## Objects, Types and Modal Logics (1996)

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Citations: | 6 - 0 self |

### BibTeX

@MISC{Andersen96objects,types,

author = {Dan S. Andersen and Lars H. Pedersen and Hans Hüttel and Josva Kleist},

title = {Objects, Types and Modal Logics},

year = {1996}

}

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### Abstract

In this paper we present a modal logic for describing properties of terms in the object calculus of Abadi and Cardelli [AC96]. The logic is essentially the modal mu-calculus of [Koz83]. The fragment allows us to express the temporal modalities of the logic CTL [BAMP83]. We investigate the connection between the type system Ob 1!: and the mu-calculus, providing a translation of types into modal formulae and an ordering on formulae that is sound w.r.t. to the subtype ordering of Ob 1!: .

### Citations

3452 | Communication and Concurrency - Milner - 1989 |

935 | A Theory of Objects
- Abadi, Cardelli
- 1996
(Show Context)
Citation Context ... Dan S. Andersen Lars H. Pedersen Hans Huttel Josva Kleist October 1998 Abstract In this paper we present a modal logic for describing properties of terms in the object calculus of Abadi and Cardelli =-=[AC96]-=-. The logic is essentially the modal mu-calculus of [Koz83]. The fragment allows us to express the temporal modalities of the logic CTL [BAMP83]. We investigate the connection between the type system ... |

704 | Concurrency and automata on infinite sequences, in - Park - 1981 |

520 | Algebraic Laws for Nondeterminism and Concurrency
- HENNESSY, MILNER
- 1985
(Show Context)
Citation Context ...f its sublogics corresponds to the Ob 1!:�� type system in a precise sense. The modal ��-calculus was introduced by Kozen in [Koz83]. It corresponds to the logic introduced by Hennessy and Mil=-=ner and [HM85] extende-=-d with (local) recursive definitions [Lar90]. 5.1 Syntax and informal semantics The set of ��-calculus formulae Form is given by F ::= F 1sF 2 j F 1sF 2 j hffiF j [ff]F j X j X:F j ��X:F j tt ... |

330 | Results on the propositional µ-calculus - Kozen - 1983 |

272 |
Results on the propositional -calculus
- Kozen
- 1983
(Show Context)
Citation Context ... October 1998 Abstract In this paper we present a modal logic for describing properties of terms in the object calculus of Abadi and Cardelli [AC96]. The logic is essentially the modal mu-calculus of =-=[Koz83]. Th-=-e fragment allows us to express the temporal modalities of the logic CTL [BAMP83]. We investigate the connection between the type system Ob 1!:�� and the mu-calculus, providing a translation of ty... |

175 |
The Temporal Logic of Branching Time
- Ben-Ari, Manna, et al.
- 1983
(Show Context)
Citation Context ...ies of terms in the object calculus of Abadi and Cardelli [AC96]. The logic is essentially the modal mu-calculus of [Koz83]. The fragment allows us to express the temporal modalities of the logic CTL =-=[BAMP83]. We-=- investigate the connection between the type system Ob 1!:�� and the mu-calculus, providing a translation of types into modal formulae and an ordering on formulae that is sound w.r.t. to the subty... |

108 |
Local model checking in the modal mu-calculus
- Stirling, Walker
- 1989
(Show Context)
Citation Context ...investigate how one can use the mu-calculus to verify interesting properties of objects. The notion of model checking, that is, algorithmically checking whether a term satisfies a given modal formula =-=[SW89], is-=- already well understood in the context of process calculi. It remains to be seen how far we can proceed within the &-calculus. We have also shown a correspondence between the type system Ob 1!:��... |

82 | A theory of primitive objects: Untyped and first-order systems
- Abadi, Cardelli
- 1994
(Show Context)
Citation Context ...tain mu-calculus formulae. 2 The &-calculus and its reduction semantics There are various versions of the &-calculus. In this paper we shall consider what is essentially the simple object calculus of =-=[AC94b]-=- with booleans added. The set of object terms, Obj, is defined by the following abstract syntax: a ::= [l i =&(x i :A)b i i2I ] objects j x self variables j a:l method activation j a:l(&(x:A)b method ... |

59 | A theory of primitive objects: Second-order systems - Abadi, Cardelli - 1995 |

52 | An interpretation of objects and object types - Abadi, Cardelli, et al. - 1996 |

