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Related papers: Realizability Toposes from Specifications

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J.L. Krivine developed a new method based on realizability to construct models of set theory where the axiom of choice fails. We attempt to recreate his results in classical settings, i.e. symmetric extensions. We also provide a new…

Logic · Mathematics 2020-02-19 Asaf Karagila

Geometric morphisms between realizability toposes are studied in terms of morphisms between partial combinatory algebras (pcas). The morphisms inducing geometric morphisms (the {\em computationally dense\/} ones) are seen to be the ones…

Logic · Mathematics 2014-08-19 Eric Faber , Jaap van Oosten

We describe a realizability framework for classical first-order logic in which realizers live in (a model of) typed {\lambda}{\mu}-calculus. This allows a direct interpretation of classical proofs, avoiding the usual negative translation to…

Logic in Computer Science · Computer Science 2017-01-11 Valentin Blot

This paper investigates the conceptual relationship between openness and reproducibility using a model-centric approach, heavily informed by probability theory and statistics. We first clarify the concepts of reliability, auditability,…

Other Statistics · Statistics 2019-10-30 Bert Baumgaertner , Berna Devezer , Erkan O. Buzbas , Luis G. Nardin

We give simple characterizations of the category PAsm(A) of partitioned assemblies, and of the realizability topos RT(A) over a partial combinatory algebra A. This answers the question for an 'extensional characterization' of realizability…

Category Theory · Mathematics 2018-08-06 Jonas Frey

Reproducibility is a key requirement for scientific progress. It allows the reproduction of the works of others, and, as a consequence, to fully trust the reported claims and results. In this work, we argue that, by facilitating…

Information Retrieval · Computer Science 2021-02-02 Alejandro Bellogín , Alan Said

This paper considers the problem of assumptions refinement in the context of unrealizable specifications for reactive systems. We propose a new counterstrategy-guided synthesis approach for GR(1) specifications based on Craig's…

Logic in Computer Science · Computer Science 2018-11-01 Davide G. Cavezza , Dalal Alrajeh

We develop a number of variants of Lifschitz realizability for CZF by building topological models internally in certain realizability models. We use this to show some interesting metamathematical results about constructive set theory with…

Logic · Mathematics 2021-07-01 Michael Rathjen , Andrew Swan

This paper draws distinctions among various concepts related to tipping points, robustness, path dependence, and other properties of system dynamics. For each concept a formal definition is provided that utilizes Markov model…

Adaptation and Self-Organizing Systems · Physics 2008-11-06 Aaron L Bramson

The exploration of pathways and alternative pathways that have a specific function is of interest in numerous chemical contexts. A framework for specifying and searching for pathways has previously been developed, but a focus on which of…

Molecular Networks · Quantitative Biology 2024-12-23 Jakob L. Andersen , Sissel Banke , Rolf Fagerberg , Christoph Flamm , Daniel Merkle , Peter F. Stadler

We show how the language of Krivine's classical realizability may be used to specify various forms of nondeterminism and relate them with properties of realizability models. More specifically, we introduce an abstract notion of…

Logic in Computer Science · Computer Science 2018-06-22 Guillaume Geoffroy

We introduce the notion of implicative algebra, a simple algebraic structure intended to factorize the model constructions underlying forcing and realizability (both in intuitionistic and classical logic). The salient feature of this…

Logic · Mathematics 2020-07-15 Alexandre Miquel

Global protocol specifications are the starting point of top-down verification methodologies, and serve as a blueprint for synthesizing local specifications that guarantee the correctness of distributed implementations. In this work, we…

Formal Languages and Automata Theory · Computer Science 2026-02-11 Elaine Li , Felix Stutz

Although a recent shift has been made in the field of predictive process monitoring to use models from the explainable artificial intelligence field, the evaluation still occurs mainly through performance-based metrics, thus not accounting…

Machine Learning · Computer Science 2023-08-01 Alexander Stevens , Johannes De Smedt

Pre-Requirement Specification traceability is the activity of capturing relations between requirements and their sources, in particular user needs. Requirements are formal technical specifications in the solution space; needs are natural…

Software Engineering · Computer Science 2007-05-23 Ramya Ravichandar , James D. Arthur , Manuel Pérez-Quiñones

We develop realizability models of intensional type theory, based on groupoids, wherein realizers themselves carry non-trivial (non-discrete) homotopical structure. In the spirit of realizability, this is intended to formalize a homotopical…

Logic in Computer Science · Computer Science 2024-05-30 Sam Speight

We introduce a tableau decision method for deciding realizability of specifications expressed in a safety fragment of LTL that includes bounded future temporal operators. Tableau decision procedures for temporal and modal logics have been…

Logic in Computer Science · Computer Science 2022-06-06 Montserrat Hermo , Paqui Lucio , César Sánchez

In this paper we introduce arrow algebras, simple algebraic structures which induce elementary toposes through the tripos-to-topos construction. This includes localic toposes as well as various realizability toposes, in particular, those…

Category Theory · Mathematics 2025-10-13 Benno van den Berg , Marcus Briet

We explain how recent developments in the fields of realisability models for linear logic -- or geometry of interaction -- and implicit computational complexity can lead to a new approach of implicit computational complexity. This…

Logic in Computer Science · Computer Science 2015-07-03 Thomas Seiller

In computability theory and computable analysis, finite programs can compute infinite objects. Presenting a computable object via any program for it, provides at least as much information as presenting the object itself, written on an…

Logic in Computer Science · Computer Science 2014-09-25 Mathieu Hoyrup , Cristobal Rojas