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96
Substitution in nonwellfounded . . .
 ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE 82 NO. 1 (2003)
, 2003
"... Inspired from the recent developments in theories of nonwellfounded syntax (coinductively defined languages) and of syntax with binding operators, the structure of algebras of wellfounded and nonwellfounded terms is studied for a very general notion of signature permitting both simple variable bin ..."
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binding operators as well as operators of explicit substitution. This is done in an extensional mathematical setting of initial algebras and final coalgebras of endofunctors on a functor category. In the nonwellfounded case, the fundamental operation of substitution is more beneficially defined in terms
Forcing With Nonwellfounded Models
 AUSTRALASIAN JOURNAL OF LOGIC, VOL 5
, 2007
"... We develop the machinery for performing forcing over an arbitrary (possibly nonwellfounded) model of set theory. For consistency results, this machinery is unnecessary since such results can always be legitimately obtained by assuming that the ground model is (countable) transitive. However, for es ..."
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We develop the machinery for performing forcing over an arbitrary (possibly nonwellfounded) model of set theory. For consistency results, this machinery is unnecessary since such results can always be legitimately obtained by assuming that the ground model is (countable) transitive. However
Universal coalgebra: a theory of systems
, 2000
"... In the semantics of programming, nite data types such as finite lists, have traditionally been modelled by initial algebras. Later final coalgebras were used in order to deal with in finite data types. Coalgebras, which are the dual of algebras, turned out to be suited, moreover, as models for certa ..."
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Cited by 408 (42 self)
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, center for the study of Languages and information, Stanford, 1988) on a theory of nonwellfounded sets, in which he introduced a proof principle nowadays called coinduction. It was formulated in terms of bisimulation, a notion originally stemming from the world of concurrent programming languages. Using
Substitution in Nonwellfounded Syntax with Variable Binding ⋆ Abstract
"... Inspired from the recent developments in theories of nonwellfounded syntax (coinductively defined languages) and of syntax with binding operators, the structure of algebras of wellfounded and nonwellfounded terms is studied for a very general notion of signature permitting both simple variable bin ..."
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Inspired from the recent developments in theories of nonwellfounded syntax (coinductively defined languages) and of syntax with binding operators, the structure of algebras of wellfounded and nonwellfounded terms is studied for a very general notion of signature permitting both simple variable
On Modal µCalculus and NonWellFounded Set Theory
"... A finitary characterization for nonwellfounded sets with finite transitive closure is established in terms of modal µcalculus. This result generalizes the standard approach in the literature where a finitary characterization is only provided for wellfounded sets with finite transitive closure ..."
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Cited by 4 (0 self)
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A finitary characterization for nonwellfounded sets with finite transitive closure is established in terms of modal µcalculus. This result generalizes the standard approach in the literature where a finitary characterization is only provided for wellfounded sets with finite transitive
THE REVIEW OF SYMBOLIC LOGIC, Page 1 of 18 NONWELLFOUNDED MEREOLOGY
"... Abstract. This paper is a systematic exploration of nonwellfounded mereology. Motivations and applications suggested in the literature are considered. Some are exotic like Borges ’ ALEPH, and the TRINITY; other examples are less so, like TIME TRAVELING BRICKS, and even Geach’s TIBBLES THE CAT. The ..."
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Abstract. This paper is a systematic exploration of nonwellfounded mereology. Motivations and applications suggested in the literature are considered. Some are exotic like Borges ’ ALEPH, and the TRINITY; other examples are less so, like TIME TRAVELING BRICKS, and even Geach’s TIBBLES THE CAT
Assertions in AFA Set Theory
, 2007
"... In this paper we consider an application of the theory of non–wellfounded sets to the modelling of epistemic updates triggered by assertions in dialogue. We concentrate mainly on what we might call defective dialogue, i.e. dialogue in epistemic contexts where the speaker has either erroneous beliefs ..."
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In this paper we consider an application of the theory of non–wellfounded sets to the modelling of epistemic updates triggered by assertions in dialogue. We concentrate mainly on what we might call defective dialogue, i.e. dialogue in epistemic contexts where the speaker has either erroneous
The AntiFoundation Axiom In Constructive Set Theories
 Stanford University Press
, 2003
"... . The paper investigates the strength of the antifoundation axiom on the basis of various systems of constructive set theories. 1. Introduction Intrinsically circular phenomena have come to the attention of researchers in differing fields such as mathematical logic, computer science, artificial inte ..."
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Cited by 8 (6 self)
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intelligence, linguistics, cognitive science, and philosophy. Logicians first explored set theories whose universe contains what are called nonwellfounded sets, or hypersets (cf. [17], [5]). But the area was considered rather exotic until these theories were put to use in developing rigorous accounts
A Complete Coinductive Logical System for Bisimulation Equivalence on Circular Objects
 in FoSSaCS'99 (ETAPS) Conf. Proc., W.Thomas ed., Springer LNCS 1578
, 1983
"... We introduce a coinductive logical system à la Gentzen for establishing bisimulation equivalences on circular nonwellfounded regular objects, inspired by work of Coquand, and of Brandt and Henglein. In order to describe circular objects, we utilize a typed language, whose coinductive types involve ..."
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Cited by 1 (1 self)
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suitable endofunctor on the category Set of nonwellfounded sets. Our system subsumes an axiomatization of regular processes, alternative to the classical one given by Milner.
Results 1  10
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96