In a seminal paper, Lin and Reiter introduced the notion of progression for basic action theories in the situation calculus. Recently, Fang and Liu extended the situation calculus to account for multi-agent knowledge and belief change. In this paper, based on their framework, we investigate progression of both belief and knowledge in the single-agent propositional case. We first present a model-theoretic definition of progression of knowledge and belief. We show that for propositional actions, i.e., actions whose precondition axioms and successor state axioms are propositional formulas, progression of knowledge and belief reduces to forgetting in the logic of knowledge and belief, which we show is closed under forgetting. Consequently, we are able to show that for propositional actions, progression of knowledge and belief is always definable in the logic of knowledge and belief.

Goal Recognition is the task of inferring an actor's goals given some or all of the actor's observed actions. There is considerable interest in Goal Recognition for use in intelligent personal assistants, smart environments, intelligent tutoring systems, and monitoring user's needs. In much of this work, the actor's observed actions are compared against a generated library of plans. Recent work by Ramirez and Geffner makes use of AI planning to determine how closely a sequence of observed actions matches plans for each possible goal. For each goal, this is done by comparing the cost of a plan for that goal with the cost of a plan for that goal that includes the observed actions. This approach yields useful rankings, but is impractical for real-time goal recognition in large domains because of the computational expense of constructing plans for each possible goal. In this paper, we introduce an approach that propagates cost and interaction information in a plan graph, and uses this information to estimate goal probabilities. We show that this approach is much faster, but still yields high quality results.

Parameterized complexity is a well recognized vehicle for understanding the multitude of complexity AI problems typically exhibit. However, the prominent problem of belief revision has not undergone a systematic investigation in this direction yet. This is somewhat surprising, since by its very nature of involving a knowledge base and a revision formula, this problem provides a perfect playground for investigating novel parameters. Among our results on the parameterized complexity of revision is thus a versatile fpt algorithm which is based on the parameter of the number of atoms shared by the knowledge base and the revision formula. Towards identifying the frontier between parameterized tractability and intractability, we also give hardness results for classes such as co-W[1], para-Theta 2 P and FPT NP[f(k)]

Belief merging is a central operation within the field of belief change and addresses the problem of combining multiple, possibly mutually inconsistent knowledge bases into a single, consistent one. A current research trend in belief change is concerned with tailored representation theorems for fragments of logic, in particular Horn logic. Hereby, the goal is to guarantee that the result of the change operations stays within the fragment under consideration. While several such results have been obtained for Horn revision and Horn contraction, merging of Horn theories has been neglected so far. In this paper, we provide a novel representation theorem for Horn merging by strengthening the standard merging postulates. Moreover, we present a concrete Horn merging operator satisfying all postulates.

The AGM theory of belief revision is based on propositional belief sets. In this paper we develop a logic for revision of temporal belief bases, containing expressions about temporal propositions (tomorrow it will rain), possibility (it may rain tomorrow), actions (the robot enters the room) and pre- and post-conditions of these actions. We prove the Katsuno-Mendelzon and the Darwiche-Pearl representation theorems by restricting the logic to formulas representing beliefs up to certain time. We illustrate our belief change model through several examples.

For instance, does it form a "nice" class, which can be characterized A formal framework is given for the postulate characterizability by postulates? of a class of belief revision operators, Proving non-characterizability presupposes a formal definition obtained from a class of partial preorders using of a postulate. However, as noted in the survey [Fermé minimization. It is shown that for classes of posets and Hansson, 2011] characterizability is equivalent to a special kind of "theories of belief change developed in the AGM definability in monadic second-order logic, which tradition are not logics in a strict sense, but rather turns out to be incomparable to first-order definability.

In this paper we combine two of the most important areas of knowledge representation, namely belief revision and (abstract) argumentation. More precisely, we show how AGM-style expansion and revision operators can be defined for Dung's abstract argumentation frameworks (AFs). Our approach is based on a reformulation of the original AGM postulates for revision in terms of monotonic consequence relations for AFs. The latter are defined via a new family of logics, called Dung logics, which satisfy the important property that ordinary equivalence in these logics coincides with strong equivalence for the respective argumentation semantics. Based on these logics we define expansion as usual via intersection of models. We show the existence of such operators. This is far from trivial and requires to study realizability in the context of Dung logics. We then study revision operators. We show why standard approaches based on a distance measure on models do not work for AFs and present an operator satisfying all postulates for a specific Dung logic.

Belief revision is concerned with incorporating new information into a pre-existing set of beliefs. When the new information comes from another agent, we must first determine if that agent should be trusted. In this paper, we define trust as a pre-processing step before revision. We emphasize that trust in an agent is often restricted to a particular domain of expertise. We demonstrate that this form of trust can be captured by associating a state partition with each agent, then relativizing all reports to this partition before revising.  We position the resulting family of trust-sensitive revision operators within the class of selective revision operators of Ferme and Hansson, and we examine its properties. In particular, we show how trust-sensitive revision is manipulable, in the sense that agents can sometimes have incentive to pass on misleading information.  When multiple reporting agents are involved, we use a distance function over states to represent differing degrees of trust; this ensures that the most trusted reports will be believed.

The AGM paradigm of belief change studies the dynamics of belief states in light of new information. Finding, or even approximating, dependent or relevant beliefs to a change is valuable because, for example, it can narrow the set of beliefs considered during belief change operations. Gärdenfors' preservation criterion (GPC) suggests that formulas independent of a belief change should remain intact. GPC allows to build dependence relations that are theoretically linked with belief change. Such dependence relations can in turn be used as a theoretical benchmark against which to evaluate other approximate dependence or relevance relations. There are already some studies, based on GPC, on the parallelism between belief change and dependence. One study offers a dependence relation parallel to AGM contraction for belief sets. Another study links base dependence relation to a more general belief base contraction, saturated kernel contraction. Here we offer yet a more general parallelism between kernel contraction and base dependence. At this level of generalization, different types of base dependence emerge. We prove that this differentiation of base dependence types is a result of possible redundancy in the base. This provides a theoretical means to distinguish between redundant and informative parts of a belief base.

When a belief state is represented as a probability function P, the resulting belief state of the contraction of a sentence (belief) from the original belief state P can be given by the probabilistic version of the Harper Identity. Specifically, the result of contracting P by a sentence h is taken to be the mixture of two states: the original state P, and the resultant state P* ~h of revising P by the negation of h. What proportion of P and P* ~h should be used in this mixture remains an open issue and is largely ignored in literature. In this paper, we first classify different belief states by their stability, and then exploit the quantitative nature of probabilities and combine it with the basic ideas of argumentation theory to determine  the mixture proportions. We, therefore, propose a novel approach to probabilistic belief contraction using argumentation.