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.

Argumentation is an inherently dynamic process. Given that argumentation can be viewed as a process as well Consequently, recent years have witnessed tremendous as a product, recent years have seen an increasing number of research efforts towards an understanding of studies on different problems in the dynamics of argumentation how the seminal AGM theory of belief change can frameworks [Baumann, 2012; Bisquert et al., 2011; 2013; be applied to argumentation, in particular for Dung's Boella et al., 2009; Booth et al., 2013; Cayrol et al., 2010; abstract argumentation frameworks (AFs). However, Doutre et al., 2014; Kontarinis et al., 2013; Krümpelmann et none of the attempts has yet succeeded in handling al., 2012; Nouioua and Würbel, 2014; Sakama, 2014]. The the natural situation where the revision of an AF is problem we tackle here is how to revise an AF when some new guaranteed to be representable by an AF as well.

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.

Stream reasoning is the task of continuously deriving conclusions on streaming data. To get results instantly one evaluates a query repeatedly on recent data chunks selected by window operators. However, simply recomputing results from scratch is impractical for rule-based reasoning with semantics similar to Answer Set Programming, due to the trade-off between complexity and data throughput. To address this problem, we present a method to efficiently update models of a rule set. In particular, we show how an answer stream (model) of a LARS program can be incrementally adjusted to new or outdated input by extending truth maintenance techniques. We obtain in this way a means towards practical rule-based stream reasoning with nonmonotonic negation, various window operators and different forms of temporal reference.

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.

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.

We propose an original particle-based implementation of the Loopy Belief Propagation (LPB) algorithm for pairwise Markov Random Fields (MRF) on a continuous state space. The algorithm constructs adaptively efficient proposal distributions approximating the local beliefs at each note of the MRF. This is achieved by considering proposal distributions in the exponential family whose parameters are updated iterately in an Expectation Propagation (EP) framework. The proposed particle scheme provides consistent estimation of the LBP marginals as the number of particles increases. We demonstrate that it provides more accurate results than the Particle Belief Propagation (PBP) algorithm of Ihler and McAllester (2009) at a fraction of the computational cost and is additionally more robust empirically. The computational complexity of our algorithm at each iteration is quadratic in the number of particles. We also propose an accelerated implementation with sub-quadratic computational complexity which still provides consistent estimates of the loopy BP marginal distributions and performs almost as well as the original procedure.

We apply belief propagation to a Bayesian bipartite graph composed of discrete independent hidden variables and discrete visible variables. The network is the Discrete counterpart of Independent Component Analysis (DICA) and it is manipulated in a factor graph form for inference and learning. A full set of simulations is reported for character images from the MNIST dataset. The results show that the factorial code implemented by the sources contributes to build a good generative model for the data that can be used in various inference modes.

Multi-context Systems (MCSs) are a formalism for systems consisting of knowledge bases (possibly heterogeneous and non-monotonic) that are interlinked via bridge rules, where the global system semantics emerges from the local semantics of the knowledge bases (also called contexts) in an equilibrium. While MCSs and related formalisms are inherently targeted for distributed set- tings, no truly distributed algorithms for their evaluation were available. We address this short- coming and present a suite of such algorithms which includes a basic algorithm DMCS, an ad- vanced version DMCSOPT that exploits topology-based optimizations, and a streaming algorithm DMCS-STREAMING that computes equilibria in packages of bounded size. The algorithms be- have quite differently in several respects, as experienced in thorough experimental evaluation of a system prototype. From the experimental results, we derive a guideline for choosing the appropriate algorithm and running mode in particular situations, determined by the parameter settings.

A formal framework is given for the postulate characterizability of a class of belief revision operators, obtained from a class of partial preorders using minimization. It is shown that for classes of posets characterizability is equivalent to a special kind of definability in monadic second-order logic, which turns out to be incomparable to first-order definability. Several examples are given of characterizable and non-characterizable classes. For example, it is shown that the class of revision operators obtained from posets which are not total is not characterizable.