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  1. Completeness and Herbrand Theorems for Nominal Logic.James Cheney - 2006 - Journal of Symbolic Logic 71 (1):299 - 320.
    Nominal logic is a variant of first-order logic in which abstract syntax with names and binding is formalized in terms of two basic operations: name-swapping and freshness. It relies on two important principles: equivariance (validity is preserved by name-swapping), and fresh name generation ("new" or fresh names can always be chosen). It is inspired by a particular class of models for abstract syntax trees involving names and binding, drawing on ideas from Fraenkel-Mostowski set theory: finite-support models in which each value (...)
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  • [Introduction].Wilfrid Hodges - 1986 - Journal of Symbolic Logic 51 (4):865.
    We consider two formalisations of the notion of a compositionalsemantics for a language, and find some equivalent statements in termsof substitutions. We prove a theorem stating necessary and sufficientconditions for the existence of a canonical compositional semanticsextending a given partial semantics, after discussing what features onewould want such an extension to have. The theorem involves someassumptions about semantical categories in the spirit of Husserl andTarski.
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  • Meta-variables as infinite lists in nominal terms unification and rewriting.M. J. Gabbay - 2012 - Logic Journal of the IGPL 20 (6):967-1000.
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  • 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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  • 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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  • Permissive nominal terms and their unification: an infinite, co-infinite approach to nominal techniques.Gilles Dowek, Murdoch J. Gabbay & Dominic P. Mulligan - 2010 - Logic Journal of the IGPL 18 (6):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 in (...)
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