Filters








11 Hits in 4.1 sec

Natural Factors of the Muchnik Lattice Capturing IPC [article]

Rutger Kuyper
2013 arXiv   pre-print
We give natural examples of factors of the Muchnik lattice which capture intuitionistic propositional logic (IPC), arising from the concepts of lowness, 1-genericity, hyperimmune-freeness and computable  ...  This provides a purely computational semantics for IPC.  ...  The author thanks Sebastiaan Terwijn for helpful discussions on the subject and for suggesting some of the classes studied above.  ... 
arXiv:1210.6538v2 fatcat:eslvk5spefhungpqod7oaw45ya

Natural factors of the Medvedev lattice capturing IPC

Rutger Kuyper
2014 Archive for Mathematical Logic  
Skvortsova showed that there is a factor of the Medvedev lattice which captures intuitionistic propositional logic (IPC).  ...  We also show that for every non-trivial factor of the Medvedev lattice its theory is contained in Jankov's logic, the deductive closure of IPC plus the weak law of the excluded middle.  ...  Acknowledgements The author thanks Sebastiaan Terwijn for helpful discussions on the subject. Furthermore, the author thanks the anonymous referees for their many useful comments.  ... 
doi:10.1007/s00153-014-0393-8 fatcat:muqi6fufdrhajddlcahke5ea4m

Intuitionistic Logic and Muchnik Degrees [article]

Andrea Sorbi, Sebastiaan A. Terwijn
2010 arXiv   pre-print
We prove that there is a factor of the Muchnik lattice that captures intuitionistic propositional logic. This complements a now classic result of Skvortsova for the Medvedev lattice.  ...  The lattice of Medvedev degrees is called the Medvedev lattice, denoted by M; the lattice of Muchnik degrees is called the Muchnik lattice, denoted by M w .  ...  The goal of this paper is to show that there are initial segments of the Muchnik lattice, in which the set of valid propositional sentences coincides with IPC.  ... 
arXiv:1003.4489v1 fatcat:bi25jwzbhbee3jvph3tyc2zxce

Constructive Logic and the Medvedev Lattice

Sebastiaan A. Terwijn
2006 Notre Dame Journal of Formal Logic  
We study the connection between factors of the Medvedev lattice and constructive logic.  ...  The algebraic properties of these factors determine logics lying in between intuitionistic propositional logic and the logic of the weak law of the excluded middle (also known as De Morgan, or Jankov logic  ...  Finally we would like to thank an anonymous referee for various useful comments and a simplification of the proof of Theorem 4.5.  ... 
doi:10.1305/ndjfl/1143468312 fatcat:xaedrfl5wffwrbrrttkmdzl2ym

Levels of uniformity [article]

Rutger Kuyper
2015 arXiv   pre-print
We introduce a hierarchy of degree structures between the Medvedev and Muchnik lattices which allow varying amounts of non-uniformity.  ...  We use these structures to introduce the notion of the uniformity of a Muchnik reduction, which expresses how uniform a reduction is.  ...  This discussion is what introduced the author to the work of Higuchi and Kihara [4, 5] , which was the main motivation for the author to study the topics discussed in this paper.  ... 
arXiv:1505.03675v1 fatcat:stzrzra5vjcpbedsheh22lcd5m

The Medvedev lattice of computably closed sets

Sebastiaan A. Terwijn
2005 Archive for Mathematical Logic  
Simpson introduced the lattice P of Π 0 1 classes under Medvedev reducibility. Questions regarding completeness in P are related to questions about measure and randomness.  ...  We also discuss properties of the class of PA-complete sets that are relevant in this context.  ...  We are grateful to Andrea Sorbi for providing us with several pointers to the literature about the Medvedev lattice. We also thank Rosalie Iemhoff for helpful remarks concerning intuitionistic logic.  ... 
doi:10.1007/s00153-005-0278-y fatcat:mgcvkwzke5er3efbkn5hvz23wi

First-Order Logic in the Medvedev Lattice

Rutger Kuyper
2015 Studia Logica: An International Journal for Symbolic Logic  
Skvortsova's result that there is a factor of the Medvedev lattice characterising intuitionistic propositional logic.  ...  This was later formalised by Medvedev and Muchnik as what has come to be called the Medvedev and Muchnik lattices.  ...  Thus, Skortsova's result tells us that there is a principal factor of the Medvedev lattice which captures exactly intuitionistic propositional logic.  ... 
doi:10.1007/s11225-015-9615-2 fatcat:uye36lm7abcojmf5k6zn3barvm

Report from Dagstuhl Seminar 13311 Duality in Computer Science

Mai Gehrke, Jean-Eric Pin, Victor Selivanov, Dieter Spreen, Mai Gehrke, Jean-Eric Pin, Victor Selivanov, Dieter Spreen, Mai Gehrke, Jean-Eric Pin, Victor Selivanov, Dieter Spreen (+1 others)
Dagstuhl Reports   unpublished
This report collects the ideas that were presented and discussed during the course of the seminar.  ...  Ershov Institute-Novosibirsk, RU, vseliv@iis.nsk.su 4 Universität Siegen, DE, spreen@math.uni-siegen.de Abstract Duality allows one to move between the two worlds: the world of certain algebras of properties  ...  Therefore this does not completely give us computational semantics for IPC. It turns out that, at least in the case of the Muchnik lattice, there are also natural factors which characterise IPC.  ... 
fatcat:sdl2vzphsjdsfdlpzuiugk3mjy

Computer Science in High Performance Sport-Applications and Implications for Professional Coaching (Dagstuhl Seminar 13272)

Benjamin Doerr, Nikolaus Hansen, Jonathan Shapiro, L Darrell, Whitley, Koen Lemmink, Stuart Morgan, Jaime Sampaio3, Dietmar Saupe, Mai Gehrke, Jean-Eric Pin, Victor Selivanov (+5 others)
2013 unpublished
We acknowledge support from the Strategic Basic Research (SBO) Programme of the Flemish Agency for Innovation through Science and Technology (IWT) in the context of the SPION project 6 under grant agreement  ...  Therefore this does not completely give us computational semantics for IPC. It turns out that, at least in the case of the Muchnik lattice, there are also natural factors which characterise IPC.  ...  exactly captures IPC.  ... 
fatcat:yg5vvzymuvcibirco4nawxes4m

Computability in constructive type theory [article]

Yannick Forster, Universität Des Saarlandes
2022
of the Coq Library of Undecidability Proofs.  ...  I feel that the final product of the journey -this thesis -is a result of a big collaboration of all the people who journeyed with me. Ein riesiger Dank geht an meine Familie.  ...  The proof of this theorem in Bauer's setting captures indeed exactly the essence of Rice's theorem, but unfortunately the statement of the theorem becomes a classical triviality: If all functions A→A have  ... 
doi:10.22028/d291-35758 fatcat:deb5muacebhsnnmk5p25mgc7ia

A Framework for Intelligent Speculative Compiler Optimizations and its Application to Memory Accesses [article]

Lars Alvincz, Technische Universität Berlin, Technische Universität Berlin, Sabine Glesner
2009
The conceptual framework is applicable to a wide range of program behavior and program optimizations. In the second part of [...]  ...  With that, we can precisely predict the behavior of arbitrary programs by selecting the most appropriate heuristics.  ...  ., the unroll factor for loop unrolling.  ... 
doi:10.14279/depositonce-2255 fatcat:uaasupjzvbbbvl4d52hbcvl6um