On a Categorical Framework for Coalgebraic Modal Logic

Chen, Liang-Ting; Jung, Achim

doi:10.1016/j.entcs.2014.10.007

Cited by 6 publications

(4 citation statements)

References 15 publications

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“…We briefly present the required theory of steps, first termed as such in [41]. This structure occurs already in work on coalgebraic modal logic [35,14,40,32,17,38] where a step gives the one-step semantics of a logic. In existing work, only what we call a forward step is considered.…”

Section: Forward and Backward Stepsmentioning

confidence: 99%

Preservation and Reflection of Bisimilarity via Invertible Steps

Turkenburg¹,

Kupke²,

Rot³

et al. 2023

Lecture Notes in Computer Science

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In the theory of coalgebras, distributive laws give a general perspective on determinisation and other automata constructions. This perspective has recently been extended to include so-called weak distributive laws, covering several constructions on state-based systems that are not captured by regular distributive laws, such as the construction of a belief-state transformer from a probabilistic automaton, and ultrafilter extensions of Kripke frames.In this paper we first observe that weak distributive laws give rise to the more general notion of what we call an invertible step: a pair of natural transformations that allows to move coalgebras along an adjunction. Our main result is that part of the construction induced by an invertible step preserves and reflects bisimilarity. This covers results that have previously been shown by hand for the instances of ultrafilter extensions and belief-state transformers.

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Section: Forward and Backward Stepsmentioning

confidence: 99%

Preservation and Reflection of Bisimilarity via Invertible Steps

Turkenburg¹,

Kupke²,

Rot³

et al. 2023

Lecture Notes in Computer Science

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“…The assumptions guarantee that the factorisation system in C lifts to the category CoAlg(F ) (cf. [Adá05,Che14]). The claim then follows from Lemma 2.17.…”

Section: 2mentioning

confidence: 99%

Limits in categories of Vietoris coalgebras

Hofmann¹,

Neves²,

Nora³

2018

Math. Struct. Comp. Sci.

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Motivated by the need to reason about hybrid systems, we study limits in categories of coalgebras whose underlying functor is a Vietoris polynomial one -intuitively, the topological analogue of a Kripke polynomial functor. Among other results, we prove that every Vietoris polynomial functor admits a final coalgebra if it respects certain conditions concerning separation axioms and compactness.When the functor is restricted to some of the categories induced by these conditions the resulting categories of coalgebras are even complete.As a practical application, we use these developments in the specification and analysis of nondeterministic hybrid systems, in particular to obtain suitable notions of stability, and behaviour.

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“…Morphisms of logics apppear in [5], where the category of logics and morphisms between them is studied. The examples in [5] involve a translation of syntax determined by τ . Our main interest in morphisms of logics is cases where τ = id.…”

Section: 2mentioning

confidence: 99%

“…Such compositions of logics appear in [14] and were studied in a slightly more concrete setting in [9,32]. In [5,Lemma 3.12], it is shown how to (horizontally) compose morphisms of logics, turning ⊚ into a bifunctor. We shall be interested in the case where the logic for T has a trivial syntax; in other words, where N = Id.…”

Section: Forgetful Logicsmentioning

confidence: 99%

Coalgebraic trace semantics via forgetful logics

Klin¹,

Rot²

2017

Logical Methods in Computer Science

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Abstract. We use modal logic as a framework for coalgebraic trace semantics, and show the flexibility of the approach with concrete examples such as the language semantics of weighted, alternating and tree automata, and the trace semantics of generative probabilistic systems. We provide a sufficient condition under which a logical semantics coincides with the trace semantics obtained via a given determinization construction. Finally, we consider a condition that guarantees the existence of a canonical determinization procedure that is correct with respect to a given logical semantics. That procedure is closely related to Brzozowski's minimization algorithm.

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On a Categorical Framework for Coalgebraic Modal Logic

Cited by 6 publications

References 15 publications

Preservation and Reflection of Bisimilarity via Invertible Steps

Preservation and Reflection of Bisimilarity via Invertible Steps

Limits in categories of Vietoris coalgebras

Coalgebraic trace semantics via forgetful logics

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