In recent years research in the planning community has moved increasingly towards application of planners to realistic problems involving both time and many types of resources. For example, interest in planning demonstrated by the space research community has inspired work in observation scheduling, planetary rover exploration and spacecraft control domains. Other temporal and resource-intensive domains including logistics planning, plant control and manufacturing have also helped to focus the community on the modelling and reasoning issues that must be confronted to make planning technology meet the challenges of application. The International Planning Competitions have acted as an important motivating force behind the progress that has been made in planning since 1998. The third competition (held in 2002) set the planning community the challenge of handling time and numeric resources. This necessitated the development of a modelling language capable of expressing temporal and numeric properties of planning domains. In this paper we describe the language, pddl2.1, that was used in the competition. We describe the syntax of the language, its formal semantics and the validation of concurrent plans. We observe that pddl2.1 has considerable modelling power — exceeding the capabilities of current planning technology — and presents a number of important challenges to the research community.

Our focus in this paper is on natural exogenous actions (Pinto [23]), namely those which occur in response to known laws of physics, like a ball bouncing at times determined by Newtonian equations of motion. The property of such actions that we wish to capture is that they must occur at their predicted times, provided no earlier actions (natural or agent initiated) prevent them from occurring. Because several such actions may occur simultaneously, we need a theory of concurrency. Because such actions may be modeled by equations of motion, we need to represent continuous time. This paper shows how to gracefully accommodate all these features within the situation calculus, without sacrificing the simple solution to the frame problem of Reiter [25]. One nice consequence of this approach is a situation calculus specification of deductive planning, with continuous time and true concurrency, and where the agent can incorporate external natural event occurrences into her...

Action languages serve for describing changes that are caused by performing actions. We define a new action language C, based on the theory of causal explanation proposed recently by McCain and Turner, and illustrate its expressive power by applying it to a number of examples. The mathematical results presented in the paper relate C to the Baral---Gelfond theory of concurrent actions. Introduction Representing properties of actions has been the subject of many papers and two recent books (Sandewall 1995), (Shanahan 1997). One direction of work makes use of "action languages," such as A (Gelfond & Lifschitz 1993) and its dialects. An action language serves for describing the effects of actions on fluents. The meaning of a set of propositions in an action language can be represented by a "transition diagram." In this paper we define a new action language C, based on the theory of causal explanation proposed in (McCain & Turner 1997) and extended in (Lifschitz 1997a). The main i...

In the situation calculus, it is sometimes necessary to prove that certain properties are true in all world states accessible from the initial state. This is the case for some forms of reasoning about the physical world, for certain planning applications, and for verifying integrity constraints in databases. Not surprisingly, this requires a suitable form of mathematical induction. This paper motivates the need for proving properties of states in the situation calculus, proposes appropriate induction principles for this task, and gives examples of their use in databases and for reasoning about the physical world. Abbreviated title: Proving Properties of States 1 Introduction The situation calculus [8] is enjoying new popularity these days. One reason is that its expressiveness is considerably richer than has been commonly believed (Gelfond, Lifschitz and Rabinov [2], Pinto and Reiter [10], Schubert [16]). Another is the possibility of precisely characterizing the strengths and limi...

This article presents the event calculus, a logic-based formalism for representing actions and their effects. A circumscriptive solution to the frame problem is deployed which reduces to monotonic predicate completion. Using a number of benchmark examples from the literature, the formalism is shown to apply to a variety of domains, including those featuring actions with indirect effects, actions with non-deterministic effects, concurrent actions, and continuous change. Introduction Central to many complex computer programs that take decisions about how they or other agents should act is some form of representation of the effects of actions, both their own and those of other agents. To the extent that the design of such programs is to be based on sound engineering principles, rather than ad hoc methods, it's vital that the subject of how actions and their effects are represented has a solid theoretical basis. Hence the need for logical formalisms for representing action, which, a...

This paper describes a novel approach to high-level robot programming based on a highly developed logical theory of action. The user provides a specification of the robot's basic actions (their preconditions and effects on the environment) as well as of relevant aspects of the environment, in an extended version of the situation calculus. He can then specify robot behaviors in terms of these actions in a programming language that allows references to world conditions (e.g. if 9c(Pop can(c) On table(c)) then pick up(c)). The programs can be executed to drive the robot. The interpreter automatically maintains the world model required to execute programs based on the specification. The theoretical framework includes a solution to the frame problem and is very general --- it handles dynamic and incompletely known worlds, as well as perception actions. Given this kind of domain specification, it is also possible to support more sophisticated reasoning, such as task planni...

We propose, and axiomatize, an extended version of the situation calculus [10] for temporal reasoning in a logic programming framework. This extended language provides for a linear temporal structure, which may be viewed as a path of actual event occurrences within the tree of possible situations of the "classical" situation calculus. The extended language provides for events to occur and fluents to hold at specific points in time. As a result, it is possible to establish a close correspondence between this extended situation calculus and other linear time formalisms which have been proposed in opposition to the situation calculus. In particular, we argue that the functionality of the event calculus [6] is subsumed by the extended situation calculus. We present a logic program for temporal reasoning which is provably sound for our axiomatization, relative to the Clark completion semantics of the program. Our logic programming approach has the advantage of being grounded in a pure (without negation as failure) first order axiomatization suitable for reasoning about events and their occurrences. Moreover, efficient algorithms can be obtained for a suitable class of temporal reasoning problems, following the ideas of Kowalski [5].

A narrative is a course of real events about which we might have incomplete information. Formalisms for reasoning about action may be broadly divided into those which are narrativebased, such as the Event Calculus of Kowalski and Sergot, and those which reason on the level of hypothetical sequences of actions, in particular the Situation Calculus. This paper bridges the gap between these types of formalism by supplying a technique for linking incomplete narrative descriptions to Situation Calculus domain formulae written in the usual style using a Result function. Particular attention is given to actions with duration and overlapping actions. By illuminating the relationship between these two different styles of representation, the paper moves us one step closer to a full understanding of the space of all possible formalisms for reasoning about action. Introduction The Situation Calculus [15] is one of A.I.'s oldest and best understood formalisms for representing change, but it has of...

A calculus of events is presented in which domain constraints, concurrent events, and events with non-deterministic effects can be represented. The paper offers a non-monotonic solution to the frame problem for this formalism that combines two of the techniques developed for the situation calculus, namely causal and state-based minimisation. A theorem is presented which guarantees that temporal projection will not interfere with minimisation in this solution, even in domains with ramifications, concurrency, and non-determinism. Finally, the paper shows how the formalism can be extended to cope with continuous change, whilst preserving the conditions for the theorem to apply. 1 Introduction The frame problem was first described by McCarthy and Hayes in the Sixties [23], and has occupied the thoughts of AI researchers ever since. In a nutshell, the problem is this: if we deploy classical logic in a straightforward way to describe the effects of actions, we have to represent explicitl...

We investigate logical formalization of the effects of actions in the situation calculus. We propose a formal criterion against which to evaluate theories of deterministic actions. We show how the criterion provides us a formal foundation upon which to tackle the frame problem, as well as its variant in the context of concurrent actions. Our main technical contributions are in formulating a wide class of monotonic causal theories that satisfy the criterion, and showing that each such theory can be reformulated succinctly in circumscription. 1 1 Introduction The histories of the frame problem [18], and of the particular Yale Shooting Problem (YSP) which has become its best known illustration [6], have followed a disturbing pattern. The frame problem itself, although introduced in the context of formalizing common sense, was never formally defined, and was only illustrated through suggestive examples. This is an initial disturbing factor. A second disturbing factor is that, despite the ...