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Model Theory and Proof Theory of Coalgebraic Predicate Logic

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&nbsp;[&hellip;]

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Unguarded Recursion on Coinductive Resumptions

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&nbsp;[&hellip;]

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Bootstrapping Inductive and Coinductive Types in HasCASL

Lutz Schröder.

We discuss the treatment of initial datatypes and final process types in the wide-spectrum language HasCASL. In particular, we present specifications that illustrate how datatypes and process types arise as bootstrapped concepts using HasCASL's type class mechanism, and we describe constructions of&nbsp;[&hellip;]

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Guarded and Unguarded Iteration for Generalized Processes

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&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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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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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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