## A Linear Logic Approach to Consistency Preserving Updates (1996)

Citations: | 2 - 1 self |

### BibTeX

@MISC{Bidoit96alinear,

author = {N. Bidoit and S. Cerrito and Ch. Froidevaux},

title = {A Linear Logic Approach to Consistency Preserving Updates},

year = {1996}

}

### OpenURL

### Abstract

The aim of this paper is to propose linear logic as a proof system allowing to perform updates of databases containing incomplete information. In our approach, a database is specified by facts, deduction rules (among which default rules) and update constraints. Updates will always preserve consistency, i.e. any update of a "consistent" database will produce a new base which is "consistent". The calculus of the "static semantics" of a database DB corresponds to the construction of a proof in a logical theory Th(DB) associated to the database. Similarly, the calculus of the "update semantics" of a database DB w.r.t. the insertion of a literal L, is the construction of a proof in Th(DB). Key words : Deductive Databases, Incomplete Information, Linear Logic, Updates. R'esum'e Ce papier propose la logique lin'eaire comme un syst`eme de preuve permettant de mettre `a jour des bases de donn'ees qui contiennent des informations incompl`etes. Selon notre approche, une base de donn'ees est spe...

### Citations

618 |
A truth maintenance system
- Doyle
- 1979
(Show Context)
Citation Context ... the technical level. For instance, our use of signed literals to compute the semantics of a DB has been largely inspired by those works. Truth Maintenance Systems (TMS) have been introduced by Doyle =-=[2]-=- and developed in the context of Artificial Intelligence. The aim of such systems is similar to ours as far as they offer an automatic procedure for restoring consistency of knowledge bases after upda... |

403 | On the difference between updating a knowledge base and revising it
- Katsuno, Mendelzon
- 1992
(Show Context)
Citation Context ...paper is to formalize update under transition constraints in an incomplete information setting. A wide variety of proposals for formalizing database (knowledge base) update semantics exists (e.g. [9] =-=[11]-=- [15] [4] [12] [13]). In this paper we investigate a substantially different proposal exploiting some features of linear logic [7]. Our aim is to provide a mechanism to perform updates such that if we... |

254 |
Reasoning about action using a possible models approach
- Winslett
- 1988
(Show Context)
Citation Context ... is to formalize update under transition constraints in an incomplete information setting. A wide variety of proposals for formalizing database (knowledge base) update semantics exists (e.g. [9] [11] =-=[15]-=- [4] [12] [13]). In this paper we investigate a substantially different proposal exploiting some features of linear logic [7]. Our aim is to provide a mechanism to perform updates such that if we star... |

65 | Updating logical databases
- Fagin, Kuper, et al.
- 1986
(Show Context)
Citation Context ...o formalize update under transition constraints in an incomplete information setting. A wide variety of proposals for formalizing database (knowledge base) update semantics exists (e.g. [9] [11] [15] =-=[4]-=- [12] [13]). In this paper we investigate a substantially different proposal exploiting some features of linear logic [7]. Our aim is to provide a mechanism to perform updates such that if we start wi... |

47 | Updates and Counterfactuals
- Grahne
- 1998
(Show Context)
Citation Context ...his paper is to formalize update under transition constraints in an incomplete information setting. A wide variety of proposals for formalizing database (knowledge base) update semantics exists (e.g. =-=[9]-=- [11] [15] [4] [12] [13]). In this paper we investigate a substantially different proposal exploiting some features of linear logic [7]. Our aim is to provide a mechanism to perform updates such that ... |

27 | On Formalizing Database Updates: Preliminary Report
- Reiter
- 1992
(Show Context)
Citation Context ...ze update under transition constraints in an incomplete information setting. A wide variety of proposals for formalizing database (knowledge base) update semantics exists (e.g. [9] [11] [15] [4] [12] =-=[13]). In-=- this paper we investigate a substantially different proposal exploiting some features of linear logic [7]. Our aim is to provide a mechanism to perform updates such that if we start with a "cons... |

25 | Formalizing database evolution in the situation calculus
- REITER
- 1992
(Show Context)
Citation Context ...rmalize update under transition constraints in an incomplete information setting. A wide variety of proposals for formalizing database (knowledge base) update semantics exists (e.g. [9] [11] [15] [4] =-=[12]-=- [13]). In this paper we investigate a substantially different proposal exploiting some features of linear logic [7]. Our aim is to provide a mechanism to perform updates such that if we start with a ... |

15 |
Proofs and Types. Cambridge Tracts in Theoretical Computer Science
- Girard, Lafont, et al.
- 1989
(Show Context)
Citation Context ...ting the update semantics of the old base w.r.t. to the insertion of A.) Linear logic, introduced by Girard in [7] can be seen as a logic allowing to express the notion of bounded resource. (See also =-=[8]-=- and [14]). Formally speaking, the main difference between the notion of linear proof and the notion of classical proof is the absence of contraction and weakening as structural rules in the associate... |

4 |
Linear logic and exceptions
- Fouquer'e, Vauzeilles
- 1993
(Show Context)
Citation Context ...like to stress that although in the paper we do insist on insertion of positive and negative facts as the typical update operation, our approach allows also to deal with deletion of facts. In [5] and =-=[6]-=- the equivalence between linear logic and default logic w.r.t. taxonomic default theories is proved. Although the kind of problems addressed in those papers, namely the representation of inheritance i... |

2 |
A Rational Construction of
- Elkan
- 1990
(Show Context)
Citation Context ...knowledge bases after updates. The main difference between the two approaches lies in the kind of bases handled. In TMS, pieces of information are of the same form as rules in extended logic programs =-=[3]-=-; default rules are missing. Moreover, in TMS the graph of rules can be modified in order to recover consistency. Finally, they do not provide a formal system to define the update semantics. There are... |

2 |
Taxonomic Linear Theories" ECSQARU-93
- Fouquer'e, Vauzeilles
- 1993
(Show Context)
Citation Context ...e would like to stress that although in the paper we do insist on insertion of positive and negative facts as the typical update operation, our approach allows also to deal with deletion of facts. In =-=[5]-=- and [6] the equivalence between linear logic and default logic w.r.t. taxonomic default theories is proved. Although the kind of problems addressed in those papers, namely the representation of inher... |

2 |
Passive and Active Rules in Deductive Databases
- Halfeld-Ferrari-Alves, Laurent, et al.
- 1994
(Show Context)
Citation Context ...graph of rules can be modified in order to recover consistency. Finally, they do not provide a formal system to define the update semantics. There are several similarities between the "philosophy=-=" of [10] and our approach to-=- the update problem, although the two works are quite independent. "Passive Rules" in [10] correspond in some way to our deduction rules, while "Active Rules" do recall our update ... |

1 |
Consistency Preserving Updates
- Bidoit, Cerrito, et al.
(Show Context)
Citation Context ...inear logic. We conclude by discussing several aspects of our approach, indicating some perspectives of future work and comparing our proposal to some related works. This paper is the full version of =-=[1]-=-. 2 Preliminary Definitions In the following, L is a set of propositional variables p; q; r; :::. Access literals (formally defined below) constitute the vertices of the graph G of rules. Intuitively,... |