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Setoids in Type Theory
, 2000
"... Formalising mathematics in dependent type theory often requires to use setoids, i.e. types with an explicit equality relation, as a representation of sets. This paper surveys some possible denitions of setoids and assesses their suitability as a basis for developing mathematics. In particular, we ..."
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Cited by 30 (4 self)
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Formalising mathematics in dependent type theory often requires to use setoids, i.e. types with an explicit equality relation, as a representation of sets. This paper surveys some possible denitions of setoids and assesses their suitability as a basis for developing mathematics. In particular, we argue that a commonly advocated approach to partial setoids is unsuitable, and more generally that total setoids seem better suited for formalising mathematics. 1
Single Assignment C  Entwurf und Implementierung einer CVariante mit spezieller Unterstützung shapeinvarianter ArrayOperationen
, 1996
"... ..."
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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Cited by 4 (1 self)
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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.
A Categorytheoretic characterization of functional completeness
, 1990
"... . Functional languages are based on the notion of application: programs may be applied to data or programs. By application one may define algebraic functions; and a programming language is functionally complete when any algebraic function f(x 1 ,...,x n ) is representable (i.e. there is a constant a ..."
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Cited by 2 (1 self)
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. Functional languages are based on the notion of application: programs may be applied to data or programs. By application one may define algebraic functions; and a programming language is functionally complete when any algebraic function f(x 1 ,...,x n ) is representable (i.e. there is a constant a such that f(x 1 ,...,x n ) = (a . x 1 . ... . x n ). Combinatory Logic is the simplest typefree language which is functionally complete. In a sound categorytheoretic framework the constant a above may be considered as an "abstract gödelnumber" for f, when gödelnumberings are generalized to "principal morphisms", in suitable categories. By this, models of Combinatory Logic are categorically characterized and their relation is given to lambdacalculus models within Cartesian Closed Categories. Finally, the partial recursive functionals in any finite higher type are shown to yield models of Combinatory Logic. ________________ (+) Theoretical Computer Science, 70 (2), 1990, pp.193211. A p...
MSet Models
"... In [1] Andrews studies elementary type theory, a form of Church’s type theory [12] without extensionality, descriptions, choice, and infinity. Since most of the automated search procedures implemented in Tps [4] do not build in principles of extensionality, descriptions, choice or infinity, they are ..."
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Cited by 2 (1 self)
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In [1] Andrews studies elementary type theory, a form of Church’s type theory [12] without extensionality, descriptions, choice, and infinity. Since most of the automated search procedures implemented in Tps [4] do not build in principles of extensionality, descriptions, choice or infinity, they are essentially
An Epistemological Approach to the Design of Training Courses on Logic
"... Introduction Mathematical logic helps to form the rational basis of common sense and, at the same time, it clashes with it. This conflict can be explained by observing that results sistematically obtained by formal logic alter deeply the rationality categories socially accepted; in this respect, it ..."
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Introduction Mathematical logic helps to form the rational basis of common sense and, at the same time, it clashes with it. This conflict can be explained by observing that results sistematically obtained by formal logic alter deeply the rationality categories socially accepted; in this respect, it is worthwhile to note that these results often express innovations of natural science, already recognized by technology, that people uses without awareness. Thus, logic is a powerful educational tool to uptodate common sense rationality, that is to transfer new paradigms of thinking. Notwithstanding this fact, mathematical logic was not given a central role in the Italian high school curriculum till few time ago. At present, the situation is changing, as the diffusion of computer science and its technology is leading to the renewal of high school curricula. This renewal recognizes the increasing importance of logic in various scientific and humanistic fields and tak