A Coalgebraic Approach to Linear-Time Logics

Cîrstea, Corina

doi:10.1007/978-3-642-54830-7_28

Cited by 13 publications

(28 citation statements)

References 7 publications

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“…In Theorem 6.4 below, we give a sufficient condition for the logical semantics on T B or BT -coalgebras to coincide with a logical semantics on determinized K-coalgebras, for the determinization constructions T κ and T κ . The same condition was recently studied in [8,Lemma 5.11], where it (more precisely, its mate) was proved to hold, under some additional assumptions, if α arises from the algebra µ 1 : T T 1 → T 1 as described in Section 5. First, we prove a general result, in the setting of (6.1), which relates the logical semantics of an H-coalgebra to a logical semantics for the K-coalgebra obtained by applying the liftingT .…”

Section: Determinizationmentioning

confidence: 79%

“…We do not know how to model precisely the standard transformation of alternating automata into nondeterministic ones in our framework. 7. Logics whose mates are isomorphisms Corollary 6.5 provides a sufficient condition for a given determinization procedure to be correct with respect to a forgetful logic.…”

Section: The Conclusion Of the Proof Is Analogous To The Above Case Omentioning

confidence: 99%

“…In a sense, this paper describes the same connection from the perspective of logic. In [8], the framework of [6,7] is rephrased in terms of coalgebraic modal logic. The result is rather similar to the one we considered, with forgetful modalities to resolve branching.…”

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confidence: 99%

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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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Section: Determinizationmentioning

confidence: 79%

Section: The Conclusion Of the Proof Is Analogous To The Above Case Omentioning

confidence: 99%

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Coalgebraic trace semantics via forgetful logics

Klin¹,

Rot²

2017

Logical Methods in Computer Science

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“…Secondly, we will study variations of our coalgebraic framework to monads that carry quantitative information to cover important cases such as probabilistic and weighted transition systems. We expect that we need to switch to a multivalued logic, using for example T (1) as truth value object, as in [3]. In general, we would also like to better understand how our exogenous logics relate to the endogenous coalgebraic logics of [3] and the weakest preconditions arising from state-and-effect triangles in, e.g., [8,9].…”

Section: Resultsmentioning

confidence: 99%

Weak Completeness of Coalgebraic Dynamic Logics

Hansen

Kupke

2015

Electron. Proc. Theor. Comput. Sci.

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We present a coalgebraic generalisation of Fischer and Ladner's Propositional Dynamic Logic (PDL) and Parikh's Game Logic (GL). In earlier work, we proved a generic strong completeness result for coalgebraic dynamic logics without iteration. The coalgebraic semantics of such programs is given by a monad T, and modalities are interpreted via a predicate lifting \^I whose transpose is a monad morphism from T to the neighbourhood monad. In this paper, we show that if the monad T carries a complete semilattice structure, then we can define an iteration construct, and suitable notions of diamond-likeness and box-likeness of predicate-liftings which allows for the definition of an axiomatisation parametric in T, \^I and a chosen set of pointwise program operations. As our main result, we show that if the pointwise operations are "negation-free" and Kleisli composition left-distributes over the induced join on Kleisli arrows, then this axiomatisation is weakly complete with respect to the class of standard models. As special instances, we recover the weak completeness of PDL and of dual-free Game Logic. As a modest new result we obtain completeness for dual-free GL extended with intersection (demonic choice) of games.Comment: In Proceedings FICS 2015, arXiv:1509.0282

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“…where the composite is from (14) and R : X → POMα is given by the current values of R(x, i, j) x,i,j in the algorithm.…”

Section: Algorithmsmentioning

confidence: 99%

Lattice-theoretic progress measures and coalgebraic model checking

2016

Self Cite

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In the context of formal verification in general and model checking in particular, parity games serve as a mighty vehicle: many problems are encoded as parity games, which are then solved by the seminal algorithm by Jurdzinski. In this paper we identify the essence of this workflow to be the notion of progress measure, and formalize it in general, possibly infinitary, lattice-theoretic terms. Our view on progress measures is that they are to nested/alternating fixed points what invariants are to safety/greatest fixed points, and what ranking functions are to liveness/least fixed points. That is, progress measures are combination of the latter two notions (invariant and ranking function) that have been extensively studied in the context of (program) verification.We then apply our theory of progress measures to a general model-checking framework, where systems are categorically presented as coalgebras. The framework's theoretical robustness is witnessed by a smooth transfer from the branching-time setting to the linear-time one. Although the framework can be used to derive some decision procedures for finite settings, we also expect the proposed framework to form a basis for sound proof methods for some undecidable/infinitary problems.

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A Coalgebraic Approach to Linear-Time Logics

Cited by 13 publications

References 7 publications

Coalgebraic trace semantics via forgetful logics

Coalgebraic trace semantics via forgetful logics

Weak Completeness of Coalgebraic Dynamic Logics

Lattice-theoretic progress measures and coalgebraic model checking

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