### Citations

3947 |
Communication and Concurrency
- Milner
- 1989
(Show Context)
Citation Context ...rning recursion for LLTS and a few fundamental problems are still open. For instance, whether ⊑RS is precongruent in the presence of (nested) recursive operator? Under usual conditions (see, e.g., 60 =-=[45]-=-), whether equations containing (nested) recursive operator still have a unique solution? Notice that, since LLTS involve consideration of inconsistencies, the answers for these questions can not be t... |

3251 | Model checking
- Clarke, Grumberg, et al.
- 1999
(Show Context)
Citation Context ...us [38] and so on, in which the most common reasonable property of concurrent systems, such as invariance (safety), liveness, etc., can be formulated without referring operational details (see, e.g., =-=[16, 57]-=-). Moreover, one of inherent advantage of logic approach is that it is ability to deal with partial specifications: one can establish that a given system realizes a particular property without involvi... |

1847 | The stable model semantics for logic programming.
- Gelfond, Lifschitz
- 1988
(Show Context)
Citation Context ...rσ), and • S(t α → s) < S(conc(rσ)) for each s ∈ T (Σ) and t α 6→∈ nprem(rσ). A TSS is said to be stratified iff there exists a stratification function for it. Definition 2.6 (Stable Transition Model =-=[13, 24]-=-) Let Γ = (Σ, A,Λ,Ξ) be a TSS and M a transition model. M is said to be a stable transition model for Γ if M =MStrip(Γ, M), where Strip(Γ,M) is the TSS (Σ, A,Λ, Strip(Ξ,M)) with Strip(Ξ,M) △ = { pprem... |

1542 | A structural approach to operational semantics
- Plotkin
- 1981
(Show Context)
Citation Context ...n [43]. 2.3 Transition system specifications Structural Operational Semantics (SOS) is a logic method of giving operational semantics, which provides a syntax oriented view on operational semantics =-=[52]-=-. Transition System Specifications (TSSs), as presented by Groote and Vaandrager in [31], are formalizations of SOS. This subsection recalls basic concepts related to TSS. Further information on this ... |

1433 |
Introduction to Lattices and Order,
- Davey, Priestley
- 1991
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Citation Context ...ion Φ over a complete lattice with the top element ⊤, its greatest fixed-point is exactly the largest lower bound of the decreasing sequence { Φi(⊤) } i∈ω (i.e., νZ.Φ = ⊓ i∈ω Φi(⊤)) (see for instance =-=[21]-=-). The next theorem gives an analogous result for p̟q. Theorem 6.3 (Approximation of ̟) For any process p and q, p̟q is the greatest lower bound of the decreasing (w.r.t ⊑RS) sequence { ηip,q(true) } ... |

1388 | Automatic Verification of Finite-State Concurrent Systems Using Temporal Logic Specifications.
- Clarke, Emerson, et al.
- 1986
(Show Context)
Citation Context ...or looking at specifications and verifications, they offer complementary advantages: On the logic side, there exist a number of logic systems, e.g., Linear temporal logic [53], Computation tree logic =-=[17]-=-, µ−calculus [38] and so on, in which the most common reasonable property of concurrent systems, such as invariance (safety), liveness, etc., can be formulated without referring operational details (s... |

608 | Algebraic laws for non-determinism and concurrency.
- Hennessy, Milner
- 1985
(Show Context)
Citation Context ...any process p and q, either p ⊲⊳ q iff ∀α ∈L(p |= α ⇔ q |= α ) (if ⊲⊳ is an equivalence) or p ⊲⊳ q iff ∀α ∈L(q |= α ⇒ p |= α ) (if ⊲⊳ is a preorder) This notion is considered by Hennesy and Milner in =-=[34]-=-, where they prove that Hennesy-Milner logic (HML) is adequate w.r.t bisimilarity for image finite CCS terms. It is one of key evens that make Milner think that CCS is definitely interesting enough1. ... |

