Functorial Coalgebraic Logic: The Case of Many-sorted Varieties

Following earlier work, a modal logic for T-coalgebras is a functor L on a suitable variety. Syntax and proof system of the logic are given by presentations of the functor. This paper makes two contributions. First, a previous result characterizing those functors that have presentations is generalized from endofunctors on one-sorted varieties to functors between many-sorted varieties. This yields an equational logic for the semantics of higher-order abstract syntax. As another application, we show how the move to functors between many-sorted varieties allows to modularly combine syntax and proof systems of different logics. Second, we show how to associate to any set-functor T a complete (finitary) logic L consisting of modal operators and Boolean connectives.

• Type: Journal
• Year: 2008
• Where: ENTCS
• Authors: Alexander Kurz, Daniela Petrisan
• Keywords: ENTCS 2008, Functors, Logic, Many-sorted Varieties