Set Theory and Nominalization, Part II

  title={Set Theory and Nominalization, Part II},
  author={Fairouz Kamareddine},
  journal={J. Log. Comput.},
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 dc;:velop a type theory based on Frege structures and use it as a theory of nominalisation. 
4 Citations

Canonical typing and pi-conversion

In usual type theory, if a function f is of type (T -+ (j' and an argument a is of type CT, then the type of fa is immediately given to be (7' and no mention is made of the fact that what has

A Uniied Approach to Type Theory through a Reened

The general structure of a system of typed lambda calculus is sketched and it is shown that this system has enough expressive power for the description of various existing systems, ranging from Automath-like systems to singly-typed Pure Type Systems.

A System at the Cross-Roads of Functional and Logic Programming

Are types needed for natural languages

The final author version and the galley proof are versions of the publication after peer review that features the final layout of the paper including the volume, issue and page numbers.



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/ Introduction In Turner [17] we developed a semantics for nominalized predicates within the general framework of Montague Grammar. We offered an extension of Montague's PTQ which sanctioned the

Three theories of nominalized predicates

It is the aim of this work to provide a model-theoretic interpretation for a formal language which admits the occurrence of such abstract singular terms.

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A perspective in which the semantics of natural language constructs are unpacked in terms of Peter Aczel's Frege structures is offered and is shown to provide promising results for both nominalisation and intensionality.

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Predication has been a central, if not the central, issue in philosophy since at least the time of Plato and Aristotle. Different theories of predication have in fact been the basis of a number of

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The informal argument that the paradoxes are blocked in ZF is that its axioms are true in the cumulative hierarchy of sets where (i) unlike the theory of types, a set may have members of various (ordinal) levels, but (ii) the level of a set is greater than that of each of its members.

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If the lesson of the paradoxes of set theory is that a predicate need no more have a set as extension than the name "Santa Claus" need denote someone, then perhaps the lessons of the liar paradox is that nothing answers to a liar sentence.

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