We study properties of programs with monotone and convex constraints. We extend to these formalisms concepts and results from normal logic programming. They include the notions of strong and uniform equivalence with their characterizations, tight programs and Fages Lemma, program completion and loop formulas. Our results provide an abstract account of properties of some recent extensions of logic programming with aggregates, especially the formalism of lparse programs. They imply a method to compute stable models of lparse programs by means of off-the-shelf solvers of pseudo-boolean constraints, which is often much faster than the smodels system.

Reaction RuleML is a general, practical, compact and user-friendly XML-serialized language for the family of reaction rules. In this white paper we give a review of the history of event / action /state processing and reaction rule approaches and systems in different domains, define basic concepts and give a classification of the event, action, state processing and reasoning space as well as a discussion of relevant / related work

The Association for the Advancement of Artificial Intelligence, in cooperation with Stanford University's Computer Science Department, was pleased to present its 2006 Spring Symposium Series held March 27-29, 2006, at Stanford University, California. The titles of the eight symposia were (1) Argumentation for Consumers of Health Care (chaired by Nancy Green); (2) Between a Rock and a Hard Place: Cognitive Science Principles Meet AI Hard Problems (chaired by Christian Lebiere); (3) Computational Approaches to Analyzing Weblogs (chaired by Nicolas Nicolov); (4) Distributed Plan and Schedule Management (chaired by Ed Durfee); (5) Formalizing and Compiling Background Knowledge and Its Applications to Knowledge Representation and Question Answering (chaired by Chitta Baral); (6) Semantic Web Meets e-Government (chaired by Ljiljana Stojanovic); (7) To Boldly Go Where No Human-Robot Team Has Gone Before (chaired by Terry Fong); and (8) What Went Wrong and Why: Lessons from AI Research and Applications (chaired by Dan Shapiro).

In a field of research about general reasoning mechanisms, it is essential to have appropriate benchmarks. Ideally, the benchmarks should reflect possible applications of the developed technology. In AI Planning, researchers more and more tend to draw their testing examples from the benchmark collections used in the International Planning Competition (IPC). In the organization of (the deterministic part of) the fourth IPC, IPC-4, the authors therefore invested significant effort to create a useful set of benchmarks. They come from five different (potential) real-world applications of planning: airport ground traffic control, oil derivative transportation in pipeline networks, model-checking safety properties, power supply restoration, and UMTS call setup. Adapting and preparing such an application for use as a benchmark in the IPC involves, at the time, inevitable (often drastic) simplifications, as well as careful choice between, and engineering of, domain encodings. For the first time in the IPC, we used compilations to formulate complex domain features in simple languages such as STRIPS, rather than just dropping the more interesting problem constraints in the simpler language subsets. The article explains and discusses the five application domains and their adaptation to form the PDDL test suites used in IPC-4. We summarize known theoretical results on structural properties of the domains, regarding their computational complexity and provable properties of their topology under the h+ function (an idealized version of the relaxed plan heuristic). We present new (empirical) results illuminating properties such as the quality of the most wide-spread heuristic functions (planning graph, serial planning graph, and relaxed plan), the growth of propositional representations over instance size, and the number of actions available to achieve each fact; we discuss these data in conjunction with the best results achieved by the different kinds of planners participating in IPC-4.

Resolution is the rule of inference at the basis of most procedures for automated reasoning. In these procedures, the input formula is first translated into an equisatisfiable formula in conjunctive normal form (CNF) and then represented as a set of clauses. Deduction starts by inferring new clauses by resolution, and goes on until the empty clause is generated or satisfiability of the set of clauses is proven, e.g., because no new clauses can be generated. In this paper, we restrict our attention to the problem of evaluating Quantified Boolean Formulas (QBFs). In this setting, the above outlined deduction process is known to be sound and complete if given a formula in CNF and if a form of resolution, called ``Q-resolution'', is used. We introduce Q-resolution on terms, to be used for formulas in disjunctive normal form. We show that the computation performed by most of the available procedures for QBFs --based on the Davis-Logemann-Loveland procedure (DLL) for propositional satisfiability-- corresponds to a tree in which Q-resolution on terms and clauses alternate. This poses the theoretical bases for the introduction of learning, corresponding to recording Q-resolution formulas associated with the nodes of the tree. We discuss the problems related to the introduction of learning in DLL based procedures, and present solutions extending state-of-the-art proposals coming from the literature on propositional satisfiability. Finally, we show that our DLL based solver extended with learning, performs significantly better on benchmarks used in the 2003 QBF solvers comparative evaluation.

