Multi-label Learning with a Cone-Based Geometric Model

Leemhuis, Mena; Özçep, Özgür Lütfü; Wolter, Diedrich

doi:10.1007/978-3-030-57855-8_13

Cited by 4 publications

(5 citation statements)

References 8 publications

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“…This logic adds to minimal orthologic further inferences for scenarios where only partial information on states is available. L min pOM is also interesting for the prospects it offers on connecting KR with machine learning (see [18,16]).…”

Section: Discussionmentioning

confidence: 99%

“…Both approaches are orthogonal to ours as they consider not only unary relations (concepts) but also binary relations [15]-as required for embeddings of knowledge graphs-or even arbitrary n-ary relations [13]. But let us note that the general idea underlying cone logic applies also to non-propositional logics, though we did not deal with these in this paper (see our [18,16]). On the other hand, cone logic provides a full orthonegation-which is not the case for [13] or for [15].…”

Section: Related Workmentioning

confidence: 99%

“…In earlier publications [18,16] we applied the idea of using cones for embedding knowledge graphs with background knowledge expressed in the semiexpressive description logic ALC and showed how to use cones for typical ML problem such as multi-label learning [10]. In those publications we assumed the logic to be given in advance and as being distributive.…”

Section: Introductionmentioning

confidence: 99%

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Orthologics for Cones

Leemhuis¹,

Özçep²,

Wolter³

2020

Preprint

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In applications that use knowledge representation (KR) techniques, in particular those that combine data-driven and logic methods, the domain of objects is not an abstract unstructured domain, but it exhibits a dedicated, deep structure of geometric objects. One example is the class of convex sets used to model natural concepts in conceptual spaces, which also links via convex optimisation techniques to machine learning. In this paper we study logics for such geometric structures. Using the machinery of lattice theory, we describe an extension of minimal orthologic with a partial modularity rule that holds for closed convex cones. This logic combines a feasible data structure (exploiting convexity/conicity) with sufficient expressivity, including full orthonegation (exploiting conicity).

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Section: Discussionmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Orthologics for Cones

Leemhuis¹,

Özçep²,

Wolter³

2020

Preprint

Self Cite

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“…Convex cones are useful structures because they are appropriate for logical reasoning with partial information, and al-cones can be used for a multi-label-learning approach as demonstrated in the next section. However, there is a catch with using al-cones: As stated in [17] the dimension of the embedding space increases exponentially in the number of concept symbols used in the ontology. We consider this not as a problem of the approach itself but as the problem of what could be considered in ML speak a wrong bias, namely, assuming that a classical propositional logic such as propositional ALC is the right ontology language.…”

Section: The Geometric Model Of Pairs Of Unions Of Convex Conesmentioning

confidence: 99%

“…Second, by choosing a specific class of logico-geometrical structures we are able to construct an approach that fulfills (QC) and (LR). The majority of the paper addresses the second line by extending our previous work [17,20] to develop a logico-geometric approach to classification that ensures prior logic information to be respected. Such approach can be particular useful where classifiers need to be geared towards avoiding false positives.…”

Section: Introductionmentioning

confidence: 99%

Learning with cone-based geometric models and orthologics

Leemhuis

Özçep

Wolter

2022

Ann Math Artif Intell

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Recent approaches for knowledge-graph embeddings aim at connecting quantitative data structures used in machine learning to the qualitative structures of logics. Such embeddings are of a hybrid nature, they are data models that also exhibit conceptual structures inherent to logics. One motivation to investigate embeddings is to design conceptually adequate machine learning (ML) algorithms that learn or incorporate ontologies expressed in some logic. This paper investigates a new approach to embedding ontologies into geometric models that interpret concepts by geometrical structures based on convex cones. The ontologies are assumed to be represented in an orthologic, a logic with a full (ortho)negation. As a proof of concept this cone-based embedding was implemented within two ML algorithms for weak supervised multi-label learning. Both algorithms rely on cones but the first addresses ontologies expressed in classical propositional logic whereas the second addresses a weaker propositional logic, namely a weak orthologic that does not fulfil distributivity. The algorithms were evaluated and showed promising results that call for investigating other (sub)classes of cones and developing fine-tuned algorithms based on them.

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