The paper presents an investigation of the use of two alternative forms of CNF formulae—prime implicates and minimal CNF—to compactly represent belief states in the context of conformant planning. For each representation, we define a transition function for computing the successor belief state resulting from the execution of an action in a belief state; results concerning soundness and completeness are provided. The paper describes a system (PIP) which dynamically selects either of these two forms to represent belief states, and an experimental evaluation of PIP against state-of-the-art conformant planners. The results show that PIP has the potential of scaling up better than other planners in problems rich in disjunctive information about the initial state.

Revising knowledge bases (KBs) in description logics (DLs) in a syntax-independent manner is an important, nontrivial problem for the ontology management and DL communities. Several attempts have been made to adapt classical model-based belief revision and update techniques to DLs, but they are restricted in several ways. In particular, they do not provide operators or algorithms for general DL KB revision. The key difficulty is that, unlike propositional logic, a DL KB may have infinitely many models with complex (and possibly infinite) structures, making it difficult to define and compute revisions in terms of models. In this paper, we study general KBs in a specific DL in the DL-Lite family. We introduce the concept of features for such KBs, develop an alternative semantic characterization of KBs using features (instead of models), define two specific revision operators for KBs, and present the first algorithm for computing best approximations for syntax-independent revisions of KBs.

Inconsistencies between different information sources may arise because of statements that are inaccurate, albeit not completely false. In such scenarios, the most natural way to restore consistency is often to interpret assertions in a more flexible way, i.e. to enlarge (or relax) their meaning. As this process inherently requires extra-logical information about the meaning of atoms, extensions of classical merging operators are needed. In this paper, we introduce syntactic merging operators, based on possibilistic logic, which employ background knowledge about the similarity of atomic propositions to appropriately relax propositional statements.

When merging belief sets from different agents, the result is normally a consistent belief set in which the inconsistency between the original sources is not represented. As probability theory is widely used to represent uncertainty, an interesting question therefore is whether it is possible to induce a probability distribution when merging belief sets. To this end, we first propose two approaches to inducing a probability distribution on a set of possible worlds, by extending the principle of indifference on possible worlds. We then study how the (in)dependence relations between atoms can influence the probability distribution. We also propose a set of properties to regulate the merging of belief sets when a probability distribution is output. Furthermore, our merging operators satisfy the well known Konieczny and Pino-Perez postulates if we use the set of possible worlds which have the maximal induced probability values. Our study shows that taking an induced probability distribution as a merging result can better reflect uncertainty and inconsistency among the original knowledge bases.

In this paper we study the sequential strategic interactive setting of two-person, two-stage, seller-offers bargaining under uncertainty. We model the epistemology of the problem in a finite interactive decision-theoretic framework and solve it for three types of agents of successively increasing (epistemological) sophistication (or, capacity to represent and reason with higher orders of beliefs). In particular, we remove common knowledge assumptions about the agents' epistemology which, if made, would be sufficient to imply the existence of a, possibly unique, game-theoretic equilibrium solution. In this context, we present a characterization of a monotonic relationship between an agent's optimal behavior and its beliefs under a particular moment-based ordering. Further, based on this characterization, we present the \emph{spread-accumulate} sampling technique -- a method of sampling an agent's higher order belief by generating ``evenly dispersed" beliefs for which we (pre)compute offline solutions. Then, we present a method for approximating higher order prior belief update to arbitrary precision by identifying a (previously solved) belief ``closest" to the true belief. In addition, these methods directly suggest a mechanism for achieving a balance between efficiency and the quality of the approximation -- either by generating a large number of offline solutions or by allowing the agent to search online for a ``closer" belief in the vicinity of best current solution.

Standard approachs to belief change assume that the underlying logic contains classical propositional logic. Recently there has been interest in investigating approaches to belief change, specifically contraction, in which the underlying logic is not as expressive as full propositional logic. In this paper we consider approaches to belief contraction in Horn knowledge bases. We develop two broad approaches for Horn contraction, corresponding to the two major approaches in belief change, based on Horn belief sets and Horn belief bases. We argue that previous approaches, which have taken Horn remainder sets as a starting point, have undesirable properties, and moreover that not all desirable Horn contraction functions are captured by these approaches. This is shown in part by examining model-theoretic considerations involving Horn contraction. For Horn belief set contraction, we develop an account based in terms of weak remainder sets. Maxichoice and partial meet Horn contraction is specified, along with a consideration of package contraction. Following this we consider Horn belief base contraction, in which the underlying knowledge base is not necessarily closed under the Horn consequence relation. Again, approaches to maxichoice and partial meet belief set contraction are developed. In all cases, constructions of the specific operators and sets of postulates are provided, and representation results are obtained. As well, we show that problems arising with earlier work are resolved by these approaches.

We present a formal semantical model to capture action, belief and intention, based on the "database perspective" (Shoham, 2009). We then provide postulates for belief and intention revision, and state a representation theorem relating our postulates to the formal model. Our belief postulates are in the spirit of the AGM theory; the intention postulates stand in rough correspondence with the belief postulates.

We provide two approaches for explaining inconsistency in multi-context systems, where decentralized and heterogeneous system parts interact via nonmonotonic bridge rules. Inconsistencies arise easily in such scenarios, and nonmonotonicity calls for specific methods of inconsistency analysis. Both our approaches characterize inconsistency in terms of involved bridge rules: either by pointing out rules which need to be altered for restoring consistency, or by finding combinations of rules which cause inconsistency. We show duality and modularity properties, give precise complexity characterizations, and provide algorithms for computation using HEX-programs. Our results form a basis for inconsistency management in heterogeneous knowledge integration systems.

Improvement operators is a class of belief change operators that is a generalization of the usual class of iterated belief revision operators. The idea is to relax the success property, so the new information is not necessarily believed after the improvement, but to ensure that its plausibility has increased in the epistemic state. In this paper we explore this large classby defining several different subclasses. In particular, as minimal change is a hallmark of belief change, we study what are the operators that produce the minimal change among several subclasses.

We present a distributed algorithm for computing equilibria of heterogeneous nonmonotonic multi-context systems (MCS). The algorithm can be parametrized to compute only partial equilibria, which can be used for reasoning tasks like query answering or satisfiability checking that need only partial information and not whole belief states. Furthermore, caching is employed to cut redundant solver calls. As a showcase, we instantiate the MCS framework with answer set program contexts. To characterize equilibria of such MCS, we develop notions of loop formulas that enable reductions to the classical satisfiability problem (SAT). Notably, loop formulas for bridge rules between contexts and for the local contexts can be combined to a uniform encoding of an MCS into a (distributed) SAT instance. As a consequence, we can use SAT solvers for belief set building. We demonstrate this approach by an experimental prototype implementation, which uses an off-the-shelf SAT solver.