#### DMCA

## • Category Theory applied in Automata Theory • Graph Transformations in a Category setting • Dynamic, Modal, and Higher-order Logics. (2005)

### Citations

608 | Algebraic laws for non-determinism and concurrency.
- Hennessy, Milner
- 1985
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Citation Context ...ems to be checked (see, e.g., [3]). Therefore, it may be worthwhile to remember that various attempts were made in the 1970s toward a unified theory of automata in a categorical framework (see, e.g., =-=[1, 2, 4]-=-). In this paper, the basic ideas are recalled. The hope is that this may enhance the recent interest in automata. Automata in a category As a particular variant of automata in a category, Mealy-autom... |

529 | Bisimulation through Probabilistic Testing.
- Larsen, Skou
- 1991
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Citation Context ... specification language CCSL [15]. Coalgebraic modal logic subsumes, besides standard Hennessy-Milner logic, well-known non-normal modal logics such as graded modal logic or probabilistic modal logic =-=[8, 3]-=-; some still relatively natural examples are even non-monotone. Coalgebraic modal logic is invariant under behavioral equivalence. Moreover, it has been shown in [13] that under suitable conditions, f... |

408 | Universal coalgebra: a theory of systems.
- Rutten
- 2000
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Citation Context ...ce. In recent years, coalgebra has emerged as an appropriate framework for the treatment of reactive systems in a vastly more general sense than the traditional concept of labelled transition systems =-=[16]-=-, covering also as diverse system types as probabilistic automata, multigraphs, branching systems, and linear automata, to name just a few; this variation is achieved by parametrizing the theory by a ... |

110 | Coalgebraic logic.
- Moss
- 1999
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Citation Context ...n. The case distinction is given by coproducts from the base, and the iteration requires the existence of fixpoints. Stateful computations can be added in two ways, either by an axiomatic description =-=[9]-=- or constructively by state threads [4]. The former allows us to model typed references and is more general, but may lead to arguments about consistency; the latter is more restrictively typed, but co... |

73 | Coalgebraic modal logic: Soundness, completeness and decidability of local consequence.
- Pattinson
- 2003
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Citation Context ...re imposed on the signature functor [7]. Weak completeness for a deduction system consisting of propositional reasoning, a congruence rule, and a given set of axioms of rank 1 has been established in =-=[12]-=-, subject to the condition that the set of axioms is complete for single-step semantic consequence; the latter property is referred to as reflexivity. It is shown in [18] that reflexively axiomatized ... |

65 |
Specifying coalgebras with modal logic
- Kurz
- 2001
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Citation Context ..., e.g., [5]). They provide as labelled transition systems the semantic foundation of concurrency and communication. Hybrid automata are used to combine discrete and continuous computation (see, e.g., =-=[6]-=-). As generalized sequential machines, they translate input languages into output languages yielding, for example, a characterization of recursively enumerable sets as translations of the twin shue l... |

55 | Expressivity of coalgebraic modal logic: The limits and beyond.
- Schroder
- 2008
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Citation Context ...nd the existence of `enough' predicate liftings, coalgebraic modal logic is expressive, i.e. logical equivalence of states implies their behavioral equivalence. The latter result has been improved in =-=[17]-=-, where it was shown that expressivity really requires only the two explicitly mentioned essential conditions, rather than also further technical side conditions. Moreover, examples were given showing... |

39 | The Coalgebraic Class Specification Language CCSL
- Rothe, Jacobs, et al.
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Citation Context ...actual software specification; variants of coalgebraic modal logic indeed appear as features in the algebraic-specification language CoCasl [10] and in the object-oriented specification language CCSL =-=[15]-=-. Coalgebraic modal logic subsumes, besides standard Hennessy-Milner logic, well-known non-normal modal logics such as graded modal logic or probabilistic modal logic [8, 3]; some still relatively nat... |

38 | Coalgebras and modal logic.
- Roßiger
- 2000
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Citation Context ...al results about them. E.g, coalgebra has provided a unifying perspective on notions such as coinduction, corecursion, and bisimulation. The search for a coalgebraic analogue of Hennessy-Milner logic =-=[5, 14, 6, 11]-=- has led to the definition of what we shall refer to as coalgebraic modal logic by Pattinson [13]; this definition is based on the crucial notion of predicate liftings, which transform predicates on X... |

37 | Expressive logics for coalgebras via terminal sequence induction
- Pattinson
(Show Context)
Citation Context ...orecursion, and bisimulation. The search for a coalgebraic analogue of Hennessy-Milner logic [5, 14, 6, 11] has led to the definition of what we shall refer to as coalgebraic modal logic by Pattinson =-=[13]-=-; this definition is based on the crucial notion of predicate liftings, which transform predicates on X into predicates on TX, where T is the signature functor. In comparison with the previously defin... |

35 | PSPACE reasoning for graded modal logics’,
- Tobies
- 2000
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Citation Context ...atisfiability problem is in NP . This applies in particular to Hennessy-Milner logic, graded modal logic, and probabilistic modal logic. While the former two examples are known to be PSPACE -complete =-=[1, 19]-=-, no complexity bound has so far been given for probabilistic modal logic. We conjecture that the generic result can be improved to PSPACE ; however, an adaption of the standard witness algorithm for ... |

34 | Probabilistic logic for type spaces - Heifetz, Mongin |

33 | Semantical principles in the modal logic of coalgebras
- Pattinson
- 2001
(Show Context)
Citation Context ...tational effects (such as stateful computations, exceptional behaviour or non-determinism). This goes back toMoggi [6], and is for example used to great effect in the pure functional language Haskell =-=[8, 11]-=-. In this talk, we use the same technique to model computational effects in higher-order logic, and in particular the theorem prover Isabelle [7], thus shallowly embedding a small imperative language ... |

31 | A finite model construction for coalgebraic modal logic
- Schröder
(Show Context)
Citation Context ...reover, polyadic modal logic has the added advantage of being closed under the modular construction of logics for coalgebras [2]. For various reasons, many coalgebraic modal logics fail to be compact =-=[18]-=-, so that generic completeness results will necessessarily be limited to weak completeness, unless further restrictions are imposed on the signature functor [7]. Weak completeness for a deduction syst... |

26 | Algebraiccoalgebraic specification in CoCASL.
- Mossakowski, Schroder, et al.
- 2006
(Show Context)
Citation Context ...gic is relatively easily understood and therefore usable in actual software specification; variants of coalgebraic modal logic indeed appear as features in the algebraic-specification language CoCasl =-=[10]-=- and in the object-oriented specification language CCSL [15]. Coalgebraic modal logic subsumes, besides standard Hennessy-Milner logic, well-known non-normal modal logics such as graded modal logic or... |

24 | Modular construction of modal logics
- Cîrstea, Pattinson
- 2004
(Show Context)
Citation Context ...the basis of the seminal paper [4], monads are being used for encapsulating side effects in modern functional programming languages; in particular, this idea is one of the central concepts of Haskell =-=[2]-=-. Intuitively, a monad associates to each type A a type TA of computations of type A; a function with side effects that takes inputs of type A and returns values of type B is, then, just a function of... |

21 | Towards a duality result in the modal logic of coalgebras
- Jacobs
- 2000
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Citation Context ... where, again, S is a fixed set of states; Dynamic logic The right framework for reasoning about both partial correctness as well as termination or total correctness is dynamic logic as introduced in =-=[5]-=-. Here, we examine the infrastructure that is needed in order to develop dynamic logic in a monad-independent way, and show that this does indeed make sense when instantiated to the usual monads menti... |