Towards Log-Linear Logics with Concrete Domains

We present $\mathcal{MEL}^{++}$ (M denotes Markov logic networks) an extension of the log-linear description logics $\mathcal{EL}^{++}$-LL with concrete domains, nominals, and instances. We use Markov logic networks (MLNs) in order to find the most probable, classified and coherent $\mathcal{EL}^{++}$ ontology from an $\mathcal{MEL}^{++}$ knowledge base. In particular, we develop a novel way to deal with concrete domains (also known as datatypes) by extending MLN's cutting plane inference (CPI) algorithm.Comment: StarAI201

Heuristic Ranking in Tightly Coupled Probabilistic Description Logics

The Semantic Web effort has steadily been gaining traction in the recent years. In particular,Web search companies are recently realizing that their products need to evolve towards having richer semantic search capabilities. Description logics (DLs) have been adopted as the formal underpinnings for Semantic Web languages used in describing ontologies. Reasoning under uncertainty has recently taken a leading role in this arena, given the nature of data found on theWeb. In this paper, we present a probabilistic extension of the DL EL++ (which underlies the OWL2 EL profile) using Markov logic networks (MLNs) as probabilistic semantics. This extension is tightly coupled, meaning that probabilistic annotations in formulas can refer to objects in the ontology. We show that, even though the tightly coupled nature of our language means that many basic operations are data-intractable, we can leverage a sublanguage of MLNs that allows to rank the atomic consequences of an ontology relative to their probability values (called ranking queries) even when these values are not fully computed. We present an anytime algorithm to answer ranking queries, and provide an upper bound on the error that it incurs, as well as a criterion to decide when results are guaranteed to be correct.Comment: Appears in Proceedings of the Twenty-Eighth Conference on Uncertainty in Artificial Intelligence (UAI2012

Time-Aware Probabilistic Knowledge Graphs

The emergence of open information extraction as a tool for constructing and expanding knowledge graphs has aided the growth of temporal data, for instance, YAGO, NELL and Wikidata. While YAGO and Wikidata maintain the valid time of facts, NELL records the time point at which a fact is retrieved from some Web corpora. Collectively, these knowledge graphs (KG) store facts extracted from Wikipedia and other sources. Due to the imprecise nature of the extraction tools that are used to build and expand KG, such as NELL, the facts in the KG are weighted (a confidence value representing the correctness of a fact). Additionally, NELL can be considered as a transaction time KG because every fact is associated with extraction date. On the other hand, YAGO and Wikidata use the valid time model because they maintain facts together with their validity time (temporal scope). In this paper, we propose a bitemporal model (that combines transaction and valid time models) for maintaining and querying bitemporal probabilistic knowledge graphs. We study coalescing and scalability of marginal and MAP inference. Moreover, we show that complexity of reasoning tasks in atemporal probabilistic KG carry over to the bitemporal setting. Finally, we report our evaluation results of the proposed model