Journal of Symbolic Logic 77 (3):828-852 (2012)
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, but also, we factor the mathematics so as to maximise the chances that it could be used off-the-shelf for other nominal reasoning systems too. Models with infinite support can be easier to work with, so it is useful to have a semi-automatic theorem to transfer results from classes of infinitely-supported nominal models to the more restricted class of models with finite support. In conclusion, we consider different permissive-nominal syntaxes and nominal models and discuss how they relate to the results proved here
|Keywords||permissive-nominal techniques infinite support finite support, nominal algebra, permissive-nominal logic, completeness infinite atoms-abstraction|
|Categories||categorize this paper)|
References found in this work BETA
Foundations of Nominal Techniques: Logic and Semantics of Variables in Abstract Syntax.Murdoch J. Gabbay - 2011 - Bulletin of Symbolic Logic 17 (2):161-229.
Permissive Nominal Terms and Their Unification: An Infinite, Co-Infinite Approach to Nominal Techniques.G. Dowek, M. J. Gabbay & D. P. Mulligan - 2010 - Logic Journal of the IGPL 18 (6):769-822.
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.
Citations of this work BETA
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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