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

ProCAVIAR: Hybrid Data-Driven and Probabilistic Knowledge-Based Activity Recognition

The recognition of physical activities using sensors on mobile devices has been mainly addressed with supervised and semi-supervised learning. The state-of-the-art methods are mainly based on the analysis of the user\u2019s movement patterns that emerge from inertial sensors data. While the literature on this topic is quite mature, existing approaches are still not adequate to discriminate activities characterized by similar physical movements. The context that surrounds the user (e.g., semantic location) could be used as additional information to significantly extend the set of recognizable activities. Since collecting a comprehensive training set with activities performed in every possible context condition is too costly, if possible at all, existing works proposed knowledge-based reasoning over ontological representation of context data to refine the predictions obtained from machine learning. A problem with this approach is the rigidity of the underlying logic formalism that cannot capture the intrinsic uncertainty of the relationships between activities and context. In this work, we propose a novel activity recognition method that combines semisupervised learning and probabilistic ontological reasoning. We model the relationships between activities and context as a combination of soft and hard ontological axioms. For each activity, we use a probabilistic ontology to compute its compatibility with the current context conditions. The output of probabilistic semantic reasoning is combined with the output of a machine learning classifier based on inertial sensor data to obtain the most likely activity performed by the user. The evaluation of our system on a dataset with 13 types of activities performed by 26 subjects shows that our probabilistic framework outperforms both a pure machine learning approach and previous hybrid approaches based on classic ontological reasoning

Pseudo-contractions as Gentle Repairs

Updating a knowledge base to remove an unwanted consequence is a challenging task. Some of the original sentences must be either deleted or weakened in such a way that the sentence to be removed is no longer entailed by the resulting set. On the other hand, it is desirable that the existing knowledge be preserved as much as possible, minimising the loss of information. Several approaches to this problem can be found in the literature. In particular, when the knowledge is represented by an ontology, two different families of frameworks have been developed in the literature in the past decades with numerous ideas in common but with little interaction between the communities: applications of AGM-like Belief Change and justification-based Ontology Repair. In this paper, we investigate the relationship between pseudo-contraction operations and gentle repairs. Both aim to avoid the complete deletion of sentences when replacing them with weaker versions is enough to prevent the entailment of the unwanted formula. We show the correspondence between concepts on both sides and investigate under which conditions they are equivalent. Furthermore, we propose a unified notation for the two approaches, which might contribute to the integration of the two areas

On an Intuitionistic Logic for Pragmatics

We reconsider the pragmatic interpretation of intuitionistic logic [21] regarded as a logic of assertions and their justications and its relations with classical logic. We recall an extension of this approach to a logic dealing with assertions and obligations, related by a notion of causal implication [14, 45]. We focus on the extension to co-intuitionistic logic, seen as a logic of hypotheses [8, 9, 13] and on polarized bi-intuitionistic logic as a logic of assertions and conjectures: looking at the S4 modal translation, we give a denition of a system AHL of bi-intuitionistic logic that correctly represents the duality between intuitionistic and co-intuitionistic logic, correcting a mistake in previous work [7, 10]. A computational interpretation of cointuitionism as a distributed calculus of coroutines is then used to give an operational interpretation of subtraction.Work on linear co-intuitionism is then recalled, a linear calculus of co-intuitionistic coroutines is dened and a probabilistic interpretation of linear co-intuitionism is given as in [9]. Also we remark that by extending the language of intuitionistic logic we can express the notion of expectation, an assertion that in all situations the truth of p is possible and that in a logic of expectations the law of double negation holds. Similarly, extending co-intuitionistic logic, we can express the notion of conjecture that p, dened as a hypothesis that in some situation the truth of p is epistemically necessary

Ontology-Based Query Answering for Probabilistic Temporal Data: Extended Version

We investigate ontology-based query answering for data that are both temporal and probabilistic, which might occur in contexts such as stream reasoning or situation recognition with uncertain data. We present a framework that allows to represent temporal probabilistic data, and introduce a query language with which complex temporal and probabilistic patterns can be described. Specifically, this language combines conjunctive queries with operators from linear time logic as well as probability operators. We analyse the complexities of evaluating queries in this language in various settings. While in some cases, combining the temporal and the probabilistic dimension in such a way comes at the cost of increased complexity, we also determine cases for which this increase can be avoided.This is an extended version of the article to appear in the proceedings of AAAI 2019