Extensions of unification modulo ACUI

Baader, Franz; Marantidis, Pavlos; Mottet, Antoine; Okhotin, Alexander

doi:10.1017/s0960129519000185

Cited by 4 publications

(2 citation statements)

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“…ACUI unification has been studied in several papers (e.g. [8][9][10]). The quintessence is that two sets of atoms A and B have a minimally complete set of unifiers containing all minimally general unifiers of the atoms in A and B (as usual, a substitution θ is more general than a substitution σ iff there is a substitution χ such that σ = θχ) -analogues of most general unifiers which do not exist for sets of atoms -which we will denote by mcsu(A, B).…”

Section: Syntaxmentioning

confidence: 99%

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Logic program proportions

Antić

2023

Ann Math Artif Intell

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The purpose of this paper is to present a fresh idea on how symbolic learning might be realized via analogical reasoning. For this, we introduce directed analogical proportions between logic programs of the form “P transforms into Q as R transforms into S” as a mechanism for deriving similar programs by analogy-making. The idea is to instantiate a fragment of a recently introduced abstract algebraic framework of analogical proportions in the domain of logic programming. Technically, we define proportions in terms of modularity where we derive abstract forms of concrete programs from a “known” source domain which can then be instantiated in an “unknown” target domain to obtain analogous programs. To this end, we introduce algebraic operations for syntactic logic program composition and concatenation. Interestingly, our work suggests a close relationship between modularity, generalization, and analogy which we believe should be explored further in the future. In a broader sense, this paper is a further step towards a mathematical theory of logic-based analogical reasoning and learning with potential applications to open AI-problems like commonsense reasoning and computational learning and creativity.

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Section: Syntaxmentioning

confidence: 99%

“…This equation asks for a list program S which is obtained from List as the program Plus on numerals is obtained from N at. In Example 29, we will see that the program for concatenating lists is a solution to (10).…”

Section: Example 17mentioning

confidence: 99%

Logic program proportions

Antić

2023

Ann Math Artif Intell

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Unification in the Description Logic $$\mathcal {ELH}_{\mathcal {R}^+}$$ Without the Top Concept Modulo Cycle-Restricted Ontologies

Baader,

Fernández Gil

2024

Automated Reasoning

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Unification has been introduced in Description Logic (DL) as a means to detect redundancies in ontologies. In particular, it was shown that testing unifiability in the DL $$\mathcal{E}\mathcal{L}$$ E L is an NP-complete problem, and this result has been extended in several directions. Surprisingly, it turned out that the complexity increases to PSpace if one disallows the use of the top concept in concept descriptions. Motivated by features of the medical ontology SNOMED CT, we extend this result to a setting where the top concept is disallowed, but there is a background ontology consisting of restricted forms of concept and role inclusion axioms. We are able to show that the presence of such axioms does not increase the complexity of unification without top, i.e., testing for unifiability remains a PSpace-complete problem.

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Temporal Multi-Agent’s Logic, Knowledge, Uncertainty, and Plausibility

Рыбаков

2021

Agents and Multi-Agent Systems: Technologies and Applications 2021

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Extensions of unification modulo ACUI

Cited by 4 publications

References 23 publications

Logic program proportions

Logic program proportions

Unification in the Description Logic $$\mathcal {ELH}_{\mathcal {R}^+}$$ Without the Top Concept Modulo Cycle-Restricted Ontologies

Temporal Multi-Agent’s Logic, Knowledge, Uncertainty, and Plausibility

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