Formalizing sensing actions A transition function based approach

In this paper we develop a high level action description language .As that mirrors the solution to the frame problem for sensing actions in situation calculus developed by Scherl and Levesque. This is similar to the role the language .4 plays w.r.t, non-sensing actions. In defining the semantics of -As we introduce the notion of a knowledge state which is a pair consisting of a state and a collection of states. The transition function of -As is defined in such a way that it mirrors the successor state axiom for sensing actions by Scherl and Levesque. We then present a sound and complete translation of domains in As into disjunctive logic programs. Most importantly, using the new language we are able to prove the soundness of different approximation semantics of-As that were developed by Baxal and Son w.r.t, the semantics of Scherl and Levesque. Introduction and Motivation Reasoning about sensing actions (also called knowledge producing actions) is important 1 when planning in presence of incomplete information. It was first formally discussed in (Moore 1985), and later Scherl and Levesque (Scherl and Levesque 1993) gave successor state axioms and a solution of the frame problem in presence of sensing actions. Recently, Lobo et al (Lobo et al. 1997) present a high level action description language to represent and reason about sensing actions, and Baral and Son (Baral and Son, 1997) present approximation semantics for reasoning about sensing actions. In Scherl and Levesque’s approach where the agent’s knowledge about the world is formalized using the possible world models, a planner needs to keep track of the accessibility relations. For n fluents, in the worst case, the planner may have to keep track of 2n possible worlds that are accessible. This increases the complexity of the planner tremendously. The same is true for Lobo et al’s approach. In response to this Baral and Son present an approximation semantics which is weaker than both 1 Due to space limitations we only cite a few of the papers dealing with planning in presence of sensing actions and incomplete information. Scherl and Levesque’s and Lobo et al’s formalization but leads to a simpler (and faster) planner. We, therefore believe that most practical planner will follow the semantics of Baral and Son. One of our main goal of this paper is to show that Baral and Son’s semantics is sound w.r.t. Scherl and Levesque’s formalization. Besides, Scherl and Levesque’s formalization given directly in classical logic is difficult to visualize and we believe it would be very useful to have a high level language with an automata-based semantics that corresponds to Scherl and Levesque’s formalization. This language would play a similar role w.r.t, sensing actions, as the role the language ,4 played w.r.t, nonsensing actions. Although, Lobo et al. do present a high level language for sensing actions, the relation between their language and that of Scherl and Levesque’s formalization is not known. Moreover, Lobo et al. are only able to provide a translation of their formalism to epistemic logic programs which are more complex than disjunctive logic programs to which translation of ,4 were provided. In this paper we present a high level language for sensing actions and show that: (i) When we translate domain descriptions in our language to Scherl and Levesque’s formulation we obtain similar conclusions, and (ii) When we make certain assumptions about our knowledge about the initial state then domain descriptions in our language have the same semantics as that of the semantics defined by Lobo et al. (Lobo et al. 1997). Moreover, we are also able to provide a sound and complete translation of descriptions in our language to disjunctive logic programs. Finally, using this high level language we are able to show the soundness of Baral and Son’s approximation semantics w.r.t. Scherl and Levesque ’ s formalization. In our formalization, we separate the actual state of the world from the knowledge of an agent by introducing the notion of a knowledge state (or k-state). A k-state is a pair (s, E) where s is a state representing the actual state of the world and E is a collection of states representing the set of possible states which an agent 13 From: AAAI Technical Report FS-98-02. Compilation copyright © 1998, AAAI (www.aaai.org). All rights reserved. believes he may be in. The semantics of-As is then defined by transition functions which map pairs of actions and k-states into k-states. The language .As In this section we introduce a variation of the language A in (Gelfond and Lifschitz, 1993), As, which allows reasoning about sensing actions. Syntax of .As We begin with two disjoint nonempty sets of symbols, called fluent names and action names. A fluent literal is either a fluent name or a fluent name preceded by --,. For a fluent f, by -’--f and 7 we mean f and --,f respectively. A v-proposition is an expression of the form