The FO Model Counting problem (FOMC) is the following: given a sentence Φ in FO and a number n, compute the number of models of Φ over a domain of size n; the Weighted variant (WFOMC) generalizes the problem by associating a weight to each tuple and defining the weight of a model to be the product of weights of its tuples. In this paper we study the complexity of the symmetric WFOMC, where all tuples of a given relation have the same weight. Our motivation comes from an important application, inference in Knowledge Bases with soft constraints, like Markov Logic Networks, but the problem is also of independent theoretical interest. We study both the data complexity, and the combined complexity of FOMC and WFOMC. For the data complexity we prove the existence of an FO 3 formula for which FOMC is #P1-complete, and the existence of a Conjunctive Query for which WFOMC is #P1-complete. We also prove that all γ-acyclic queries have polynomial time data complexity. For the combined complexity, we prove that, for every fragment FO k , k ≥ 2, the combined complexity of FOMC (or WFOMC) is #P-complete.

Elementary-level science exams pose significant knowledge acquisition and reasoning challenges for automatic question answering. We develop a system that reasons with knowledge derived from textbooks, represented in a subset of firstorder logic. Automatic extraction, while scalable, often results in knowledge that is incomplete and noisy, motivating use of reasoning mechanisms that handle uncertainty. Markov Logic Networks (MLNs) seem a natural model for expressing such knowledge, but the exact way of leveraging MLNs is by no means obvious. We investigate three ways of applying MLNs to our task. First, we simply use the extracted science rules directly as MLN clauses and exploit the structure present in hard constraints to improve tractability. Second, we interpret science rules as describing prototypical entities, resulting in a drastically simplified but brittle network. Our third approach, called Praline, uses MLNs to align lexical elements as well as define and control how inference should be performed in this task. Praline demonstrates a 15% accuracy boost and a 10x reduction in runtime as compared to other MLNbased methods, and comparable accuracy to word-based baseline approaches.

Use of graphs is growing rapidly in social networks, semantic web, biological databases, scientific workflow provenance, and other areas. Regular Path Queries (RPQs) can be seen as a core graph query language to answer pattern-based reachability queries. Unfortunately, the number of freely available systems for querying graphs using RPQs is rather limited, and available implementations do not provide direct support for a number of desirable variants of RPQs, e.g., to return those edges that are contained in some (or all) paths that match the given regular expression R. Thus, by returning not just a pair (x, y) of end points of paths that match R, but also "witness edges" (u, v) inbetween, our RPQ variants can be understood as returning additional provenance information about the answer (x, y), i.e., those edges (u, v) that are in some (or all) paths from x to y matching R. We propose a number of such RPQ variants and show how they can be implemented using either Datalog or a suitable RDBMS. Our initial experimental results indicate that RPQs and our provenance-aware variants (RPQProv), when implemented using conventional relational technologies, yield reasonable performance even for relatively large graphs. On the other hand, the overhead associated with some of these variants also makes efficient handling of provenance-aware graph queries an interesting challenge for future research.

No abstract

Increasingly large Knowledge Bases are being created, by crawling the Web or other corpora of documents, and by extracting facts and relations using machine learning techniques. To manage the uncertainty in the data, these KBs rely on probabilistic engines based on Markov Logic Networks (MLN), for which probabilistic inference remains a major challenge. Today's state of the art systems use variants of MCMC, which have no theoretical error guarantees, and, as we show, suffer from poor performance in practice. In this paper we describe SlimShot (Scalable Lifted Inference and Monte Carlo Sampling Hybrid Optimization Technique), a probabilistic inference engine for knowledge bases. SlimShot converts the MLN to a tuple-independent probabilistic database, then uses a simple Monte Carlo-based inference, with three key enhancements: (1) it combines sampling with safe query evaluation, (2) it estimates a conditional probability by jointly computing the numerator and denominator, and (3) it adjusts the proposal distribution based on the sample cardinality. In combination, these three techniques allow us to give formal error guarantees, and we demonstrate empirically that SlimShot outperforms to-day's state of the art probabilistic inference engines used in knowledge bases.