Presenting functors on many-sorted varieties and applications

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 g 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. Contents

• Type: Journal
• Year: 2010
• Where: IANDC
• Authors: Alexander Kurz, Daniela Petrisan
• Keywords: IANDC 2010, Logics, Many-sorted Case, Straightforward Generalisation