526 | Testing equivalences for processes.
- Nicola, Hennessy
- 1984
(Show Context)
Citation Context ...i automata and LTS augmented with a predicate, Cleaveland and Lüttgen provide a semantic framework for heterogenous system design [18, 19], where must-testing preorder offered by Nicola and Hennessy =-=[48]-=- is adopted to describe refinement relation. In addition to usual operational operators, such framework also involves logic connectives. However, since must-testing preorder is not a precongruence in ... |

444 |
Algebraic Theory of Processes
- Hennessy
- 1988
(Show Context)
Citation Context ...activity. Action-based approaches put attention to behavior of systems, which have tended to use formalisms in algebraic style. These formalisms are referred to as process algebra or process calculus =-=[45, 36, 35, 10]-=-. In such paradigm, a specification and its implementation usually are formulated by the same notations, which are terms (expressions) of a formal language built from a number of operators, and the un... |

375 | The Linear Time – Branching Time Spectrum I. In:
- Glabbeek
- 2001
(Show Context)
Citation Context ...ment”). At the present time, due to lack of consensus on what constitutes an appropriate notion of observable behavior, a variety of observation criterions and behavioral relations have been proposed =-=[25]-=-. The correctness of an implementation may be verified in a proof–theory oriented manner or in a semantics oriented manner. The former is rooted in an axiomatization of the behavioral relation, while ... |

329 |
Results on the propositional mu-calculus.
- Kozen
- 1983
(Show Context)
Citation Context ...cifications and verifications, they offer complementary advantages: On the logic side, there exist a number of logic systems, e.g., Linear temporal logic [53], Computation tree logic [17], µ−calculus =-=[38]-=- and so on, in which the most common reasonable property of concurrent systems, such as invariance (safety), liveness, etc., can be formulated without referring operational details (see, e.g., [16, 57... |

266 |
Algebra of communicating processes with abstraction.
- Bergstra, Klop
- 1985
(Show Context)
Citation Context ...activity. Action-based approaches put attention to behavior of systems, which have tended to use formalisms in algebraic style. These formalisms are referred to as process algebra or process calculus =-=[45, 36, 35, 10]-=-. In such paradigm, a specification and its implementation usually are formulated by the same notations, which are terms (expressions) of a formal language built from a number of operators, and the un... |

242 | Bisimulation can’t be traced.
- Bloom, Istrail, et al.
- 1995
(Show Context)
Citation Context ...e considered as a “proof” for a negative formula, it is much less trivial to associate a model with a TSS containing negative premises [32]. The first generic answer to this question is formulated in =-=[32, 12]-=-, where the above notion of supported model is introduced. However, this notion doesn’t always work well. Several alternatives have been proposed, and a good overview on this issue is provided in [26]... |

212 |
Structured operational semantics and bisimulation as a congruence.
- Groote, Vaandrager
- 1992
(Show Context)
Citation Context ... a logic method of giving operational semantics, which provides a syntax oriented view on operational semantics [52]. Transition System Specifications (TSSs), as presented by Groote and Vaandrager in =-=[31]-=-, are formalizations of SOS. This subsection recalls basic concepts related to TSS. Further information on this issue may be found in [9, 13, 31]. Given an infinite set V of variables and a signature ... |

165 |
Characterizing finite Kripke structures in propositional temporal logic.
- Browne, Clarke, et al.
- 1988
(Show Context)
Citation Context ...tures, e.g., finite LTS, Kripke structures, time automata and so on, a number of examples of characteristic-formula constructions for various behavioral relations have been reported in the literature =-=[4, 15, 20, 23, 39, 40, 46, 56, 59]-=-. The underlying structures of these constructions are identical, that is, characteristic formulae often are defined as fixed points of some functions. Recently, ground on this phenomenon, L.Aceto et ... |

138 |
Transition system specifications with negative premises.
- Groote
- 1993
(Show Context)
Citation Context ... naturally. However, since it is not immediately clear what can be considered as a “proof” for a negative formula, it is much less trivial to associate a model with a TSS containing negative premises =-=[32]-=-. The first generic answer to this question is formulated in [32, 12], where the above notion of supported model is introduced. However, this notion doesn’t always work well. Several alternatives have... |

