## How to Progress a Database (and Why) I. Logical Foundations (1994)

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Venue: | In Proceedings of the Fourth International Conference on Principles of Knowledge Representation |

Citations: | 31 - 9 self |

### BibTeX

@INPROCEEDINGS{Lin94howto,

author = {Fangzhen Lin and Ray Reiter},

title = {How to Progress a Database (and Why) I. Logical Foundations},

booktitle = {In Proceedings of the Fourth International Conference on Principles of Knowledge Representation},

year = {1994},

pages = {425--436},

publisher = {Morgan Kaufmann Publishing}

}

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### Abstract

One way to think about STRIPS is as a mapping from databases to databases, in the following sense: Suppose we want to know what the world would be like if an action, represented by the STRIPS operator ff, were done in some world, represented by the STRIPS database D 0 . To find out, simply perform the operator ff on D 0 (by applying ff's elementary add and delete revision operators to D 0 ). We describe this process as progressing the database D 0 in response to the action ff. In this paper, we consider the general problem of progressing an initial database in response to a given sequence of actions. We appeal to the situation calculus and an axiomatization of actions which addresses the frame problem (Reiter [13], Lin and Reiter [8]). This setting is considerably more general than STRIPS. Our results concerning progression are mixed. The (surprising) bad news is that, in general, to characterize a progressed database we must appeal to second order logic. The good news is that there...

### Citations

576 |
The Frame Problem in the Situation Calculus: A Simple Solution (Sometimes) and a Completeness Result for Goal Regression
- Reiter
- 1991
(Show Context)
Citation Context ...) denotes the situation resulting from performing the sequence of actions A beginning with the initial situation S 0 . This can be done using regression (cf. Waldinger [17], Pednault [10], and Reiter =-=[12]-=-) to reduce the projection problem to one of entailment from the initial database, consisting of sentences about the initial situationsS 0 . Unfortunately, regression suffers from a number of drawback... |

312 |
Exploring the Middle Ground Between STRIPS and the situation calculus
- Pednault
- 1989
(Show Context)
Citation Context ...ike systems. Ever since STRIPS was first introduced (Fikes and Nilsson [4]), its logical semantics has been problematic. There have been many proposals in the literature (e.g. Lifschitz [6], Pednault =-=[11]-=-, Bacchus and Yang [2]). These all have in common a reliance on meta-theoretic operations on logical theories in order to capture the add and delete lists of STRIPS operators, but it has never been cl... |

236 |
Predicate Calculus and Program Semantics
- Dijkstra, Scholten
- 1989
(Show Context)
Citation Context ...e DS ff j= '. If D S ff j= ', then D j= ' by Proposition 4.1. From this theorem, we see that if D S ff is a progression, then it is a strongest post-condition (cf. Pednault [9], Dijkstra and Scholten =-=[3]-=-, and others) of the precondition DS0 wrt the action ff. A result by Pednault [9] shows that D S ff cannot in general be a finite set of first-order sentences in L S ff . In the following, we shall ex... |

229 | State constraints revisited
- Lin, Reiter
- 1994
(Show Context)
Citation Context ...ing an initial database in response to a given sequence of actions. We appeal to the situation calculus and an axiomatization of actions which addresses the frame problem (Reiter [13], Lin and Reiter =-=[8]-=-). This setting is considerably more general than STRIPS. Our results concerning progression are mixed. The (surprising) bad news is that, in general, to characterize a progressed database we must app... |

134 | On the semantics of strips
- Lifschitz
- 1987
(Show Context)
Citation Context ...cs of STRIPS-like systems. Ever since STRIPS was first introduced (Fikes and Nilsson [4]), its logical semantics has been problematic. There have been many proposals in the literature (e.g. Lifschitz =-=[6]-=-, Pednault [11], Bacchus and Yang [2]). These all have in common a reliance on meta-theoretic operations on logical theories in order to capture the add and delete lists of STRIPS operators, but it ha... |

112 |
Achieving several goals simultaneously
- Waldinger
- 1977
(Show Context)
Citation Context ...Q(do(A; S 0 )), where do(A; S 0 ) denotes the situation resulting from performing the sequence of actions A beginning with the initial situation S 0 . This can be done using regression (cf. Waldinger =-=[17]-=-, Pednault [10], and Reiter [12]) to reduce the projection problem to one of entailment from the initial database, consisting of sentences about the initial situationsS 0 . Unfortunately, regression s... |

108 | Proving properties of states in the situation calculus
- Reiter
- 1993
(Show Context)
Citation Context ...e, ns0. We shall denote by L 2 the second-order extension of L. Our foundational axioms for the situation calculus will be in L 2 (Lin and Reiter [8]), because we need induction on situations (Reiter =-=[14]-=-). We shall frequently need to restrict the situation calculus to a particular situation. For instance, the initial database is defined to be a finite set of sentences in L that do not mention any sta... |

