Results 11 to 20 of about 698,564 (314)
A realizability semantics for inductive formal topologies, Church's Thesis and Axiom of Choice [PDF]
Logical Methods in Computer Science, 2021 We present a Kleene realizability semantics for the intensional level of the Minimalist Foundation, for short mtt, extended with inductively generated formal topologies, Church's thesis and axiom of choice.
Maria Emilia Maietti +2 more
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A Normalizing Intuitionistic Set Theory with Inaccessible Sets [PDF]
Logical Methods in Computer Science, 2007 We propose a set theory strong enough to interpret powerful type theories underlying proof assistants such as LEGO and also possibly Coq, which at the same time enables program extraction from its constructive proofs.
Wojciech Moczydlowski
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A characterization of trees with equal 2-domination and 2-independence numbers [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 A set $S$ of vertices in a graph $G$ is a $2$-dominating set if every vertex of $G$ not in $S$ is adjacent to at least two vertices in $S$, and $S$ is a $2$-independent set if every vertex in $S$ is adjacent to at most one vertex of $S$.
Christoph Brause +2 more
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Normalization of IZF with Replacement [PDF]
Logical Methods in Computer Science, 2008 ZF is a well investigated impredicative constructive version of Zermelo-Fraenkel set theory. Using set terms, we axiomatize IZF with Replacement, which we call \izfr, along with its intensional counterpart \iizfr.
Wojciech Moczydlowski
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Assembling the Proofs of Ordered Model Transformations [PDF]
Electronic Proceedings in Theoretical Computer Science, 2013 In model-driven development, an ordered model transformation is a nested set of transformations between source and target classes, in which each transformation is governed by its own pre and post- conditions, but structurally dependent on its parent ...
Maribel Fernández, Jeffrey Terrell
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A Note on OTM-Realizability and Constructive Set Theories [PDF]
, 2019 We define an ordinalized version of Kleene's realizability interpretation of intuitionistic logic by replacing Turing machines with Koepke's ordinal Turing machines (OTMs), thus obtaining a notion of realizability applying to arbitrary statements in the ...
Merlin Carl
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The generalised type-theoretic interpretation of constructive set theory [PDF]
, 2006 We present a generalisation of the type-theoretic interpretation of constructive set theory into Martin-Löf type theory. The original interpretation treated logic in Martin-Löf type theory via the propositions-as-types interpretation.
Nicola Gambino, Peter Aczel
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Direct spectra of Bishop spaces and their limits [PDF]
Logical Methods in Computer Science, 2021 We apply fundamental notions of Bishop set theory (BST), an informal theory that complements Bishop's theory of sets, to the theory of Bishop spaces, a function-theoretic approach to constructive topology.
Iosif Petrakis
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Al-Lisaniyyat, 2022 The aim of our paper is to present the Constructive Type Theory (CTT) and some related concepts for the Swedish logician Per Martin Löf, who constructed a formal logic system in order to establish a philosophical foundation of constructive mathematics ...
Terkia Mechouet, Farid Zidani
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Quotients, inductive types, and quotient inductive types [PDF]
Logical Methods in Computer Science, 2022 This paper introduces an expressive class of indexed quotient-inductive types, called QWI types, within the framework of constructive type theory. They are initial algebras for indexed families of equational theories with possibly infinitary operators ...
Marcelo P. Fiore +2 more
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