130 | A Congruence Theorem for Structured Operational Semantics with Predicates and Negative Premises,
- Verhoef
- 1995
(Show Context)
Citation Context ...uantifier symbol does not occur in (Rp16) explicitly, it is not difficult to see that the premise of (Rp16) involves universal quantifier in spirit. Analogous to CLL, we may adopt the method given in =-=[58]-=- to avoid this. In detail, for each α ∈ Actτ , the auxiliary predicates Fα is added to CLLT and the rule (Rp16) is replaced by two rules below, where the topmost operator of p is in {∧, ♯,△,⊙}. (Rp16−... |

108 |
Actions versus State based Logics for Transition Systems”,
- Nicola, Vaandrager
- 1990
(Show Context)
Citation Context ...ttgen and Vogler’s constructions but depends on the greatest fixed-point characterization obtained in this paper. Moreover, the connections between the resulting calculus (that we call CLLT) and ACTL =-=[49]-=- are explored from angles recalled in the preceding subsection. These connections include characteristic formulae of process terms, characteristic processes of formulae and Galois connection. The rema... |

91 | Modal and temporal logics for processes
- Stirling
- 2001
(Show Context)
Citation Context ...us [38] and so on, in which the most common reasonable property of concurrent systems, such as invariance (safety), liveness, etc., can be formulated without referring operational details (see, e.g., =-=[16, 57]-=-). Moreover, one of inherent advantage of logic approach is that it is ability to deal with partial specifications: one can establish that a given system realizes a particular property without involvi... |

85 | The meaning of negative premises in transition system specifications.
- Bol, Groote
- 1996
(Show Context)
Citation Context ...ecifications (TSSs), as presented by Groote and Vaandrager in [31], are formalizations of SOS. This subsection recalls basic concepts related to TSS. Further information on this issue may be found in =-=[9, 13, 31]-=-. Given an infinite set V of variables and a signature Σ, we assume that the resulting notions of term, closed (ground) terms, substitution and closed (ground) substitution are already familiar to the... |

71 |
de Rijke /
- Nivelle, M
- 2003
(Show Context)
Citation Context ...rious behavioral relations. A good overview on this subject may be found in [9]. In the realm of modal logic, more generalized results concerning Hennesy-Milner property (class) have been established =-=[8, 11, 27, 28, 37]-=-. Recently, such issue is also considered in depth in the framework of coalgebras2 (see, e.g., [47, 51]). As pointed out by Pnueli in [54], the requirement of adequacy is the weakest one of compatibil... |

64 | On the origins of bisimulation and coinduction. - Sangiorgi - 2009 |

60 | From timed automata to logic – and back
- Laroussinie, Larsen, et al.
- 1995
(Show Context)
Citation Context ...tures, e.g., finite LTS, Kripke structures, time automata and so on, a number of examples of characteristic-formula constructions for various behavioral relations have been reported in the literature =-=[4, 15, 20, 23, 39, 40, 46, 56, 59]-=-. The underlying structures of these constructions are identical, that is, characteristic formulae often are defined as fixed points of some functions. Recently, ground on this phenomenon, L.Aceto et ... |

51 | A constraint oriented proof methodology based on modal transition systems, in: Tools and Algorithms for Construction and Analysis of Systems,
- Larsen, Steffen, et al.
- 1995
(Show Context)
Citation Context ... the process term involved in the corresponding reduction is required to be in T (ΣCLLT ) −. In the literature, various work on combining operational operators with logic operators have been reported =-=[33, 41, 50]-=-. Olderog provides a framework in which operational operators may be combined with trace formula [50]. But such framework does not allow one to freely mix operational and logic specifications. Guerra ... |

44 | The meaning of negative premises in transition system specifications II.
- Glabbeek
- 2004
(Show Context)
Citation Context ... 12], where the above notion of supported model is introduced. However, this notion doesn’t always work well. Several alternatives have been proposed, and a good overview on this issue is provided in =-=[26]-=-. In the following, we recall the notions of stratification and stable transition model, which play an important role in this field. Definition 2.5 (Stratification [13]) Let Γ = (Σ, A,Λ,Ξ) be a TSS an... |

