As an alternative to planning, an approach to high-level agent control based on concurrent program execution is considered. The language includes facilities for prioritizing the concurrent execution, interrupting the execution when certain conditions become true, and dealing with exogenous actions. The language di ers from other procedural formalisms for concurrency in that the initial state can be incompletely speci ed and the primitive actions can be user-de ned by axioms in the situation calculus. In a companion paper, a formal de nition in the situation calculus of such a programming language is presented and illustrated with detailed examples. In this paper, the mathematical properties of the programming language are explored. 1

We study the complexity of several recently proposed methods for updating or revising propositional knowledge bases. In particular, we derive complexity results for the following problem: given a knowledge base T , an update p, and a formula q, decide whether q is derivable from T p, the updated (or revised) knowledge base. This problem amounts to evaluating the counterfactual p > q over T . Besides the general case, also subcases are considered, in particular where T is a conjunction of Horn clauses, or where the size of p is bounded by a constant.

This paper addresses complexity issues for important problems arising with disjunctive logic programming. In particular, the complexity of deciding whether a disjunctive logic program is consistent is investigated for a variety of well-known semantics, as well as the complexity of deciding whether a propositional formula is satised by all models according to a given semantics. We concentrate on nite propositional disjunctive programs with as wells as without integrity constraints, i.e., clauses with empty heads; the problems are located in appropriate slots of the polynomial hierarchy. In particular, we show that the consistency check is P 2 -complete for the disjunctive stable model semantics (in the total as well as partial version), the iterated closed world assumption, and the perfect model semantics, and we show that the inference problem for these semantics is P 2 -complete; analogous results are derived for the an

Circumscription and the closed world assumption with its variants are well-known nonmonotonic techniques for reasoning with incomplete knowledge. Their complexity in the propositional case has been studied in detail for fragments of propositional logic. One open problem is whether the deduction problem for arbitrary propositional theories under the extended closed world assumption or under circumscription is $\Pi^P_2$-complete, i.e., complete for a class of the second level of the polynomial hierarchy. We answer this question by proving these problems $\Pi^P_2$-complete, and we show how this result applies to other variants of closed world reasoning.

Like classical planning, the execution of high-level agent programs requires a reasoner to look all the way to a final goal state before even a single action can be taken in the world. This deferral is a serious problem in practice for large programs. Furthermore, the problem is compounded in the presence of sensing actions which provide necessary information, but only after they are executed in the world. To deal with this, we propose (characterize formally in the situation calculus, and implement in Prolog) a new incremental way of interpreting such high-level programs and a new high-level language construct, which together, and without loss of generality, allow much more control to be exercised over when actions can be executed. We argue that such a scheme is the only practical way to deal with large agent programs containing both nondeterminism and sensing.

Recently Lakemeyer and Levesque proposed the logic, which amalgamates both the situation calculus and Levesque’s logic of only knowing. While very expressive the practical relevance of the formalism is unclear because it heavily relies on second-order logic. In this paper we demonstrate that the picture is not as bleak as it may seem. In particular, we show that for large classes of knowledge bases and queries, including epistemic ones, query evaluation requires first-order reasoning only. We also provide a simple semantic definition of progressing a knowledge base. For a particular class of knowledge bases, adapted from earlier results by Lin and Reiter, we show that progression is first-order representable and easy to compute. 1

In this paper, we consider the projection task (determining what does or does not hold after performing a sequence of actions) in a general setting where a solution to the frame problem may or may not be available, and where online information from sensors may or may not be applicable. We formally characterize the projection task for actions theories of this sort, and show how a generalized form of regression produces correct answers whenever it can be used. We characterize conditions on action theories, sequences of actions, and sensing information that are sufficient to guarantee that regression can be used, and present a provably correct regressionbased procedure in Prolog for performing the task under these conditions.

Filtering denotes any method whereby an agent updates its belief state—its knowledge of the state of the world—from a sequence of actions and observations. In logical filtering, the belief state is a logical formula describing possible world states and the agent has a (possibly nondeterministic) logical model of its environment and sensors. This paper presents efficient logical filtering algorithms that maintain a compact belief state representation indefinitely, for a broad range of environment classes including nondeterministic, partially observable STRIPS environments and environments in which actions permute the state space. Efficient filtering is also possible when the belief state is represented using prime implicates, or when it is approximated by a logically weaker formula. 1

Over the years, many different agent programming languages have been proposed. In this paper, we propose a concept called Agent Programs using which, the way an agent should act in various situations can be declaratively specified by the creator of that agent. Agent Programs may be built on top of arbitrary pieces of software code and may be used to specify what an agent is obliged to do, what an agent may do, and what an agent may not do. In this paper, we define several successively more sophisticated and epistemically satisfying declarative semantics for agent programs. We further show that agent programs cleanly extend well understood semantics for logic programs, and thus are clearly linked to existing results on logic programming and nonmonotonic reasoning.

In this tutorial-overview, which resulted from a lecture course given by the authors at