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A type reduction from proofconditional to dynamic semantics
 Journal of Philosophical Logic
"... Abstract. Dynamic and proofconditional approaches to discourse (exemplified by Discourse Representation Theory and TypeTheoretical Grammar, respectively) are related through translations and transitions labeled by firstorder formulas with anaphoric twists. Typetheoretic contexts are defined rela ..."
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Abstract. Dynamic and proofconditional approaches to discourse (exemplified by Discourse Representation Theory and TypeTheoretical Grammar, respectively) are related through translations and transitions labeled by firstorder formulas with anaphoric twists. Typetheoretic contexts are defined relative to a signature and instantiated modeltheoretically, subject to change. 1
The proper treatment of context in NL
 COMPUTATIONAL LINGUISTICS IN THE NETHERLANDS 1999; SELECTED PAPERS FROM THE TENTH CLIN MEETING
, 2000
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A realizability interpretation of MartinLöf's type theory
"... In this paper we present a simple argument for normalization of the fragment of MartinLöf's type theory that contains the natural numbers, dependent function types and the first universe. We do this by building a realizability model of this theory which directly reflects that terms and types are ge ..."
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In this paper we present a simple argument for normalization of the fragment of MartinLöf's type theory that contains the natural numbers, dependent function types and the first universe. We do this by building a realizability model of this theory which directly reflects that terms and types are generated simultaneously.
Types and Models for HigherOrder Action Calculi
, 1997
"... . Milner introduced action calculi as a framework for representing models of interactive behaviour. He also introduced the higherorder action calculi, which add higherorder features to the basic setting. We present type theories for action calculi and higherorder action calculi, and give the categ ..."
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. Milner introduced action calculi as a framework for representing models of interactive behaviour. He also introduced the higherorder action calculi, which add higherorder features to the basic setting. We present type theories for action calculi and higherorder action calculi, and give the categorical models of the higherorder calculi. As applications, we give a semantic proof of the conservativity of higherorder action calculi over action calculi, and a precise connection with Moggi's computational lambda calculus and notions of computation. 1 Introduction Milner introduced action calculi as a framework for representing models of interactive behaviour [Mil96]. He also introduced two conservative extensions: higherorder action calculi [Mil94a], which add higherorder features to the basic setting, and reflexive action calculi [Mil94b], which give recursion in the presence of the higherorder features. Various examples, which explore the role of action calculi as a general frame...
Three Processes in Natural Language Interpretation
 Reflections on the Foundations of Mathematics: Essays in Honor of Solomon Feferman. Natick, Mass.: Association for Symbolic Logic
, 2000
"... . To address complications involving ambiguity, presupposition and implicature, three processes underlying natural language interpretation are isolated: translation, entailment and attunement. A metalanguage integrating these processes is outlined, elaborating on a prooftheoretic approach to pr ..."
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. To address complications involving ambiguity, presupposition and implicature, three processes underlying natural language interpretation are isolated: translation, entailment and attunement. A metalanguage integrating these processes is outlined, elaborating on a prooftheoretic approach to presupposition. To appear: Festschrift for Solomon Feferman (ASL Lecture Notes series) x1. Introduction. However outrageous Montague's slogan "English as a formal language" [24] may sound, the pressure to push the claim as far as it can go is, for many, irresistible. Basic to Montague's understanding of a formal language is the possibility of a modeltheoretic interpretation  of obvious interest in various applications (e.g. databases) that employ models. But formulas of predicate logic (firstorder or higherorder, modal or otherwise) differ significantly from English sentences marked with ambiguity and presupposition. Consider, for instance, (s) If Sylvester gets holds of a canary, the...
A Framework for the Hyperintensional Semantics of Natural Language with Two Implementations
 Logical Aspects of Computational Linguistics, Springer Lecture Notes in Artificial Intelligence
, 2001
"... In this paper we present a framework for constructing hyperintensional semantics for natural language. On this approach, the axiom of extensionality is discarded from the axiom base of a logic. Weaker conditions are specified for the connection between equivalence and identity which prevent the redu ..."
