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Abstract TERMGRAPH 2006 Preliminary Version Implementing Nominal Unification
"... Nominal matching and unification underly the dynamics of nominal rewriting. Urban, Pitts and Gabbay gave a nominal unification algorithm which finds the most general solution to a nominal matching or unification problem, if one exists. Later the algorithm was extended by Fernández and Gabbay to deal ..."
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Nominal matching and unification underly the dynamics of nominal rewriting. Urban, Pitts and Gabbay gave a nominal unification algorithm which finds the most general solution to a nominal matching or unification problem, if one exists. Later the algorithm was extended by Fernández and Gabbay
General Terms
"... Nominal rewriting extends firstorder rewriting with GabbayPitts abstractors: bound entities are named, matching respects αconversion and can be directly implemented thanks to the use of freshness constraints. In this paper we study two extensions to nominal rewriting. First we introduce a quantif ..."
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Nominal rewriting extends firstorder rewriting with GabbayPitts abstractors: bound entities are named, matching respects αconversion and can be directly implemented thanks to the use of freshness constraints. In this paper we study two extensions to nominal rewriting. First we introduce a
2011): Nominal terms and nominal logics: from foundations to metamathematics
 In: Handbook of Philosophical Logic
"... ABSTRACT: Nominal techniques concern the study of names using mathematical semantics. Whereas in much previous work names in abstract syntax were studied, here we will study them in metamathematics. More specifically, we survey the application of nominal techniques to languages for unification, rew ..."
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Cited by 14 (9 self)
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, rewriting, algebra, and firstorder logic. What characterises the languages of this chapter is that they are firstorder in character, and yet they can specify and reason on names. In the languages we develop, it will be fairly straightforward to give firstorder ‘nominal ’ axiomatisations of name
Captureavoiding Substitution as a Nominal Algebra
 Formal Aspects of Computing
, 2008
"... Abstract. Substitution is fundamental to computer science, underlying for example quantifiers in predicate logic and betareduction in the lambdacalculus. So is substitution something we define on syntax on a casebycase basis, or can we turn the idea of ‘substitution ’ into a mathematical objec ..."
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Cited by 15 (5 self)
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ematical object? We exploit the new framework of Nominal Algebra to axiomatise substitution. We prove our axioms sound and complete with respect to a canonical model; this turns out to be quite hard, involving subtle use of results of rewriting and algebra. 1
Extending DLLiteA with (Singleton) Nominals
"... Abstract. In this paper we study the extension of description logics of the DLLite family with singleton nominals, which correspond in OWL 2 to the ObjectHasValue construct. Differently from arbitrary (nonsingleton) nominals, which make query answering intractable in data complexity, we show that b ..."
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that both knowledge base satisfiability and conjunctive query answering stay firstorder rewritable when DLLiteA is extended with singleton nominals. Our technique is based on a practically implementable algorithm based on rewriting rules, in the style of those implemented in current stateoftheart OBDA
Polynomial Disjunctive Datalog Rewritings of Instance Queries in Expressive Description Logics
"... Abstract. Rewriting ontology mediated queries (OMQs) into traditional query languages like FOqueries and Datalog is central for understanding their relative expressiveness, and plays a crucial role in the ongoing efforts to develop OMQ answering tools by reusing existing database technologies. How ..."
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Cited by 1 (1 self)
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DL ALCHI, into polynomialsized disjunctive Datalog programs. The translation is based on a simple gamelike algorithm, and can be extended to accommodate nominals. We can also rewrite OMQs with closedpredicates into Datalog programs with (limited) negation. Closed predicates are useful
unknown title
"... Metavariables as infinite lists in nominal terms unification and rewriting ..."
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Metavariables as infinite lists in nominal terms unification and rewriting
A type system for embedded rewriting languages with associative pattern matching: from theory to practice
, 2011
"... Programmers are often interested in a way to write errorfree programs, i.e. to avoid undesired behaviors. In this context, a type system was conceived as the formal method for specification and proof of programs written in the Tom rewriting language. The Tom programming language is an extension of ..."
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Programmers are often interested in a way to write errorfree programs, i.e. to avoid undesired behaviors. In this context, a type system was conceived as the formal method for specification and proof of programs written in the Tom rewriting language. The Tom programming language is an extension
Under consideration for publication in Formal Aspects of Computing CaptureAvoiding Substitution as a Nominal Algebra
"... Abstract. Substitution is fundamental to the theory of logic and computation. Is substitution something that we define on syntax on a casebycase basis, or can we turn the idea of substitution into a mathematical object? We give axioms for substitution and prove them sound and complete with respect ..."
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with respect to a canonical model. As corollaries we obtain a useful conservativity result, and prove that equalityuptosubstitution is a decidable relation on terms. These results involve subtle use of techniques both from rewriting and algebra. A special feature of our method is the use of nominal
Twolevel Lambdacalculus
 Electron. Notes Theor. Comput. Sci
, 2009
"... Twolevel lambdacalculus is designed to provide a mathematical model of capturing substitution, also called instantiation. Instantiation is a feature of the ‘informal metalevel’; it appears pervasively in specifications of the syntax and semantics of formal languages. The twolevel lambdacalculus ..."
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Cited by 3 (2 self)
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. In doing this we take a step towards longerterm goals of developing a foundation for theoremprovers which directly support reasoning in the style of nominal rewriting and nominal algebra, and towards a mathematics of functions which can bind names in their arguments.
Results 11  20
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