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Exploring the Boundaries of Monad Tensorability on Set

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&nbsp;[&hellip;]

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Generic Modal Cut Elimination Applied to Conditional Logics

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&nbsp;[&hellip;]

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Efficient and Modular Coalgebraic Partition Refinement

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&nbsp;[&hellip;]

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Quasilinear-time Computation of Generic Modal Witnesses for Behavioural Inequivalence

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&nbsp;[&hellip;]

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Characteristic Logics for Behavioural Hemimetrics via Fuzzy Lax Extensions

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&nbsp;[&hellip;]

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Coalgebraic Satisfiability Checking for Arithmetic $\mu$-Calculi

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&nbsp;[&hellip;]

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