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Functorial coalgebraic logic: The case of many-sorted varieties

By Alexander Kurz


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 presheaf 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

Topics: Coalgebra, Modal Logic, Stone Duality, Coalgebraic Logic, Sifted Colimits, Variety, Universal Algebra, Presentation by Operations and Equations
Year: 2011
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