1,721,004 research outputs found
On the Progression of Situation Calculus Basic Action Theories: Resolving a 10-year-old Conjecture
No full textIn a seminal paper, Lin and Reiter introduced a model-theoretic definition for the progression of the initial knowledge base of a basic action theory. This definition comes with a strong negative result, namely that for certain kinds of action theories, first-order logic is not expressive enough to correctly characterize this form of progression, and second-order axioms are necessary. However, Lin and Reiter also considered an alternative definition for progression which is always first-order definable. They conjectured that this alternative definition is incorrect in the sense that the progressed theory is too weak and may sometimes lose information. This conjecture, and the status of first-order definable progression, has remained open since then. In this paper we present two significant results about this alternative definition of progression. First, we prove the Lin and Reiter conjecture by presenting a case where the progressed theory indeed does lose information. Second, we prove that the alternative definition is nonetheless correct for reasoning about a large class of sentences, including some that quantify over situations. In this case the alternative definition is a preferred option due to its simplicity and the fact that it is always first-order. Copyright © 2008, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved
Progression of Situation Calculus Action Theories with Incomplete Information
No full textIn this paper, we propose a new progression mechanism for a restricted form of incomplete knowledge formulated as a basic action theory in the situation calculus. Specifically, we focus on functional fluents and deal directly with the possible values these fluents may have and how these values are affected by both physical and sensing actions. The method we propose is logically complete and can be calculated efficiently using database techniques under certain reasonable assumptions
First-Order Strong Progression for Local-Effect Basic Action Theories
No full textIn a seminal paper Lin and Reiter introduced the notion of progression for basic action theories in the situation calculus. The idea is to replace an initial database by a new set of sentences which reflect the changes due to an action. Unfortunately, progression requires secondorder logic in general. In this paper, we introduce the notion of strong progression, a slight variant of Lin and Reiter that has the intended properties, and we show that in case actions have only local effects, progression is always first-order representable. Moreover, for a restricted class of local-effect axioms we show how to construct a new database that is finite
On the limits of planning over belief states under strict uncertainty
No full textA recent trend in planning with incomplete information is to model the actions of a planning problem as nondeterministic transitions over the belief states of a planner, and to search for a plan that terminates in a desired goal state no matter how these transitions turn out. We show that this view of planning is fundamentally limited. Any plan that is successful by this criteria has an upper bound on the number of actions it can execute. Specifically, the account will not work when iterative plans are needed. We also show that by modifying the definition slightly, we obtain another account of planning that does work properly even for iterative plans. Although the argument is presented in an abstract form, we illustrate the issues using a simple concrete example. Copyright © 2006, American Association for Artificial Intelligence
Progressing basic action theories with non-local effect actions
No full textIn this paper we propose a practical extension to some recent work on the progression of action theories in the situation calculus. In particular, we argue that the assumption of local-effect actions is too restrictive for realistic settings. Based on the notion of safe-range queries from database theory and just-in-time action histories, we present a new type of action theory, called range-restricted, that allows actions to have non-local effects with a restricted range. These theories can represent incomplete information in the initial database in terms of possible closures for fluents and can be progressed by directly updating the database in an algorithmic manner. We prove the correctness of our method and argue for the applicability of range-restricted theories in realistic settings
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