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14
Finite and infinite support in nominal algebra and logic: nominal completeness theorems for free
 Journal of Symbolic Logic
, 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 permissivenominal models, so the construction hinges on generating from an insta ..."
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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 permissivenominal 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 atomsabstraction. 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 offtheshelf for other nominal reasoning systems too. Models with infinite support can be easier to work with, so it is useful to have a semiautomatic theorem to transfer results from classes of infinitelysupported nominal models to the more restricted class of models with finite support. In conclusion, we consider different permissivenominal syntaxes and nominal models and discuss how they relate to the results proved here.
Principal Types for Nominal Theories
"... Abstract. We define rank 1 polymorphic types for nominal rewrite rules and equations. Typing environments type atoms, variables, and function symbols, and since we follow a Currystyle approach there is no need to fully annotate terms with types. Our system has principal types, and we give rule and ..."
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Abstract. We define rank 1 polymorphic types for nominal rewrite rules and equations. Typing environments type atoms, variables, and function symbols, and since we follow a Currystyle approach there is no need to fully annotate terms with types. Our system has principal types, and we give rule and axiom formats to guarantee preservation of types under both rewriting and equality reasoning. This is nontrivial because substitution does not avoid capture, so a substituted symbol can—if we are not careful—appear in inconsistent typing contexts.
www.gabbay.org.uk
"... We present a model of games based on nominal sequences, which generalise sequences with atoms and a new notion of coabstraction. This gives a new, precise, and compositional mathematical treatment of justification pointers in game semantics. Keywords: Game semantics, nominal sets, nominal abstractio ..."
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We present a model of games based on nominal sequences, which generalise sequences with atoms and a new notion of coabstraction. This gives a new, precise, and compositional mathematical treatment of justification pointers in game semantics. Keywords: Game semantics, nominal sets, nominal abstraction and coabstraction, equivariance
Nominal Henkin Semantics: simplytyped
"... lambdacalculus models in nominal sets ..."
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Consistency of Quine’s New Foundations using nominal techniques
"... We build a model in nominal sets for TST+; typed set theory with typical ambiguity. It is known that this is equivalent to the consistency of Quine’s New Foundations. The model is in the spirit of a representation theorem and is built out of points, in the sense of filters of predicates. The model i ..."
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We build a model in nominal sets for TST+; typed set theory with typical ambiguity. It is known that this is equivalent to the consistency of Quine’s New Foundations. The model is in the spirit of a representation theorem and is built out of points, in the sense of filters of predicates. The model is absolute, meaning that variables are interpreted directly as atoms of the nominal theory. Predicates are interpreted as possibly nonequivariant sets of points, and sets are interpreted using nominal atomsabstraction, which behaves in this
connecting the logic of permutation models with the logic
"... From nominal sets binding to functions and λabstraction: ..."
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Unity in nominal equational reasoning: the algebra of
"... equality on nominal sets ..."
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