8 found
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  1.  30
    Foundations of Nominal Techniques: Logic and Semantics of Variables in Abstract Syntax.Murdoch J. Gabbay - 2011 - Bulletin of Symbolic Logic 17 (2):161-229.
    We are used to the idea that computers operate on numbers, yet another kind of data is equally important: the syntax of formal languages, with variables, binding, and alpha-equivalence. The original application of nominal techniques, and the one with greatest prominence in this paper, is to reasoning on formal syntax with variables and binding. Variables can be modelled in many ways: for instance as numbers (since we usually take countably many of them); as links (since they may `point' to a (...)
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  2.  20
    Finite and Infinite Support in Nominal Algebra and Logic: Nominal Completeness Theorems for Free.Murdoch J. Gabbay - 2012 - Journal of Symbolic Logic 77 (3):828-852.
    By operations on models we show how to relate completeness with respect to permissivenominal models to completeness with respect to nominal models with finite support. Models with finite support are a special case of permissive-nominal models, so the construction hinges on generating from an instance of the latter, some instance of the former in which sufficiently many inequalities are preserved between elements. We do this using an infinite generalisation of nominal atoms-abstraction. The results are of interest in their own right, (...)
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  3.  14
    Fresh Logic: Proof-Theory and Semantics for FM and Nominal Techniques.Murdoch J. Gabbay - 2007 - Journal of Applied Logic 5 (2):356-387.
  4.  3
    Permissive Nominal Terms and Their Unification: An Infinite, Co-Infinite Approach to Nominal Techniques (Vol 8, Pg 769, 2010). [REVIEW]Gilles Dowek, Murdoch J. Gabbay & Dominic Mulligan - 2012 - Logic Journal of the IGPL 20 (1):769-822.
    Nominal terms extend first-order terms with binding. They lack some properties of first- and higher-order terms: Terms must be reasoned about in a context of ‘freshness assumptions’; it is not always possible to ‘choose a fresh variable symbol’ for a nominal term; it is not always possible to ‘α-convert a bound variable symbol’ or to ‘quotient by α-equivalence’; the notion of unifier is not based just on substitution. Permissive nominal terms closely resemble nominal terms but they recover these properties, and (...)
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  5.  11
    Representation and Duality of the Untyped Λ-Calculus in Nominal Lattice and Topological Semantics, with a Proof of Topological Completeness.Murdoch J. Gabbay & Michael Gabbay - 2017 - Annals of Pure and Applied Logic 168 (3):501-621.
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  6.  6
    Denotation of Contextual Modal Type Theory : Syntax and Meta-Programming.Murdoch J. Gabbay & Aleksandar Nanevski - 2013 - Journal of Applied Logic 11 (1):1-29.
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  7. Some Formal Considerations on Gabbay's Restart Rule in Natural Deduction and Goal-Directed Reasoning.Michael Gabbay & Murdoch J. Gabbay - 2005 - In We Will Show Them! Essays in Honour of Dov Gabbay, volume 1. pp. 701-null.
    In this paper we make some observations about Natural Deduction derivations [Prawitz, 1965, van Dalen, 1986, Bell and Machover, 1977]. We assume the reader is familiar with it and with proof-theory in general. Our development will be simple, even simple-minded, and concrete. However, it will also be evident that general ideas motivate our examples, and we think both our specific examples and the ideas behind them are interesting and may be useful to some readers. In a sentence, the bare technical (...)
     
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  8.  2
    Unity in Nominal Equational Reasoning: The Algebra of Equality on Nominal Sets.Murdoch J. Gabbay - 2012 - Journal of Applied Logic 10 (2):199-217.
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