Weighted Counting for Constraint Satisfaction with Default Values (#CSPD) is a powerful special case of the sum-of-products problem that admits succinct encodings of #CSP, #SAT, and inference in probabilistic graphical models. We investigate #CSPD under the fundamental parameter of incidence treewidth (i.e., the treewidth of the incidence graph of the constraint hypergraph). We show that if the incidence treewidth is bounded, #CSPD can be solved in polynomial time. More specifically, we show that the problem is fixed-parameter tractable for the combined parameter incidence treewidth, domain size, and support size (the maximum number of non-default tuples in a constraint). This generalizes known results on the fixed-parameter tractability of #CSPD under the combined parameter primal treewidth and domain size. We further prove that the problem is not fixed-parameter tractable if any of the three components is dropped from the parameterization.

A Knowledge Graph (KG), popularly used in both industry and academia, is an effective representation of knowledge. It consists of a collection of knowledge elements, each of which in turn is extracted from the web or other sources. Information extractors that use natural language processing techniques or other complex algorithms are usually noisy. That is, the vast number of knowledge elements extracted from the web may not only be associated with different confidence values but may also be inconsistent with each other. Many applications such as question answering systems that are built on top of large-scale KGs are required to reason efficiently about these confidence values and inconsistencies. In addition, they are required to incorporate ontological constraints in their reasoning. One way to do this is to extract a subgraph of a KG that is consistent with the ontological constraints and is of maximum total confidence value. Such a subgraph is referred to as the top hypothesis and is combinatorially hard to find. In this paper, we introduce an algorithmic framework for efficiently addressing the combinatorial hardness and selecting the top K hypotheses. Our approach is based on powerful algorithmic techniques recently invented in the context of the Weighted Constraint Satisfaction Problem (WCSP).

Applying learning techniques to acquire action models is an area of intense research interest. Most previous works in this area have assumed that there is a significant amount of training data available in a planning domain of interest, which we call target domain, where action models are to be learned. However, it is often difficult to acquire sufficient training data to ensure that the learned action models are of high quality. In this paper, we develop a novel approach to learning action models with limited training data in the target domain by transferring knowledge from related auxiliary or source domains. We assume that the action models in the source domains have already been created before, and seek to transfer as much of the the available information from the source domains as possible to help our learning task. We first exploit a Web searching method to bridge the target and source domains, such that transferrable knowledge from source domains is identified. We then encode the transferred knowledge together with the available data from the target domain as constraints in a maximum satisfiability problem, and solve these constraints using a weighted MAX-SAT solver. We finally transform the solutions thus obtained into high-quality target-domain action models. We empirically show that our transfer-learning based framework is effective in several domains, including the International Planning Competition (IPC) domains and some synthetic domains.