9 results
Nathan Bowler ; Sergey Goncharov ; Paul Blain Levy ; Lutz Schröder.
We study a composition operation on monads, equivalently presented as large equational theories. Specifically, we discuss the existence of tensors, which are combinations of theories that impose mutual commutation of the operations from the component theories. As such, they extend the sum of two […]
Published on September 18, 2013
Sergey Goncharov ; Lutz Schröder ; Christoph Rauch ; Maciej Piróg.
Models of iterated computation, such as (completely) iterative monads, often depend on a notion of guardedness, which guarantees unique solvability of recursive equations and requires roughly that recursive calls happen only under certain guarding operations. On the other hand, many models of […]
Published on July 4, 2019
Thorsten Wißmann ; Ulrich Dorsch ; Stefan Milius ; Lutz Schröder.
We present a generic partition refinement algorithm that quotients coalgebraic systems by behavioural equivalence, an important task in system analysis and verification. Coalgebraic generality allows us to cover not only classical relational systems but also, e.g. various forms of weighted systems […]
Published on January 31, 2020
Dirk Pattinson ; Lutz Schröder.
We develop a general criterion for cut elimination in sequent calculi for propositional modal logics, which rests on absorption of cut, contraction, weakening and inversion by the purely modal part of the rule system. Our criterion applies also to a wide variety of logics outside the realm of normal […]
Published on March 17, 2011
Tadeusz Litak ; Dirk Pattinson ; Katsuhiko Sano ; Lutz Schröder.
We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras. We discuss axiomatization and completeness results for several natural classes of such […]
Published on March 20, 2018
Sergey Goncharov ; Lutz Schröder ; Christoph Rauch ; Julian Jakob.
We study a model of side-effecting processes obtained by starting from a monad modelling base effects and adjoining free operations using a cofree coalgebra construction; one thus arrives at what one may think of as types of non-wellfounded side-effecting trees, generalizing the infinite resumption […]
Published on August 27, 2018
Paul Wild ; Lutz Schröder.
In systems involving quantitative data, such as probabilistic, fuzzy, or metric systems, behavioural distances provide a more fine-grained comparison of states than two-valued notions of behavioural equivalence or behaviour inclusion. Like in the two-valued case, the wide variation found in system […]
Published on June 15, 2022
Thorsten Wißmann ; Stefan Milius ; Lutz Schröder.
We provide a generic algorithm for constructing formulae that distinguish behaviourally inequivalent states in systems of various transition types such as nondeterministic, probabilistic or weighted; genericity over the transition type is achieved by working with coalgebras for a set functor in the […]
Published on November 17, 2022
Daniel Hausmann ; Lutz Schröder.
The coalgebraic $\mu$-calculus provides a generic semantic framework for fixpoint logics over systems whose branching type goes beyond the standard relational setup, e.g. probabilistic, weighted, or game-based. Previous work on the coalgebraic $\mu$-calculus includes an exponential-time upper bound […]
Published on July 23, 2024