99 |
Synthesizing plans that contain actions with context dependent effects
- Pednault
- 1988
(Show Context)
Citation Context ... where do(A; S 0 ) denotes the situation resulting from performing the sequence of actions A beginning with the initial situation S 0 . This can be done using regression (cf. Waldinger [17], Pednault =-=[10]-=-, and Reiter [12]) to reduce the projection problem to one of entailment from the initial database, consisting of sentences about the initial situationsS 0 . Unfortunately, regression suffers from a n... |

98 | The frame problem and knowledge-producing actions
- Scherl, Levesque
- 1993
(Show Context)
Citation Context ...world state often becomes so rearranged that significantly many final steps of the regression become entirely unnecessary. 3. Most significantly, for robotics, perceptual actions (Scherl and Levesque =-=[16]-=-) lead to new facts being added to the database. But such facts are true in the current situation -- the one immediately following the perceptual action -- whereas the other (old) database facts are t... |

78 | On specifying database updates
- Reiter
- 1995
(Show Context)
Citation Context ...l problem of progressing an initial database in response to a given sequence of actions. We appeal to the situation calculus and an axiomatization of actions which addresses the frame problem (Reiter =-=[13]-=-, Lin and Reiter [8]). This setting is considerably more general than STRIPS. Our results concerning progression are mixed. The (surprising) bad news is that, in general, to characterize a progressed ... |

73 |
Mathematical logic
- Kleene
- 1967
(Show Context)
Citation Context ...Therefore there is not a model M 0 of D such that M �� S ff M 0 . We now show that there is a model M 0 of D such that for any sentence ' in LSA , M j= ' iff M 0 j= '. By Skolem's theorem (cf. Kle=-=ene [5]-=-, page 326), there is a first-order structure M such that for any sentence ' in LSA , M j= ' iff M j= ', and (M; 0; succ) and (M ; 0; succ) are not isomorphic, i.e., M and M are not isomorphic on sort... |

62 |
S.:Updates a new Frontier
- Abiteboul
- 1988
(Show Context)
Citation Context ...he initial situationsS 0 . Unfortunately, regression suffers from a number of drawbacks in this application: 1 This is also the way that database practitioners think about database updates (Abiteboul =-=[1]-=-). In fact, the STRIPS action and database update paradigms are essentially the same. Accordingly, this paper is as much about database updates as it is about STRIPS actions and their generalizations.... |

56 | Downward refinement and the efficiency of hierarchical problem solving
- Bacchus, Yang
- 1994
(Show Context)
Citation Context ... STRIPS was first introduced (Fikes and Nilsson [4]), its logical semantics has been problematic. There have been many proposals in the literature (e.g. Lifschitz [6], Pednault [11], Bacchus and Yang =-=[2]-=-). These all have in common a reliance on meta-theoretic operations on logical theories in order to capture the add and delete lists of STRIPS operators, but it has never been clear exactly what these... |

50 |
Plan synthesis: A logical perspective
- Rosenschein
- 1981
(Show Context)
Citation Context ...d and delete revision operators to D 0 ). We describe this process as Fellow of the Canadian Institute for Advanced Research progressing the database D 0 in response to the action ff (cf. Rosenschein =-=[15]-=- and Pednault [9]). The resulting database describes the effects of the action on the world represented by the initial database. 1 However, it may not always be convenient or even possible to describe... |

41 |
Toward a mathematical theory of plan synthesis
- Pednault
- 1987
(Show Context)
Citation Context ...ion operators to D 0 ). We describe this process as Fellow of the Canadian Institute for Advanced Research progressing the database D 0 in response to the action ff (cf. Rosenschein [15] and Pednault =-=[9]-=-). The resulting database describes the effects of the action on the world represented by the initial database. 1 However, it may not always be convenient or even possible to describe the effects of a... |

39 |
STRIPS: A new approach to theorem proving in problem solving
- Fikes, Nilsson
- 1971
(Show Context)
Citation Context ...In a companion paper (Lin and Reiter [7]) we explore the consequences of our results on progression for the semantics of STRIPS-like systems. Ever since STRIPS was first introduced (Fikes and Nilsson =-=[4]-=-), its logical semantics has been problematic. There have been many proposals in the literature (e.g. Lifschitz [6], Pednault [11], Bacchus and Yang [2]). These all have in common a reliance on meta-t... |

24 | How to progress a database II: The STRIPS connection
- Lin, Reiter
- 1994
(Show Context)
Citation Context ...ny successor state axioms. On the other hand, even for context free successor state axioms, progression is not guaranteed to yield finite first-order theories. 6. In a companion paper (Lin and Reiter =-=[7]-=-) we explore the consequences of our results on progression for the semantics of STRIPS-like systems. Ever since STRIPS was first introduced (Fikes and Nilsson [4]), its logical semantics has been pro... |