Conformant planning is the problem of finding a sequence of actions for achieving a goal in the presence of uncertainty in the initial state or action effects. The problem has been approached as a path-finding problem in belief space where good belief representations and heuristics are critical for scaling up. In this work, a different formulation is introduced for conformant problems with deterministic actions where they are automatically converted into classical ones and solved by an off-the-shelf classical planner. The translation maps literals L and sets of assumptions t about the initial situation, into new literals KL/t that represent that L must be true if t is initially true. We lay out a general translation scheme that is sound and establish the conditions under which the translation is also complete. We show that the complexity of the complete translation is exponential in a parameter of the problem called the conformant width, which for most benchmarks is bounded. The planner based on this translation exhibits good performance in comparison with existing planners, and is the basis for T0, the best performing planner in the Conformant Track of the 2006 International Planning Competition.

In this paper we explore a class of belief update operators, in which the definition of the operator is compositional with respect to the sentence to be added. The goal is to provide an update operator that is intuitive, in that its definition is based on a recursive decomposition of the update sentences structure, and that may be reasonably implemented. In addressing update, we first provide a definition phrased in terms of the models of a knowledge base. While this operator satisfies a core group of the benchmark Katsuno-Mendelzon update postulates, not all of the postulates are satisfied. Other Katsuno-Mendelzon postulates can be obtained by suitably restricting the syntactic form of the sentence for update, as we show. In restricting the syntactic form of the sentence for update, we also obtain a hierarchy of update operators with Winsletts standard semantics as the most basic interesting approach captured. We subsequently give an algorithm which captures this approach; in the general case the algorithm is exponential, but with some not-unreasonable assumptions we obtain an algorithm that is linear in the size of the knowledge base. Hence the resulting approach has much better complexity characteristics than other operators in some situations. We also explore other compositional belief change operators: erasure is developed as a dual operator to update; we show that a forget operator is definable in terms of update; and we give a definition of the compositional revision operator. We obtain that compositional revision, under the most natural definition, yields the Satoh revision operator.

In real-world applications, knowledge bases consisting of all the information at hand for a specific domain, along with the current state of affairs, are bound to contain contradictory data coming from different sources, as well as data with varying degrees of uncertainty attached. Likewise, an important aspect of the effort associated with maintaining knowledge bases is deciding what information is no longer useful; pieces of information (such as intelligence reports) may be outdated, may come from sources that have recently been discovered to be of low quality, or abundant evidence may be available that contradicts them. In this paper, we propose a probabilistic structured argumentation framework that arises from the extension of Presumptive Defeasible Logic Programming (PreDeLP) with probabilistic models, and argue that this formalism is capable of addressing the basic issues of handling contradictory and uncertain data. Then, to address the last issue, we focus on the study of non-prioritized belief revision operations over probabilistic PreDeLP programs. We propose a set of rationality postulates -- based on well-known ones developed for classical knowledge bases -- that characterize how such operations should behave, and study a class of operators along with theoretical relationships with the proposed postulates, including a representation theorem stating the equivalence between this class and the class of operators characterized by the postulates.

Max-product ‘belief propagation’ (BP) is a popular distributed heuristic for finding the Maximum A Posteriori (MAP) assignment in a joint probability distribution represented by a Graphical Model (GM). It was recently shown that BP converges to the correct MAP assignment for a class of loopy GMs with the following common feature: the Linear Programming (LP) relaxation to the MAP problem is tight (has no integrality gap). Unfortunately, tightness of the LP relaxation does not, in general, guarantee convergence and correctness of the BP algorithm. The failure of BP in such cases motivates reverse engineering a solution – namely, given a tight LP, can we design a ‘good’ BP algorithm. In this paper, we design a BP algorithm for the Maximum Weight Matching (MWM) problem over general graphs. We prove that the algorithm converges to the correct optimum if the respective LP relaxation, which may include inequalities associated with non-intersecting odd-sized cycles, is tight. The most significant part of our approach is the introduction of a novel graph transformation designed to force convergence of BP. Our theoretical result suggests an efficient BP-based heuristic for the MWM problem, which consists of making sequential, “cutting plane”, modifications to the underlying GM. Our experiments show that this heuristic performs as well as traditional cutting-plane algorithms using LP solvers on MWM problems.

The sigma point (SP) filter, also known as unscented Kalman filter, is an attractive alternative to the extended Kalman filter and the particle filter. Here, we extend the SP filter to nonsequential Bayesian inference corresponding to loopy factor graphs. We propose sigma point belief propagation (SPBP) as a low-complexity approximation of the belief propagation (BP) message passing scheme. SPBP achieves approximate marginalizations of posterior distributions corresponding to (generally) loopy factor graphs. It is well suited for decentralized inference because of its low communication requirements. For a decentralized, dynamic sensor localization problem, we demonstrate that SPBP can outperform nonparametric (particle-based) BP while requiring significantly less computations and communications.

