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.

In this paper, we develop a heuristic, progression based conformant planner, called CNF, which represents belief states by a special type of CNF formulae, called CNF CNF-state. We define a transition function φ CNF for computing the successor belief state resulting from the execution of an action in a belief state and prove that it is sound and complete with respect to the complete semantics defined in the literature for conformant planning. We evaluate the performance of CNF against other state-of-the-art conformant planners and identify the classes of problems where CNF is comparable with other state-of-the-art planners or scales up better than other planners. We also develop a technique called oneof relaxation which helps boost the performance of CNF. We characterize the domains where this technique can be applied and validate this idea by proposing a new set of benchmarks that is really difficult for other planners yet easy for CNF.

Research effort, with its emphasis on evaluation and measurable progress, things began to change. Instead SHRDLU (WIN72) is perhaps the canonical example. of systems whose architecture and vocabulary were The rapid growth of efforts to found the next generation of based on linguistic theory (in this case acoustic phonetics), systems on general-purpose knowledge representation languages new approaches based on statistical modelling and Bayesian (I'm thinking of several varieties of semantic nets, probability emerged and quickly spread. "Every time I fire a from plain to partitioned, as well as KRL, KL-ONE and linguist my system's performance improves" (Fred Jellinek, their successors, ending (not yet, of course) with CYC (See head of speech recognition at IBM, c. 1980, latterly repudiated (BRA08) for all these) stumbled to a halt once their failure by Fred but widely attested). As advanced from resolution theorem provers through a number more and more problems are re-conceived as instances of of stages to the current proliferation of a range of Description the noisy channel model, the empiricist paradigm continually Logic'reasoners'; Whereas in the 1970s and 1980s there grew, so did the need to manage the impact of change and was real energy and optimism at the interface between computational conflict: enter'truth maintenance', subsequently renamed and theoretical linguistics, the overwhelming success'reason maintenance'. While still using some of But outflanking these'normal science' advances of AI, the terminology of linguistic theory, computational linguistics the paradigm shifters were coming up fast on the outside: practioners are increasingly detached from theory itself, over the last ten years machine learning has spread from which has suffered a, perhaps connected, loss of energy and small specialist niches such as speech recognition to become sense of progress.

We propose a new approach to the analysis of Loopy Belief Propagation (LBP) by establishing a formula that connects the Hessian of the Bethe free energy with the edge zeta function. The formula has a number of theoretical implications on LBP. It is applied to give a sufficient condition that the Hessian of the Bethe free energy is positive definite, which shows non-convexity for graphs with multiple cycles. The formula clarifies the relation between the local stability of a fixed point of LBP and local minima of the Bethe free energy. We also propose a new approach to the uniqueness of LBP fixed point, and show various conditions of uniqueness.

We study the profit-maximization problem of a monopolistic market-maker who sets two-sided prices in an asset market. The sequential decision problem is hard to solve because the state space is a function. We demonstrate that the belief state is well approximated by a Gaussian distribution. We prove a key monotonicity property of the Gaussian state update which makes the problem tractable, yielding the first optimal sequential market-making algorithm in an established model. The algorithm leads to a surprising insight: an optimal monopolist can provide more liquidity than perfectly competitive market-makers in periods of extreme uncertainty, because a monopolist is willing to absorb initial losses in order to learn a new valuation rapidly so she can extract higher profits later.

We show that an important and computationally challenging solution space feature of the graph coloring problem (COL), namely the number of clusters of solutions, can be accurately estimated by a technique very similar to one for counting the number of solutions. This cluster counting approach can be naturally written in terms of a new factor graph derived from the factor graph representing the COL instance. Using a variant of the Belief Propagation inference framework, we can efficiently approximate cluster counts in random COL problems over a large range of graph densities. We illustrate the algorithm on instances with up to 100, 000 vertices. Moreover, we supply a methodology for computing the number of clusters exactlyusing advanced techniques from the knowledge compilation literature.

Empirical studies have documented cases of belief polarization, where two people withopposing prior beliefs both strengthen their beliefs after observing the same evidence. Belief polarization is frequently offered as evidence of human irrationality, but we demonstrate that this phenomenon is consistent with a fully Bayesian approach to belief revision. Simulation results indicate that belief polarization isnot only possible but relatively common within the set of Bayesian models that we consider. Suppose that Carol has requested a promotion at her company and has received a score of 50 on an aptitude test. Alice, one of the company's managers, began with a high opinion of Carol and became even more confident of her abilities after seeing her test score.

We propose a new approach to the analysis of Loopy Belief Propagation (LBP) by establishing a formula that connects the Hessian of the Bethe free energy with the edge zeta function. The formula has a number of theoretical implications on LBP. It is applied to give a sufficient condition that the Hessian of the Bethe free energy is positive definite, which shows non-convexity for graphs with multiple cycles. The formula clarifies the relation between the local stability of a fixed point of LBP and local minima of the Bethe free energy. We also propose a new approach to the uniqueness of LBP fixed point, and show various conditions of uniqueness.

We address the problem of belief change in (nonmonotonic) logic programming under answer set semantics. Unlike previous approaches to belief change in logic programming, our formal techniques are analogous to those of distance-based belief revision in propositional logic. In developing our results, we build upon the model theory of logic programs furnished by SE models. Since SE models provide a formal, monotonic characterisation of logic programs, we can adapt techniques from the area of belief revision to belief change in logic programs. We introduce methods for revising and merging logic programs, respectively. For the former, we study both subset-based revision as well as cardinality-based revision, and we show that they satisfy the majority of the AGM postulates for revision. For merging, we consider operators following arbitration merging and IC merging, respectively. We also present encodings for computing the revision as well as the merging of logic programs within the same logic programming framework, giving rise to a direct implementation of our approach in terms of off-the-shelf answer set solvers. These encodings reflect in turn the fact that our change operators do not increase the complexity of the base formalism.