## Independence: Logics and Concurrency (2000)

Venue: | P.O. Box 1047, Arlington, TX |

Citations: | 5 - 2 self |

### BibTeX

@INPROCEEDINGS{Bradfield00independence:logics,

author = {J. C. Bradfield},

title = {Independence: Logics and Concurrency},

booktitle = {P.O. Box 1047, Arlington, TX},

year = {2000},

pages = {817--261},

publisher = {Springer}

}

### OpenURL

### Abstract

We consider Hintikka et al.'s `independence-friendly first-order logic'. We apply it to a modal logic setting, defining a notion of `independent' modal logic, and we examine the associated fixpoint logics.

### Citations

448 | Alternating-time temporal logic
- Alur, Henzinger, et al.
(Show Context)
Citation Context ...pens. Of course, with an eye on Henkin quantifiers, the obvious answer is to define a modality [] hi so one can write [A] hEi Ewins, with the intended meaning. Recently, Alur, Henzinger and Kupferman =-=[AHK97]-=- have implicitly taken this approach in their Alternating Temporal Logic, apparently without awareness of Henkin quantifiers: they express, rather, their logic directly in terms of games and strategie... |

264 |
A stubborn attack on state explosion
- Valmari
- 1991
(Show Context)
Citation Context ... in which a partial order of causality is established between events. There have also been several major practical advances in exploiting partial order structure, such as stubborn sets and sleep sets =-=[Val91]-=- and unfolding techniques [McM92]. Naturally, one wishes to have modal and temporal logics for concurrent systems. There are several ways to apply the paradigm of normal temporal logic, typically by w... |

159 |
Using unfoldings to avoid the state explosion problem in the verification of asynchronous circuits
- McMillan, L
- 1992
(Show Context)
Citation Context ...ality is established between events. There have also been several major practical advances in exploiting partial order structure, such as stubborn sets and sleep sets [Val91] and unfolding techniques =-=[McM92]-=-. Naturally, one wishes to have modal and temporal logics for concurrent systems. There are several ways to apply the paradigm of normal temporal logic, typically by working on event structures, or si... |

51 | Compositional semantics for a language of imperfect information
- Hodges
- 1997
(Show Context)
Citation Context ...oise chooses for v, she does not know what Abelard chose for x. To make this explicit, the logic is written with a more general syntax which is linear rather than two dimensional. We here use Hodges' =-=[Hod97]-=- syntax, which addresses certain flaws in Hintikka's; and for reasons of space and simplicity, we omit some operators in this version. IF-FOL + is obtained from FOL + by modifying the syntax of quanti... |

34 | The modal mu-calculus alternation hierarchy is strict
- Bradfield
- 1997
(Show Context)
Citation Context ...trict. Proof. If one considers arithmetic with fixpoints and the Henkin quantifier, the fixpoint alternation hierarchy is strict -- see the next section. Then a natural extension of the techniques of =-=[Bra97]-=-, in which a Henkin modality is used to encode a first-order Henkin quantifier, transfers this hierarchy tosH M L 2 on 2-component systems. However, for this result to transfer down to finite models, ... |

25 | Relativized logspace and generalized quantifiers over finite ordered structures
- Gottlob
- 1997
(Show Context)
Citation Context ...= v)s(y = v ) x = u)s(y 6= c).) (4) It follows via Fagin's Theorem that on finite structures FOL + + 89 89 expresses NP-hard properties [BlG86]; in fact, as one would expect, FOL+ 89 89 captures L NP =-=[Got97]-=-. 2.2 Partial knowledge games and quantifiers `a la Hintikka An alternative way of giving semantics to branching quantifiers is via games. Recall the Hintikka model-checking game for FOL + : given a f... |

24 | Henkin quantifiers and complete problems
- Blass, Gurevich
- 1986
(Show Context)
Citation Context ...; and this can be written using 89 89 as 8x 9y 8u9v :(x = u ) y = v)s(y = v ) x = u)s(y 6= c).) (4) It follows via Fagin's Theorem that on finite structures FOL + + 89 89 expresses NP-hard properties =-=[BlG86]-=-; in fact, as one would expect, FOL+ 89 89 captures L NP [Got97]. 2.2 Partial knowledge games and quantifiers `a la Hintikka An alternative way of giving semantics to branching quantifiers is via game... |

