Presenting functors on many-sorted varieties and applications |
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Authors: | Alexander Kurz Daniela Petrişan |
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Affiliation: | Department of Computer Science, University of Leicester, UK;Technische Universität Braunschweig, Institut für Theoretische Informatik, Mühlenpfordtstr. 22-23, D-38106 Braunschweig, Germany;Imperial College London, Department of Computing, 180 Queen’s Gate, London SW7 2AZ, United Kingdom |
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Abstract: | This paper studies several applications of the notion of a presentation of a functor by operations and equations. We show that the technically straightforward generalisation of this notion from the one-sorted to the many-sorted case has several interesting consequences. First, it can be applied to give equational logic for the binding algebras modelling abstract syntax. Second, it provides a categorical approach to algebraic semantics of first-order logic. Third, this notion links the uniform treatment of logics for coalgebras of an arbitrary type T with concrete syntax and proof systems. Analysing the many-sorted case is essential for modular completeness proofs of coalgebraic logics. |
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