43 |
Compositional verification of probabilistic processes
- Larsen, Skou
- 1992
(Show Context)
Citation Context ...tures, e.g., finite LTS, Kripke structures, time automata and so on, a number of examples of characteristic-formula constructions for various behavioral relations have been reported in the literature =-=[4, 15, 20, 23, 39, 40, 46, 56, 59]-=-. The underlying structures of these constructions are identical, that is, characteristic formulae often are defined as fixed points of some functions. Recently, ground on this phenomenon, L.Aceto et ... |

38 |
Characteristic formulae for processes with divergence.
- Steffen, Ingolfsdottir
- 1994
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Citation Context |

37 | Expressive logics for coalgebras via terminal sequence induction
- Pattinson
(Show Context)
Citation Context ... generalized results concerning Hennesy-Milner property (class) have been established [8, 11, 27, 28, 37]. Recently, such issue is also considered in depth in the framework of coalgebras2 (see, e.g., =-=[47, 51]-=-). As pointed out by Pnueli in [54], the requirement of adequacy is the weakest one of compatibility between a process algebra and a logic. A symptom of its weakness is that the same logic may be adeq... |

37 |
Linear and Branching Structures in the Semantics and Logics of Reactive Systems.
- Pnueli
- 1985
(Show Context)
Citation Context ... relation |= between process terms and formulas. Given such satisfiability relation, three connections between a process algebra and a logic deserve special mention, which are considered by Pnueli in =-=[54]-=- and recalled in the following. Let P be a process algebra equipped with a behavioral relation ⊲⊳, and L a logic language associated with a satisfiability relation |=. • Adequacy of (L, |=) w.r.t (P, ... |

36 |
Process algebra with propositional signals.
- Baeten, Bergstra
- 1997
(Show Context)
Citation Context ...tors is not considered in [41]. There also exist investigations of operational behavior involving logic ingredient but without admitting the free mixing of operational and logic operators, see, e.g., =-=[7, 22]-=-. We conclude this paper with giving several possible avenues for further work. Firstly, finding a complete proof system for CLLT would be the next task. Secondly, although this paper provides recursi... |

32 | Graphical versus logical specifications - Boudol, Larsen - 1990 |

32 | Computing behavioural relations, logically.
- Cleaveland, Steffen
- 1991
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29 |
A modal characterization of observational congruence on finite terms of CCS.
- Graf, Sifakis
- 1986
(Show Context)
Citation Context ...nd between implementation verification and model checking [2]. Graf and Sifakis provide a method of constructing characteristic formula modulo observational congruence for any recursion-free CCS term =-=[30]-=-. Hitherto, over different structures, e.g., finite LTS, Kripke structures, time automata and so on, a number of examples of characteristic-formula constructions for various behavioral relations have ... |

23 | Derivation of characteristic formulae.
- Muller-Olm
- 1998
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22 |
A logic for the description of non-deterministic programs and their properties
- Graf, Sifakis
- 1986
(Show Context)
Citation Context ...fication of an assertion p |= ϕ can be transformed into the validity problem within L by (E2). Graf and Sifakis were probably the first to develop logics which are expressive for process algebras. In =-=[29]-=-, they present Synchronization Tree Logic (STL, for short) for a process algebra with a congruence relation ≈. STL contains process terms as formulae, and its semantic is defined so that both (E1) and... |

15 |
Characteristic formulae for timed automata.
- Aceto, Ingolfsdottir, et al.
- 2000
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12 | Conjunction on processes: Full abstraction via ready-tree semantics.
- Luttgen, Vogler
- 2007
(Show Context)
Citation Context ...f r implements both p and q. Recently, Lüttgen and Vogler introduce the notion of a Logic LTS (LLTS, for short), which combines operational and logic styles of specification in one unified framework =-=[42, 43]-=-. In order to handle logic conjunctions of specifications, LLTS involves consideration of inconsistencies, which, compared with usual LTS, is one distinguishing feature of it. Two kinds of constructor... |

11 |
Benthem, Modal logic and Classical Logic, Bibliopolis
- van
- 1985
(Show Context)
Citation Context ...rious behavioral relations. A good overview on this subject may be found in [9]. In the realm of modal logic, more generalized results concerning Hennesy-Milner property (class) have been established =-=[8, 11, 27, 28, 37]-=-. Recently, such issue is also considered in depth in the framework of coalgebras2 (see, e.g., [47, 51]). As pointed out by Pnueli in [54], the requirement of adequacy is the weakest one of compatibil... |