Belief Propagation has been widely used for marginal inference, however it is slow on problems with large-domain variables and high-order factors. Previous work provides useful approximations to facilitate inference on such models, but lacks important anytime properties such as: 1) providing accurate and consistent marginals when stopped early, 2) improving the approximation when run longer, and 3) converging to the fixed point of BP. To this end, we propose a message passing algorithm that works on sparse (partially instantiated) domains, and converges to consistent marginals using dynamic message scheduling. The algorithm grows the sparse domains incrementally, selecting the next value to add using prioritization schemes based on the gradients of the marginal inference objective. Our experiments demonstrate local anytime consistency and fast convergence, providing significant speedups over BP to obtain low-error marginals: up to 25 times on grid models, and up to 6 times on a real-world natural language processing task.

In classical, AGM-style belief change, it is assumed that the underlying logic contains classical propositional logic. This is clearly a limiting assumption, particularly in Artificial Intelligence. Consequently there has been recent interest in studying belief change in approaches where the full expressivity of classical propositional logic is not obtained. In this paper we investigate belief contraction in Horn knowledge bases. We point out that the obvious extension to the Horn case, involving Horn remainder sets as a starting point, is problematic. Not only do Horn remainder sets have undesirable properties, but also some desirable Horn contraction functions are not captured by this approach. For Horn belief set contraction, we develop an account in terms of a model-theoretic characterisation involving weak remainder sets. Maxichoice and partial meet Horn contraction is specified, and we show that the problems arising with earlier work are resolved by these approaches. As well, constructions of the specific operators and sets of postulates are provided, and representation results are obtained. We also examine Horn package contraction, or contraction by a set of formulas. Again, we give a construction and postulate set, linking them via a representation result. Last, we investigate the closely-related notion of forgetting in Horn clauses. This work is arguably interesting since Horn clauses have found widespread use in AI; as well, the results given here may potentially be extended to other areas which make use of Horn-like reasoning, such as logic programming, rule-based systems, and description logics. Finally, since Horn reasoning is weaker than classical reasoning, this work sheds light on the foundations of belief change

Defeasible inheritance networks are a non-monotonic framework that deals with hierarchical knowledge. On the other hand, rational closure is acknowledged as a landmark of the preferential approach to non-monotonic reasoning. We will combine these two approaches and define a new non-monotonic closure operation for propositional knowledge bases that combines the advantages of both. Then we redefine such a procedure for Description Logics (DLs), a family of logics well-suited to model structured information. In both cases we will provide a simple reasoning method that is built on top of the classical entailment relation and, thus, is amenable of an implementation based on existing reasoners. Eventually, we evaluate our approach on well-known landmark test examples.

Computational models of goal recognition hold considerable promise for enhancing the capabilities of drama managers and director agents for interactive narratives. The problem of goal recognition, and its more general form plan recognition, has been the subject of extensive investigation in the AI community. However, there have been relatively few empirical investigations of goal recognition models in the intelligent narrative technologies community to date, and little is known about how computational models of interactive narrative can inform goal recognition. In this paper, we investigate a novel goal recognition model based on Markov Logic Networks (MLNs) that leverages narrative discovery events to enrich its representation of narrative state. An empirical evaluation shows that the enriched model outperforms a prior state-of-the-art MLN model in terms of accuracy, convergence rate, and the point of convergence.

One of Judea Pearl's many, many important contributions to the study of causality was the first attempt to use the mathematical tools of causal modeling to give an account of "actual causation", a notion that has been of considerable interest among philosophers and legal theorists (Pearl, 2000, Chapter 10). Pearl later revised his account of actual causation in joint work with Halpern (Halpern & Pearl, 2005). A number of authors (Hall, 2007; Halpern, 2008; Hitchcock, 2007; Menzies, 2004) have suggested that an account of actual causation must be sensitive to considerations of normality, as well as to causal structure. In (Halpern & Hitchcock, 2011), we suggest a way of incorporating considerations of normality into the Halpern-Pearl theory, and show how to extend the account to illuminate features of the psychology of causal judgment, as well as features of causal reasoning in the law. Our account of actual causation makes use of "extended causal models", which include both structural equations among a set of variables, and a partial preorder on possible worlds, which represents the relative "normality" of those worlds. We actually want to think of people as working with the structural equations and normality order to evaluate actual causation. However, consideration of even simple examples immediately suggests a problem. A direct representation of the equations and normality order is too cumbersome for cognitively limited agents to use effectively. If our account of actual causation is to be at all realistic as a model of human causal judgment, some form of compact representation will be needed.