A Journey into Ontology Approximation: From Non-Horn to Horn

• URL: http://arxiv.org/abs/2001.07754v4
• Date: Mon, 15 Jun 2020 20:01:03 GMT
• Title: A Journey into Ontology Approximation: From Non-Horn to Horn
• Authors: Anneke Haga, Carsten Lutz, Johannes Marti, Frank Wolter
• Abstract summary: We study complete approximations of an ontology formulated in a non-Horn description logic (DL) We provide concrete approximation schemes that are necessarily infinite and observe that in the $mathcalELU$-to-$mathcalEL$ case finite approximations tend to exist in practice. In contrast, neither of these is the case for $mathcalELU_bot$-to-$mathcalEL_bot$ and for $mathcalALC$-to-$mathcalEL_bot$
• Score: 17.210841426842816
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study complete approximations of an ontology formulated in a non-Horn description logic (DL) such as $\mathcal{ALC}$ in a Horn DL such as~$\mathcal{EL}$. We provide concrete approximation schemes that are necessarily infinite and observe that in the $\mathcal{ELU}$-to-$\mathcal{EL}$ case finite approximations tend to exist in practice and are guaranteed to exist when the original ontology is acyclic. In contrast, neither of this is the case for $\mathcal{ELU}_\bot$-to-$\mathcal{EL}_\bot$ and for $\mathcal{ALC}$-to-$\mathcal{EL}_\bot$ approximations. We also define a notion of approximation tailored towards ontology-mediated querying, connect it to subsumption-based approximations, and identify a case where finite approximations are guaranteed to exist.

Related papers

• A Theory of Interpretable Approximations [61.90216959710842]
  We study the idea of approximating a target concept $c$ by a small aggregation of concepts from some base class $mathcalH$. For any given pair of $mathcalH$ and $c$, exactly one of these cases holds: (i) $c$ cannot be approximated by $mathcalH$ with arbitrary accuracy. We show that, in the case of interpretable approximations, even a slightly nontrivial a-priori guarantee on the complexity of approximations implies approximations with constant (distribution-free and accuracy-
  arXiv  Detail & Related papers  (2024-06-15T06:43:45Z)
• Estimating the Mixing Coefficients of Geometrically Ergodic Markov Processes [5.00389879175348]
  We estimate the individual $beta$-mixing coefficients of a real-valued geometrically ergodic Markov process from a single sample-path. Naturally no density assumptions are required in this setting; the expected error rate is shown to be of order $mathcal O(log(n) n-1/2)$.
  arXiv  Detail & Related papers  (2024-02-11T20:17:10Z)
• A Unified Framework for Uniform Signal Recovery in Nonlinear Generative Compressed Sensing [68.80803866919123]
  Under nonlinear measurements, most prior results are non-uniform, i.e., they hold with high probability for a fixed $mathbfx*$ rather than for all $mathbfx*$ simultaneously. Our framework accommodates GCS with 1-bit/uniformly quantized observations and single index models as canonical examples. We also develop a concentration inequality that produces tighter bounds for product processes whose index sets have low metric entropy.
  arXiv  Detail & Related papers  (2023-09-25T17:54:19Z)
• Detection-Recovery Gap for Planted Dense Cycles [72.4451045270967]
  We consider a model where a dense cycle with expected bandwidth $n tau$ and edge density $p$ is planted in an ErdHos-R'enyi graph $G(n,q)$. We characterize the computational thresholds for the associated detection and recovery problems for the class of low-degree algorithms.
  arXiv  Detail & Related papers  (2023-02-13T22:51:07Z)
• A Newton-CG based barrier-augmented Lagrangian method for general nonconvex conic optimization [53.044526424637866]
  In this paper we consider finding an approximate second-order stationary point (SOSP) that minimizes a twice different subject general non conic optimization. In particular, we propose a Newton-CG based-augmentedconjugate method for finding an approximate SOSP.
  arXiv  Detail & Related papers  (2023-01-10T20:43:29Z)
• Local approximation of operators [0.0]
  We study the problem of determining the degree of approximation of a non-linear operator between metric spaces $mathfrakX$ and $mathfrakY$. We establish constructive methods to do this efficiently, i.e., with the constants involved in the estimates on the approximation on $mathbbSd$ being $mathcalO(d1/6)$.
  arXiv  Detail & Related papers  (2022-02-13T19:28:34Z)
• Universal Regular Conditional Distributions via Probability Measure-Valued Deep Neural Models [3.8073142980733]
  We find that any model built using the proposed framework is dense in the space $C(mathcalX,mathcalP_1(mathcalY))$. The proposed models are also shown to be capable of generically expressing the aleatoric uncertainty present in most randomized machine learning models.
  arXiv  Detail & Related papers  (2021-05-17T11:34:09Z)
• Non-Parametric Estimation of Manifolds from Noisy Data [1.0152838128195467]
  We consider the problem of estimating a $d$ dimensional sub-manifold of $mathbbRD$ from a finite set of noisy samples. We show that the estimation yields rates of convergence of $n-frack2k + d$ for the point estimation and $n-frack-12k + d$ for the estimation of tangent space.
  arXiv  Detail & Related papers  (2021-05-11T02:29:33Z)
• Linear Time Sinkhorn Divergences using Positive Features [51.50788603386766]
  Solving optimal transport with an entropic regularization requires computing a $ntimes n$ kernel matrix that is repeatedly applied to a vector. We propose to use instead ground costs of the form $c(x,y)=-logdotpvarphi(x)varphi(y)$ where $varphi$ is a map from the ground space onto the positive orthant $RRr_+$, with $rll n$.
  arXiv  Detail & Related papers  (2020-06-12T10:21:40Z)
• Reinforcement Learning with General Value Function Approximation: Provably Efficient Approach via Bounded Eluder Dimension [124.7752517531109]
  We establish a provably efficient reinforcement learning algorithm with general value function approximation. We show that our algorithm achieves a regret bound of $widetildeO(mathrmpoly(dH)sqrtT)$ where $d$ is a complexity measure. Our theory generalizes recent progress on RL with linear value function approximation and does not make explicit assumptions on the model of the environment.
  arXiv  Detail & Related papers  (2020-05-21T17:36:09Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.