Other Computer Engineering Commons^™

Strongly Complete Logics For Coalgebras, Alexander Kurz, Jiří Rosický

Engineering Faculty Articles and Research

Coalgebras for a functor model different types of transition systems in a uniform way. This paper focuses on a uniform account of finitary logics for set-based coalgebras. In particular, a general construction of a logic from an arbitrary set-functor is given and proven to be strongly complete under additional assumptions. We proceed in three parts.

Part I argues that sifted colimit preserving functors are those functors that preserve universal algebraic structure. Our main theorem here states that a functor preserves sifted colimits if and only if it has a finitary presentation by operations and equations. Moreover, the presentation of the …

Equational Coalgebraic Logic, Alexander Kurz, Raul Leal

Engineering Faculty Articles and Research

Coalgebra develops a general theory of transition systems, parametric in a functor T; the functor T specifies the possible one-step behaviours of the system. A fundamental question in this area is how to obtain, for an arbitrary functor T, a logic for T-coalgebras. We compare two existing proposals, Moss’s coalgebraic logic and the logic of all predicate liftings, by providing one-step translations between them, extending the results in [21] by making systematic use of Stone duality. Our main contribution then is a novel coalgebraic logic, which can be seen as an equational axiomatization of Moss’s logic. The three logics are …