17 found
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  1.  67
    From If to Bi.Samson Abramsky & Jouko Väänänen - 2009 - Synthese 167 (2):207 - 230.
    We take a fresh look at the logics of informational dependence and independence of Hintikka and Sandu and Väänänen, and their compositional semantics due to Hodges. We show how Hodges’ semantics can be seen as a special case of a general construction, which provides a context for a useful completeness theorem with respect to a wider class of models. We shed some new light on each aspect of the logic. We show that the natural propositional logic carried by the semantics (...)
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  2.  13
    Coalgebras, Chu Spaces, and Representations of Physical Systems.Samson Abramsky - 2013 - Journal of Philosophical Logic 42 (3):551-574.
    We investigate the use of coalgebra to represent quantum systems, thus providing a basis for the use of coalgebraic methods in quantum information and computation. Coalgebras allow the dynamics of repeated measurement to be captured, and provide mathematical tools such as final coalgebras, bisimulation and coalgebraic logic. However, the standard coalgebraic framework does not accommodate contravariance, and is too rigid to allow physical symmetries to be represented. We introduce a fibrational structure on coalgebras in which contravariance is represented by indexing. (...)
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  3. Handbook of Logic in Computer Science.Samson Abramsky, Dov M. Gabbay & Thomas S. E. Maibaum - 1992
     
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  4.  6
    Domain Theory in Logical Form.Samson Abramsky - 1991 - Annals of Pure and Applied Logic 51 (1-2):1-77.
    Abramsky, S., Domain theory in logical form, Annals of Pure and Applied Logic 51 1–77. The mathematical framework of Stone duality is used to synthesise a number of hitherto separate developments in theoretical computer science.• Domain theory, the mathematical theory of computation introduced by Scott as a foundation for detonational semantics• The theory of concurrency and systems behaviour developed by Milner, Hennesy based on operational semantics.• Logics of programsStone duality provides a junction between semantics and logics . Moreover, the underlying (...)
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  5.  46
    Big Toy Models: Representing Physical Systems as Chu Spaces.Samson Abramsky - 2012 - Synthese 186 (3):697 - 718.
    We pursue a model-oriented rather than axiomatic approach to the foundations of Quantum Mechanics, with the idea that new models can often suggest new axioms. This approach has often been fruitful in Logic and Theoretical Computer Science. Rather than seeking to construct a simplified toy model, we aim for a 'big toy model', in which both quantum and classical systems can be faithfully represented—as well as, possibly, more exotic kinds of systems. To this end, we show how Chu spaces can (...)
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  6. Relational Hidden Variables and Non-Locality.Samson Abramsky - 2013 - Studia Logica 101 (2):411-452.
    We use a simple relational framework to develop the key notions and results on hidden variables and non-locality. The extensive literature on these topics in the foundations of quantum mechanics is couched in terms of probabilistic models, and properties such as locality and no-signalling are formulated probabilistically. We show that to a remarkable extent, the main structure of the theory, through the major No-Go theorems and beyond, survives intact under the replacement of probability distributions by mere relations.
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  7.  68
    Logical Bell Inequalities.Samson Abramsky & Lucien Hardy - 2012 - Physical Review A 85:062114-1 - 062114-11.
    Bell inequalities play a central role in the study of quantum nonlocality and entanglement, with many applications in quantum information. Despite the huge literature on Bell inequalities, it is not easy to find a clear conceptual answer to what a Bell inequality is, or a clear guiding principle as to how they may be derived. In this paper, we introduce a notion of logical Bell inequality which can be used to systematically derive testable inequalities for a very wide variety of (...)
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  8.  26
    Socially Responsive, Environmentally Friendly Logic.Samson Abramsky - 2006 - Acta Philosophica Fennica 78:17.
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  9.  6
    A Game Semantics for Generic Polymorphism.Samson Abramsky & Radha Jagadeesan - 2005 - Annals of Pure and Applied Logic 133 (1-3):3-37.
    Genericity is the idea that the same program can work at many different data types. Longo, Milstead and Soloviev proposed to capture the inability of generic programs to probe the structure of their instances by the following equational principle: if two generic programs, viewed as terms of type , are equal at any given instance A[T], then they are equal at all instances. They proved that this rule is admissible in a certain extension of System F, but finding a semantically (...)
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  10.  3
    Linear Realizability and Full Completeness for Typed Lambda-Calculi.Samson Abramsky & Marina Lenisa - 2005 - Annals of Pure and Applied Logic 134 (2-3):122-168.
    We present the model construction technique called Linear Realizability. It consists in building a category of Partial Equivalence Relations over a Linear Combinatory Algebra. We illustrate how it can be used to provide models, which are fully complete for various typed λ-calculi. In particular, we focus on special Linear Combinatory Algebras of partial involutions, and we present PER models over them which are fully complete, inter alia, w.r.t. the following languages and theories: the fragment of System F consisting of ML-types, (...)
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  11.  21
    Arrow’s Theorem by Arrow Theory. [REVIEW]Samson Abramsky - 2015 - In Andrés Villaveces, Roman Kossak, Juha Kontinen & Åsa Hirvonen (eds.), Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics. De Gruyter. pp. 15-30.
  12.  5
    New Orleans Marriott and Sheraton New Orleans Hotels New Orleans, LA January 8–9, 2011.Jeremy Avigad, Ulrich W. Kohlenbach, Henry Towsner, Samson Abramsky, Andreas Blass, Larry Moss, Alf Onshuus Nino, Patrick Speissegger, Juris Steprans & Monica VanDieren - 2012 - Bulletin of Symbolic Logic 18 (1).
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  13.  3
    Foreword.Samson Abramsky & Dan R. Ghica - 2013 - Annals of Pure and Applied Logic 164 (11):1037.
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  14.  3
    National Park of Itatiaia, Rio de Janeiro, Brazil, May 25–28, 1999.Samson Abramsky, John Baldwin, Craig Boutilier, Daniel Leivant & Francisco Miraglia - 1999 - Bulletin of Symbolic Logic 5 (3).
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  15. Logic and Categories as Tools for Building Theories.Samson Abramsky - 2010 - Journal of the Indian Council of Philosophical Research 27 (1).
     
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  16. Nijmegen, The Netherlands July 27–August 2, 2006.Rodney Downey, Ieke Moerdijk, Boban Velickovic, Samson Abramsky, Marat Arslanov, Harvey Friedman, Martin Goldstern, Ehud Hrushovski, Jochen Koenigsmann & Andy Lewis - 2007 - Bulletin of Symbolic Logic 13 (2).
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  17. Visions of Computer Science.Erol Gelenbe, Samson Abramsky & Vladimiro Sassone (eds.) - 2008 - British Computer Society.