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Other Mathematics

Modal Logic

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Coalgebraic Logics (Dagstuhl Seminar 12411), Ernst-Erich Doberkat, Alexander Kurz Jan 2012

Coalgebraic Logics (Dagstuhl Seminar 12411), Ernst-Erich Doberkat, Alexander Kurz

Engineering Faculty Articles and Research

This report documents the program and the outcomes of Dagstuhl Seminar 12411 “Coalgebraic Logics”. The seminar deals with recent developments in the area of coalgebraic logic, a branch of logics which combines modal logics with coalgebraic semantics. Modal logic finds its uses when reasoning about behavioural and temporal properties of computation and communication, coalgebras have evolved into a general theory of systems. Consequently, it is natural to combine both areas for a mathematical description of system specification. Coalgebraic logics are closely related to the broader categories semantics/formal methods and verification/logic.


Functorial Coalgebraic Logic: The Case Of Many-Sorted Varieties, Alexander Kurz, Daniela Petrişan Jan 2008

Functorial Coalgebraic Logic: The Case Of Many-Sorted Varieties, Alexander Kurz, Daniela Petrişan

Engineering Faculty Articles and Research

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 ...