [Chierchia, Turner 88] and [Kamareddine, Klein 93]) and hence other approaches were needed. For example, the approach carried out by Parsons is based on creating a notion of floating types which can be instantiated to particular instances of types whereas the approaches of Chierchia, Turner and Kamareddine, Klein are based on a type free framework. In this paper, we will embed the typing system of [Parsons 79] into a version of the one proposed in [Kamareddine, Klein 93] giving an interpretation of Parsons' system in a type free theory...
Systems for open terms: An overview
, 2001
"... In this paper we make an overview of some existing systems of open (incomplete) terms including ALF, Typelab, OLEG, L, Automath, c and s e. ..."
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In this paper we make an overview of some existing systems of open (incomplete) terms including ALF, Typelab, OLEG, L, Automath, c and s e.
Jumping around the box: Graphical and operational studies on λcalculus and Linear Logic
"... 1.1 λtrees, λjdags and sharing..................... 10 1.2 The structural λcalculus...................... 13 1.2.1 Using λj to revisit λcalculus................ 14 ..."
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1.1 λtrees, λjdags and sharing..................... 10 1.2 The structural λcalculus...................... 13 1.2.1 Using λj to revisit λcalculus................ 14
Are Types needed for Natural Language? In Applied Logic: How, What and Why, Polos and Masuch
, 1996
"... Logic, due to the paradoxes, is absent from the type free calculus. This makes such a calculus an unsuitable device for Natural Language Semantics. Moreover, the problems that arise from mixing the type free calculus with logic lead to type theory and hence formalisations of Natural Language were ..."
Abstract
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Logic, due to the paradoxes, is absent from the type free calculus. This makes such a calculus an unsuitable device for Natural Language Semantics. Moreover, the problems that arise from mixing the type free calculus with logic lead to type theory and hence formalisations of Natural Language were carried out in a strictly typed framework. It was shown however, that strict type theory cannot capture the selfreferential nature of language ([Parsons 79], [Chierchia, Turner 88] and [Kamareddine, Klein 93]) and hence other approaches were needed. For example, the approach carried out by Parsons is based on creating a notion of
oating types which can be instantiated to particular instances of types whereas the approaches of Chierchia, Turner and Kamareddine, Klein are based on a type free framework. In this paper, we will embed the typing system of [Parsons 79] into a version of the one proposed in [Kamareddine, Klein 93] giving an interpretation of Parsons ' system in a type free theory where logic is present. In other words, we take the standpoint that type freeness is needed yet types are also indispensable. On this ground, by constructing types in the type free theory, we obtain a framework which can be seen as a formalisation of Parsons ' claim that Natural Language needs type freeness in order to accommodate self referentiality yet many sentences should be understood as implicitly typed.