Actions as Special Cases

This paper is motivated by the idea of interaction between two directions of research in knowledge representation: the design of action description languages and the development of libraries of reusable, general-purpose knowledge components. Writing an action description that characterizes actions in terms of their effects, as common today, can be compared to writing a program that does not use standard subroutines. We conjecture that a library of standard descriptions for a number of “basic” actions can facilitate writing, understanding and modifying action descriptions. In this paper, we take some steps towards determining how such a library, written in the action language C+, can be used. When using an instance of a library action description, we relate the library constants to the domain-specific constants by providing definitions. Therefore, a theory of explicit definitions in C+ is developed. To illustrate the use of the library, we show how the action PushBox in the Monkey and Bananas domain can be described as a special case of the “library action” Move. Introduction Research on describing actions started with the invention of STRIPS (Fikes & Nilsson 1971) and ADL (Pednault 1994) and led in recent years to the design of very expressive action languages, such as C+ (Giunchiglia et al. 2004). The heart of every action language is a syntactic mechanism for describing effects of actions on fluents. When we define, for instance, the Monkey and Bananas domain in STRIPS, we can specify how pushing the box affects the location of the box by including appropriate atoms in the add list and delete list of the operator PushBox(l). In C+ the same idea can be expressed by the causal law PushBox(l) causes Loc(Box)= l (1) (quoted from (Giunchiglia et al. 2004), Figure 2, reproduced below). Descriptions like these are common in knowledge representation, but they are strikingly different from the descriptions of actions that humans give to each other informally. The dictionary says, for instance, that pushing is moving by steady pressure. This phrase explains the meaning of the word push not by listing the effects of this action, but by presenting it as a special case of another action, move, that is Copyright c © 2006, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. supposed to be already familiar to the reader. Some actions may need to be described directly in terms of the changes that they cause; to move, for instance, means to cause to change position, according to the dictionary. But in most cases the easiest way to describe an action is to relate it to more basic actions. We would like to apply the idea of a library of reusable, general-purpose knowledge components (Barker, Porter, & Clark 2001) to the design of action languages. We conjecture that a library of standard descriptions for “basic” actions, such as move and give, can facilitate writing, understanding and modifying action descriptions. Additionally, we conjecture that the constructs of language C+ are rich enough to capture the features needed to build and use such a library. In this paper, we take some steps towards determining how such a C+ library of standard actions can be used when writing action descriptions. Specifically, we introduce a general form of causal laws for relating special-case actions and fluents to the library constants. These laws “explicitly define” a constant in terms of other constants. Therefore, after a brief review of C+, we develop a theory of explicit definitions in C+. The laws used to define constants in terms of others can be called “bridge rules” because they provide a connection between the library and the specific domain description. With the theory of explicit definitions in C+, bridge rules can be used to completely eliminate all references to the library and thus obtain an alternative action description in terms of the domain-specific constants. The causal laws used in the bridge rules are nondefinite (see the review of C+ below). Since the Causal Calculator1 is an implementation of the definite fragment of C+, it will not be possible to use that system, at least directly, to process action descriptions containing bridge rules. However, one of the propositions from our theory of explicit definitions shows that, under certain conditions, bridge rules may be replaced by definite causal laws. In the rest of the paper, a specific example is used to illustrate how action domains can be specified with libraries. First we give a C+ description of the action Move that can be included, in principle, in a library of general-purpose action http://www.cs.utexas.edu/ ̃tag/ccalc/.