24 |
Finite partially-ordered quantification
- Walkoe
- 1970
(Show Context)
Citation Context ...ormal semantics is given by using suitable Skolem functions. The Henkin quantifier and its generalizations received some attention: the main papers were at the beginning of the 70s, by William Walkoe =-=[Wal70]-=- and Herbert Enderton [End70], and later also by Krynicki and Barwise. It was shown that 89 89 suffices to express all partially ordered or branching quantifiers (that is, quantifiers where the depend... |

23 | Verification of Temporal Properties of Concurrent Systems - Andersen - 1993 |

15 |
Some remarks on infinitely long formulas, Infinitistic Methods
- Henkin
- 1961
(Show Context)
Citation Context ...dependence in logic, which seems quite natural when specifying concurrent systems, but which has not, with one notable exception, received much attention in concurrency theory. 1 In 1961, Leon Henkin =-=[Hen61]-=- introduced the quantifier 8x 9y 8u9v , which is intended to mean that the choice of y depends only on x, not on u; and similarly the choice of v depends only on u; a formal semantics is given by usin... |

14 | On the logic of information independence and its applications - Sandu - 1993 |

13 | Fixpoint alternation: Arithmetic, transition systems, and the binary tree - Bradfield - 1999 |

11 | Generalized Quantifiers - Barwise, Cooper - 1981 |

11 | Bisimulations, games and logic
- Nielsen, Clausen
- 1994
(Show Context)
Citation Context ...in semantic accounts of true concurrency? There appear to be some links between logics of causality and locality, including history-sensitive logics such as the hereditary history-preserving logic of =-=[NiC94]-=-, and these should be investigated. ffl Independence-friendly logics are philosophically and mathematically interesting, but are they really useful? Putative applications such as distributed system de... |

11 | On udecidability of propositional temporal logics on trace systems - Penczek - 1992 |

10 |
Traces and logic
- Penczek, Kuiper
- 1995
(Show Context)
Citation Context ...e several ways to apply the paradigm of normal temporal logic, typically by working on event structures, or similar models, and having explicit operators representing concurrency or independence: see =-=[PK95]-=- for a survey of such logics. In some models, and therefore in the associated logics, the notion of independence is abstract; in others, it is more concrete, perhaps derived from a notion of location;... |

6 | ยต-definable sets of integers - Lubarsky - 1993 |

4 |
Enderton, Finite partially ordered quantifiers
- B
- 1970
(Show Context)
Citation Context ...sing suitable Skolem functions. The Henkin quantifier and its generalizations received some attention: the main papers were at the beginning of the 70s, by William Walkoe [Wal70] and Herbert Enderton =-=[End70]-=-, and later also by Krynicki and Barwise. It was shown that 89 89 suffices to express all partially ordered or branching quantifiers (that is, quantifiers where the dependence of variables need not be... |

3 |
Monotone inductive definitions over the continuum
- Cenzer
(Show Context)
Citation Context ...ction over the continuum, which is, unrestricted, extremely powerful: ! ! induction over a \Pi 1 1 formula gives \Sigma 1 2 , and then induction over \Delta 1 2 gives all the semihyperprojective sets =-=[Cen76]-=- (including, for example, the entire analytical hierarchy). In our framework, it is natural to conjecture that the expressive power of IF-LFP is much less than this (and in fact I conjecture it is in ... |

3 |
A revolution in logic
- Hintikka, Sandu
- 1996
(Show Context)
Citation Context ...aakko Hintikka, Gabriel Sandu and Jouko Vaananen, have returned with a vengeance to the study of `independent' quantifiers as a basic logic, rather than a specialist extension, and Hintikka and Sandu =-=[HiS96]-=- have gone so far as to claim that their absence from Frege's logic was a `fundamental error', a `horror', and to claim that their reintroduction heralds `a revolution in logic' (albeit with a questio... |

3 |
A general tableau technique for verifying temporal properties of concurrent programs
- Stirling, Walker
- 1990
(Show Context)
Citation Context ...f the theory can be made to carry through in a rather uninteresting way, by ignoring the concurrency and using rather the Skolem semantics: Proposition 9 Consider the tableau model-checking system of =-=[StW90]-=-, and add rules for the Henkin modalities in the following form: s 1 ks 2 ` ([A 1 ]hB 1 i\Omega [A 2 ]hB 2 i)OE s 11 ks 21 ` OE : : : s 1m ks 2m ` OE where the states on the bottom are given by: for e... |

2 | Verification on local states - Huhn, Niebert, et al. - 1993 |

1 | Fixpoint alternation and the game quantifier - Bradfield - 1999 |