Mario Román

Elena Di Lavore, Jonas Forster, Mario Román

Functor coalgebras capture a wide range of transition systems that must however evolve in discrete steps. We introduce graded coalgebras of graded monads and propose them to model continuous-time transition systems. We develop the theory of graded coalgebras-including graded distributive laws between graded monads-and we give conditions for the existence of terminal coalgebras. We define both branching-time and trace semantics, linking them to recent work on Feller-Dynkin processes. Finally, we develop coalgebraic modal logics for both process semantics and state criteria for invariance and expressivity.

Giovanni de Felice, Elena Di Lavore, Mario Román et al.

We present some categorical investigations into Wittgenstein's language-games, with applications to game-theoretic pragmatics and question-answering in natural language processing.