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In previous work we have developed Property Theory with Curry Typing ( PTCT , an intensional first-order logic for natural language semantics. PTCT permits fine-grained specifications of meaning. It also supports polymorphic types and separation types. 1 We develop an intensional number theory...
Functions of type 〈 n 〉 are characteristic functions on n -ary relations. Keenan established their importance for natural language semantics, by showing that natural language has many examples of irreducible type 〈 n 〉 functions, i.e. functions of type 〈 n 〉 that cannot be represented...
This is a continuation of a paper in which the role of types in semantic theory was explored. Inevitably, in that paper some issues in type theory and semantics were treated only in passing. In particular, little was said about Stratified Type Theories . This paper concentrates on these theories...
Interaction nets provide a graphical paradigm of computation based on net rewriting. They have proved most successful in understanding the dynamics of reduction in the λ-calculus, where very efficient evaluators have been obtained. Most work in this area is heavily based on the pure λ-calculus,...
The paper develops a semantics for natural language interrogatives which identifies questions—the denotations of interrogatives—with propositional abstracts. The paper argues that a theory of Questions as Propositional Abstracts (QPA), is a simple, transparently implementable theory that has...
This paper explores possibilities for formulating linguistic semantics in terms of records and record types of the kind used in recent developments of Martin-Löf type theory. We will suggest that this gives us tools to develop a single theory which includes aspects of Montague semantics,...
The representation of free variables is crucial for the efficiency of the implementation of various kinds of rewrite systems. We give an innovative, although very natural, representation of variables abstract enough to fit in many different frameworks and more satisfactory from an operational...
We show how the framework of probabilistic abstract interpretation can be applied to statically analyse a probabilistic version of the λ-calculus. The resulting analysis allows for a more speculative use of its outcomes based on the consideration of statistically defined quantities. After...
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