Non-distributive logics: from semantics to meaning

Conradie, Willem; Palmigiano, Alessandra; Robinson, Claudette; Wijnberg, Nachoem

doi:10.48550/arxiv.2002.04257

Cited by 2 publications

(3 citation statements)

References 51 publications

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“…The approach of [11] considers minimal quantum logic which does not fulfill distributivity but (only) a weakening: orthomodularity (see preliminaries for a technical definition). But, as argued for in [7], the ability to express non-distributive concept hierarchies means a benefit, as it enables modeling uncertainty w.r.t. the extensions of concepts.…”

Section: Related Workmentioning

confidence: 99%

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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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Section: Related Workmentioning

confidence: 99%

“…Fig 7. Accuracy and Precision for our approach (black) and the other approach (white), based on the proposed test set.…”

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confidence: 99%

Learning with cone-based geometric models and orthologics

Leemhuis

Özçep

Wolter

2022

Ann Math Artif Intell

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“…The procedure described below serves both to compute the first order correspondent of the given inequality in various semantic settings, as discussed e.g. in [13,11,8,14], and to compute the shape of the analytic structural rules corresponding to the given inequality, as discussed in [26,6].…”

Section: Non-distributive Alba On Analytic Inductive Le-inequalitiesmentioning

confidence: 99%

Slanted canonicity of analytic inductive inequalities

Rudder¹,

Palmigiano²

2020

Preprint

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We prove an algebraic canonicity theorem for normal LE-logics of arbitrary signature, in a generalized setting in which the non-lattice connectives are interpreted as operations mapping tuples of elements of the given lattice to closed or open elements of its canonical extension. Interestingly, the syntactic shape of LE-inequalities which guarantees their canonicity in this generalized setting turns out to coincide with the syntactic shape of analytic inductive inequalities, which guarantees LEinequalities to be equivalently captured by analytic structural rules of a proper display calculus. We show that this canonicity result connects and strengthens a number of recent canonicity results in two different areas: subordination algebras, and transfer results via Gödel-McKinsey-Tarski translations.

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Non-distributive logics: from semantics to meaning

Cited by 2 publications

References 51 publications

Learning with cone-based geometric models and orthologics

Learning with cone-based geometric models and orthologics

Slanted canonicity of analytic inductive inequalities

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