11 | A logical process calculus
- Cleaveland, Lüttgen
- 2002
(Show Context)
Citation Context ... integrate these two specification styles. Among them, based on Büchi automata and LTS augmented with a predicate, Cleaveland and Lüttgen provide a semantic framework for heterogenous system design =-=[18, 19]-=-, where must-testing preorder offered by Nicola and Hennessy [48] is adopted to describe refinement relation. In addition to usual operational operators, such framework also involves logic connectives... |

11 |
Nets, Terms and Formulas in: Cambridge Tracts in Theoretical
- Olderog
- 1991
(Show Context)
Citation Context ... the process term involved in the corresponding reduction is required to be in T (ΣCLLT ) −. In the literature, various work on combining operational operators with logic operators have been reported =-=[33, 41, 50]-=-. Olderog provides a framework in which operational operators may be combined with trace formula [50]. But such framework does not allow one to freely mix operational and logic specifications. Guerra ... |

10 | Ready simulation for concurrency: It’s logical
- Lüttgen, Vogler
- 2010
(Show Context)
Citation Context ...f r implements both p and q. Recently, Lüttgen and Vogler introduce the notion of a Logic LTS (LLTS, for short), which combines operational and logic styles of specification in one unified framework =-=[42, 43]-=-. In order to handle logic conjunctions of specifications, LLTS involves consideration of inconsistencies, which, compared with usual LTS, is one distinguishing feature of it. Two kinds of constructor... |

9 | Characteristic formulae for fixed-point semantics: a general framework.
- Aceto, Ingolfsdottir, et al.
- 2012
(Show Context)
Citation Context ...ovides lower-level details indicating how this behavior is to be achieved. The verification amounts to compare terms, which is often referred to as implementation verification or equivalence checking =-=[2]-=-. The comparison of a specification to an implementation is based on behavioral relations. Such relations depend on particular observation criterions, and are typically equivalences (or preorders), wh... |

9 | A semantic theory for heterogeneous system design
- Cleaveland, Lüttgen
- 1974
(Show Context)
Citation Context ... integrate these two specification styles. Among them, based on Büchi automata and LTS augmented with a predicate, Cleaveland and Lüttgen provide a semantic framework for heterogenous system design =-=[18, 19]-=-, where must-testing preorder offered by Nicola and Hennessy [48] is adopted to describe refinement relation. In addition to usual operational operators, such framework also involves logic connectives... |

7 | Safe reasoning with Logic LTS
- Lüttgen, Vogler
- 2011
(Show Context)
Citation Context ...ns induced by them are denoted by ≈RS and =RS , respectively, that is ≈RS △ = ⊏ ∼RS ⋂ (⊏ ∼RS )−1 and =RS △ = ⊑RS ⋂ (⊑RS)−1. The notion of ready simulation presented in Def. 2.2 is a central notion in =-=[43, 44, 60]-=- and this paper. It is natural to wonder why such notion is adopted to formalize the refinement relation. From our point of view, whenever we try to mix process-algebraic and logic styles of specifica... |

6 |
Galois connections and fixed point calculus, Algebraic and
- Backhouse
(Show Context)
Citation Context ...x ∈ B and y ∈ A, F (x) A y if and only if x B G(y). It is well known that (F,G) is a Galois connection if and only if F and G are monotonic and satisfy the cancellation laws below (see for instance =-=[6]-=-) (C1) x B G(F (x)) for all x ∈ B, and (C2) F (G(y)) A y for all y ∈ A. Using Lemma 8.4, it is easy to see that (E2) holds if and only if the pair (∗, [·]) is a Galois connection between preordered ... |

6 |
The temporal logic of programs, FOCS’77
- Pnueli
- 1977
(Show Context)
Citation Context ...quence of actions. State-based approaches devote themselves to specifying and verifying abstract properties of systems, which often involve formalisms in logic style. Since the seminal work of Pnueli =-=[53]-=-, logics have been adopted to serve as useful tools for specifying and verifying of reactive and concurrent systems. In such framework, a ∗This work received financial support of the National Natural ... |