We introduce a logic for reasoning about evidence that essentially views evidence as a function from prior beliefs (before making an observation) to posterior beliefs (after making the observation). We provide a sound and complete axiomatization for the logic, and consider the complexity of the decision problem. Although the reasoning in the logic is mainly propositional, we allow variables representing numbers and quantification over them. This expressive power seems necessary to capture important properties of evidence.

A delta-model is a satisfying assignment of a Boolean formula for which any small alteration, such as a single bit flip, can be repaired by flips to some small number of other bits, yielding a new satisfying assignment. These satisfying assignments represent robust solutions to optimization problems (e.g., scheduling) where it is possible to recover from unforeseen events (e.g., a resource becoming unavailable). The concept of delta-models was introduced by Ginsberg, Parkes and Roy (AAAI 1998) , where it was proved that finding delta-models for general Boolean formulas is NP-complete. In this paper, we extend that result by studying the complexity of finding delta-models for classes of Boolean formulas which are known to have polynomial time satisfiability solvers. In particular, we examine 2-SAT, Horn-SAT, Affine-SAT, dual-Horn-SAT, 0-valid and 1-valid SAT. We see a wide variation in the complexity of finding delta-models, e.g., while 2-SAT and Affine-SAT have polynomial time tests for delta-models, testing whether a Horn-SAT formula has one is NP-complete.

In recent years, CP-nets have emerged as a useful tool for supporting preference elicitation, reasoning, and representation. CP-nets capture and support reasoning with qualitative conditional preference statements, statements that are relatively natural for users to express. In this paper, we extend the CP-nets formalism to handle another class of very natural qualitative statements one often uses in expressing preferences in daily life - statements of relative importance of attributes. The resulting formalism, TCP-nets, maintains the spirit of CP-nets, in that it remains focused on using only simple and natural preference statements, uses the ceteris paribus semantics, and utilizes a graphical representation of this information to reason about its consistency and to perform, possibly constrained, optimization using it. The extra expressiveness it provides allows us to better model tradeoffs users would like to make, more faithfully representing their preferences.

Most autonomous robots are equipped with restricted, unreliable, and inaccurate sensors and effectors and operate in complex and dynamic environments. A successful approach to deal with the resulting uncertainty is the use of controllers that prescribe the robots' behavior in terms of concurrent reactive plans (CRPs) -- plans that specify how the robots are to react to sensory input in order to accomplish their jobs reliably (e.g., McDermott, 1992a; Beetz, 1999). Reactive plans are successfully used to produce situation specific behavior, to detect problems and recover from them automatically, and to recognize and exploit opportunities (Beetz et al., 2001). These kinds of behaviors are particularly important for autonomous robots that have only uncertain information about the world, act in dynamically changing environments, and are to accomplish complex tasks efficiently. Besides reliability and flexibility, foresight is another important capability of competent autonomous robots (McDermott, 1992a).

We present a uniform non-monotonic solution to the problems of reasoning about action on the basis of an argumentation-theoretic approach. Our theory is provably correct relative to a sensible minimisation policy introduced on top of a temporal propositional logic. Sophisticated problem domains can be formalised in our framework. As much attention of researchers in the field has been paid to the traditional and basic problems in reasoning about actions such as the frame, the qualification and the ramification problems, approaches to these problems within our formalisation lie at heart of the expositions presented in this paper.