Results 21 to 30 of about 5,869 (280)
Realizability algebras: a program to well order R [PDF]
Logical Methods in Computer Science, 2011 The theory of classical realizability is a framework in which we can develop the proof-program correspondence. Using this framework, we show how to transform into programs the proofs in classical analysis with dependent choice and the existence of a well
Jean-Louis Krivine
doaj +1 more source
On Goodman Realizability [PDF]
Notre Dame Journal of Formal Logic, 2019 25 pages. Updated.
openaire +5 more sources
Realizability Without Symmetry [PDF]
, 2021 In categorical realizability, it is common to construct categories of assemblies and modest sets from applicative structures. In this paper, we introduce several classes of applicative structures and apply the categorical realizability construction to ...
Tomita, Haruka
core +1 more source
On new universal realizability criteria
Special Matrices, 2022 A list Λ={λ1,λ2,…,λn}\Lambda =\left\{{\lambda }_{1},{\lambda }_{2},\ldots ,{\lambda }_{n}\right\} of complex numbers is said to be realizable if it is the spectrum of an entrywise nonnegative matrix and is said to be universally realizable (UR), if it is
Arrieta Luis E., Soto Ricardo L.
doaj +1 more source
On completeness and parametricity in the realizability semantics of System F [PDF]
Logical Methods in Computer Science, 2019 We investigate completeness and parametricity for a general class of realizability semantics for System F defined in terms of closure operators over sets of $\lambda$-terms.
Paolo Pistone
doaj +1 more source
REALIZING REALIZABILITY RESULTS WITH CLASSICAL CONSTRUCTIONS [PDF]
The Bulletin of Symbolic Logic, 2019 AbstractJ. 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 condition for preserving well ordered, and other particular type of choice, in the general settings of ...
openaire +4 more sources
Detecting Unrealizability of Distributed Fault-tolerant Systems [PDF]
Logical Methods in Computer Science, 2015 Writing formal specifications for distributed systems is difficult. Even simple consistency requirements often turn out to be unrealizable because of the complicated information flow in the distributed system: not all information is available in every ...
Bernd Finkbeiner, Leander Tentrup
doaj +1 more source
Existential witness extraction in classical realizability and via a negative translation [PDF]
Logical Methods in Computer Science, 2011 We show how to extract existential witnesses from classical proofs using Krivine's classical realizability---where classical proofs are interpreted as lambda-terms with the call/cc control operator.
Alexandre Miquel
doaj +1 more source
Instance reducibility and Weihrauch degrees [PDF]
Logical Methods in Computer Science, 2022 We identify a notion of reducibility between predicates, called instance reducibility, which commonly appears in reverse constructive mathematics. The notion can be generally used to compare and classify various principles studied in reverse constructive
Andrej Bauer
doaj +1 more source
On the realizability of the critical points of a realizable list
Linear Algebra and its Applications, 2018 The nonnegative inverse eigenvalue problem (NIEP) is to characterize the spectra of entrywise nonnegative matrices. A finite multiset of complex numbers is called realizable if it is the spectrum of an entrywise nonnegative matrix. Monov conjectured that the k\textsuperscript{th}-moments of the list of critical points of a realizable list are ...
Sarah L. Hoover +3 more
openaire +4 more sources