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On First-Order Definability and Computability of Progression for Local-Effect Actions and Beyond

Authors: Yongmei Liu and Gerhard Lakemeyer

Published in: Dagstuhl Seminar Proceedings, Volume 10081, Cognitive Robotics (2010)


Abstract
In a seminal paper, Lin and Reiter introduced the notion of progression for basic action theories in the situation calculus. Unfortunately, progression is not first-order definable in general. Recently, Vassos, Lakemeyer, and Levesque showed that in case actions have only local effects, progression is firstorder representable. However, they could show computability of the first-order representation only for a restricted class. Also, their proofs were quite involved. In this paper, we present a result stronger than theirs that for local-effect actions, progression is always first-order definable and computable. We give a very simple proof for this via the concept of forgetting. We also show first-order definability and computability results for a class of knowledge bases and actions with non-local effects. Moreover, for a certain class of local-effect actions and knowledge bases for representing disjunctive information, we show that progression is not only firstorder definable but also efficiently computable.

Cite as

Yongmei Liu and Gerhard Lakemeyer. On First-Order Definability and Computability of Progression for Local-Effect Actions and Beyond. In Cognitive Robotics. Dagstuhl Seminar Proceedings, Volume 10081, pp. 1-7, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2010)


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@InProceedings{liu_et_al:DagSemProc.10081.12,
  author =	{Liu, Yongmei and Lakemeyer, Gerhard},
  title =	{{On First-Order Definability and Computability of Progression for Local-Effect Actions and Beyond}},
  booktitle =	{Cognitive Robotics},
  pages =	{1--7},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10081},
  editor =	{Gerhard Lakemeyer and Hector J. Levesque and Fiora Pirri},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10081.12},
  URN =		{urn:nbn:de:0030-drops-26380},
  doi =		{10.4230/DagSemProc.10081.12},
  annote =	{Keywords: Action and change, knowledge representation}
}
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