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In this paper we present a framework for constructing hyperintensional semantics for natural language. On this approach, the axiom of extensionality is discarded from the axiom base of a logic. Weaker conditions are specified for the connection between equivalence and identity which prevent the reduction of the former relation to the latter. In addition, by axiomatising an intensional number theory we can provide an internal account of proportional cardinality quantifiers, like most. We use a (pre)lattice defined in terms of a (pre)order that models the entailment relation. Possible worlds/situations/indices are then prime filters of propositions in the (pre)lattice. Truth in a world/situation is then reducible to membership of a prime filter. We show how this approach can be implemented within (i) an intensional higherorder type theory, and (ii) firstorder property theory.
An expressive firstorder logic with flexible typing for natural language semantics
 Logic Journal of the Interest Group in Pure ans Applied Logics 12(2):135–168
, 2003
"... We present Property Theory with Curry Typing (PTCT), an intensional firstorder logic for natural language semantics. PTCT permits finegrained specifications of meaning. It also supports polymorphic types and separation types. 1 We develop an intensional number theory within PTCT in order to repres ..."
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We present Property Theory with Curry Typing (PTCT), an intensional firstorder logic for natural language semantics. PTCT permits finegrained specifications of meaning. It also supports polymorphic types and separation types. 1 We develop an intensional number theory within PTCT in order to represent proportional generalized quantifiers like most. We use the type system and our treatment of generalized quantifiers in natural language to construct a typetheoretic approach to pronominal anaphora that avoids some of the difficulties that undermine previous typetheoretic analyses of this phenomenon. 1
Existence Presuppositions and Category Mistakes
, 1994
"... This paper is concerned with two such examples of infelicity, both of which involve false existence presuppositions, one with a nondenoting definite descriptor, the other with a nondenoting anaphor: ..."
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This paper is concerned with two such examples of infelicity, both of which involve false existence presuppositions, one with a nondenoting definite descriptor, the other with a nondenoting anaphor:
Set Theory and Nominalisation, Part I
 Journal of Logic and Computation
, 1996
"... This paper argues that the basic problems of nominalisation are those of set theory. We shall therefore overview the problems of set theory, the various solutions and assess the influence on nominalisation. We shall then discuss Aczel's Frege structures and compare them with Scott domains. Moreover, ..."
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This paper argues that the basic problems of nominalisation are those of set theory. We shall therefore overview the problems of set theory, the various solutions and assess the influence on nominalisation. We shall then discuss Aczel's Frege structures and compare them with Scott domains. Moreover, we shall set the ground for the second part which demonstrates that Frege structures are a suitable framework for dealing with nominalisation. Keywords: Frege structures, Nominalisation, Logic and Type freeness. 1 The Problems We shall examine the problem of the semantics of nominalised terms from two angles: the formal theory and the existence of models. 1.1 The problem of the formal theory Any theory of nominalisation should be accompanied by some ontological views on concepts  for predicates and open wellformed formulae act semantically as concepts. This is vague, however, if only because where I use the word concept, someone else might use class, predicate, set, property or even...
Set Theory and Nominalisation, Part II
 Journal of Logic and Computation
, 1992
"... In this paper we shall meet the application of Scott domains to nominalisation and explain its problem of predication. We claim that it is not possible to find a solution to such a problem within semantic domains without logic. Frege structures are more conclusive than a solution to domain equations ..."
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In this paper we shall meet the application of Scott domains to nominalisation and explain its problem of predication. We claim that it is not possible to find a solution to such a problem within semantic domains without logic. Frege structures are more conclusive than a solution to domain equations and can be used as models for nominalisation. Hence we develop a type theory based on Frege structures and use it as a theory of nominalisation. Keywords: Frege structures, Nominalisation, Logic and Type freeness. 1 Frege structures, a formal introduction Having in part I informally introduced Frege structures, I shall here fill in all the technical details and show that Frege structures exist. Consider F 0 , F 1 ; : : : ; a family F of collections where F 0 is a collection of objects, and (8n ? 0)[F n is a collection of nary functions from F n 0 to F 0 ]. Definition 1.1 (An explicitly closed family) A family F as above is explicitly closed iff: For every expression e[x 1 ; : : : ; x n...