45 | Bisimilarity for a first-order calculus of objects with subtyping
- Gordon, Rees
(Show Context)
Citation Context ...lus is that of studying various type systems of object-oriented programming languages within a unified framework. In this paper we shall consider the type system Ob 1!:�� from [AC94b] as presented=-= in [GR96]. 3.1 Th-=-e type language The set of Ob 1!:�� type expressions Type is defined via the following abstract syntax: A ::= Bool j [l i :A i i2I ] j Top j ��(X)A j X Here Bool denotes the only ground type, ... |

35 | A Semantics of Object Types - Abadi, Cardelli |

33 |
Characteristic formulae for processes with divergence
- Steffen, Ingólfsdóttir
- 1994
(Show Context)
Citation Context ... we have to use the maximal fixed point operator. In other words, the �� becomes aswhen passing from types to formulae. The translation defined by T is similar to the notion of characteristic form=-=ula [IS94]-=- for the typings of objects. It is not the case, though, that these characteristic formulae express all possible behaviors of objects. In particular, it is not possible to prove that the logic for obj... |

33 |
Proof systems for satisfiability in Hennessy–Milner logic with recursion
- LARSEN
- 1990
(Show Context)
Citation Context ...stem in a precise sense. The modal ��-calculus was introduced by Kozen in [Koz83]. It corresponds to the logic introduced by Hennessy and Milner and [HM85] extended with (local) recursive definiti=-=ons [Lar90]. 5.1 Sy-=-ntax and informal semantics The set of ��-calculus formulae Form is given by F ::= F 1sF 2 j F 1sF 2 j hffiF j [ff]F j X j X:F j ��X:F j tt j ff ff ::= l j unfold j l ( &(x)b Here X ranges ove... |

33 | A Presheaf Semantics of Value-Passing Processes - Winskel - 1996 |

17 |
Handbook of Theoretical Computer Science, chapter Temporal and Modal Logic
- Emerson
- 1990
(Show Context)
Citation Context ... The modal mu-calculus is very powerful when used a temporal logic of labelled transition systems. It is well-known that the temporal modalities of the propositional branching time temporal logic CTL =-=[Eme94]-=- are expressible within the mu-calculus (in fact, it can be shown that all of CTL [Eme94] can be expressed within the mu-calculus). In this short section we shall describe how properties of &-calculus... |

12 | Concurrency and automata on in¯nite sequences - Park - 1981 |

9 | A theory of primitive objects: Untyped and rst-order systems - Abadi, Cardelli - 1994 |

5 | Bisimilarity for a rst-order calculus of objects with subtyping - Gordon, Rees - 1996 |

5 | Andreev and Sergei Soloviev. A Decision Algorithm for Linear Isomorphism of Types with Complexity Cn(log 2 - E - 1996 |

5 | Weak Semantics Based on Lighted Button Pressing Experiments: An Alternative Characterization of the Readiness Semantics - Ingólfsdóttir - 1996 |

1 |
An operational approach to the &-calculus
- Andersen, Pedersen
- 1996
(Show Context)
Citation Context ...that a; b 2 Obj and let oe be either a pre- or post-model. Then, a �� b m 8F 2 Form : a 2 [[F ]]oe , b 2 [[F ]]oe The proof of Theorem 4, which is lengthy but standard, is omitted; it can be found=-= in [AP96]-=-. 6 Specifying objects The modal mu-calculus is very powerful when used a temporal logic of labelled transition systems. It is well-known that the temporal modalities of the propositional branching ti... |

1 |
A lattice-theoretical fixpoint and its applications
- Tarski
- 1955
(Show Context)
Citation Context ...ironments ordered under inclusion, constitutes a complete lattice and that the function D F is a monotonic function for any recursive formula X:F or ��X:F . Consequently, Tarski's fixed point theo=-=rem [Tar55] for-=- complete lattices and monotonic functions, guarantees that models always exist for any recursive formula. Theorem 2 (Maximal and minimal model) Given a recursive formula F of the form X:F or ��X:... |

1 | Characteristic formulae for processes with divergence - Inglfsdttir, Steoeen - 1994 |

1 | Proof systems for satisability in HennessyMilner logic with recursion - Larsen - 1990 |

1 | A lattice-theoretical xpoint and its applications. Paci c - Tarski - 1955 |