4 |
Finite abstract models for deterministic transition systems
- Fecher, Grabe
- 2007
(Show Context)
Citation Context ...tors is not considered in [41]. There also exist investigations of operational behavior involving logic ingredient but without admitting the free mixing of operational and logic operators, see, e.g., =-=[7, 22]-=-. We conclude this paper with giving several possible avenues for further work. Firstly, finding a complete proof system for CLLT would be the next task. Secondly, although this paper provides recursi... |

4 | Characteristic µ-calculus formula for an underspecified transition system
- Fecher, Steffen
(Show Context)
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4 | Final coalgebras and the Hennessy-Milner property
- Goldblatt
(Show Context)
Citation Context ...rious behavioral relations. A good overview on this subject may be found in [9]. In the realm of modal logic, more generalized results concerning Hennesy-Milner property (class) have been established =-=[8, 11, 27, 28, 37]-=-. Recently, such issue is also considered in depth in the framework of coalgebras2 (see, e.g., [47, 51]). As pointed out by Pnueli in [54], the requirement of adequacy is the weakest one of compatibil... |

3 |
de Frutos Escrig, Anna Ingólfsdóttir & Miguel Palomino (2011): Relating modal refinements, covariant-contravariant simulations and partial bisimulations
- Aceto, Fábregas, et al.
(Show Context)
Citation Context ...la in a contrary way. In fact, characteristicformula construction and ζ(.) indeed induce a Galois connection between (Θ,⊑) and the set of consistent prime formulae augment with some preorder [14]. In =-=[1]-=-, L.Aceto et al. address the same issue, and show that, modulo the covariantcontravariant simulation preorder, any consistent and prime formula in the covariantcontravariant modal logic also admits a ... |

3 |
and G.Winskel, A compositional proof system for the modal µ-calculus
- Andersen, Stirling
(Show Context)
Citation Context ...ages in developing systems, such as, supporting modular design and verification, avoiding verifying the whole system from scratch when its parts are modified, allowing reusability of proofs and so on =-=[5]-=-. Thus algebraic approaches offer significant support for rigorous systematic development of reactive and concurrent systems. However, since algebraic approaches specify a system by means of prescribi... |

2 |
Processes with local and global liveness requirements
- Guerra, Costa
- 2008
(Show Context)
Citation Context ... the process term involved in the corresponding reduction is required to be in T (ΣCLLT ) −. In the literature, various work on combining operational operators with logic operators have been reported =-=[33, 41, 50]-=-. Olderog provides a framework in which operational operators may be combined with trace formula [50]. But such framework does not allow one to freely mix operational and logic specifications. Guerra ... |

1 |
Anna Inglfsdttir, Characteristic Formulae for Relations with Nested Fixed Points
- Aceto
- 1202
(Show Context)
Citation Context ...acteristic formulae often are defined as fixed points of some functions. Recently, ground on this phenomenon, L.Aceto et al. offer a general framework for the constructions of characteristic formulae =-=[2, 3]-=-. • Expressivity of (P, ⊲⊳) w.r.t (L, |=) Another stronger association between process algebras and logics involves an inverse translation, which associates with each formula ϕ ∈ L a set P (ϕ) that co... |

1 |
Saturation and the Hennessy-Milner property, in: A.Ponse, M.de Rijke and
- Goldblatt
- 1995
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1 |
Classes and Process algebra, in: A.Ponse, M.de Rijke and
- Hollenberg
- 1995
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1 |
Connection between logical and algebraic approaches to concurrent systems
- Zhan
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1 |
Jinjin Zhang and Yong Zhou, A process calculus with logical operators
- Zhang, Zhu
(Show Context)
Citation Context ... in temporal logics, such as always and unless, are also integrated into this framework [44]. Along the direction suggested by Lüttgen and Vogler in [43], we propose a process calculus called CLL in =-=[60]-=-, which reconstructs their setting in process algebraic style. In addition to prefix α.(), external choice and parallel operator ‖A, CLL contains logic operators ∧ and ∨ over process terms, which co... |