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Non-distributive description logic

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arxiv 2307.09561 v3 pith:373LCAIS submitted 2023-07-18 math.LO

Ineke van der Berg , Andrea De Domenico , Giuseppe Greco , Krishna B. Manoorkar , Alessandra Palmigiano , Mattia Panettiere This is my paper · ORCID
classification math.LO
keywords le-alclogicdescriptionformaltboxesacycliccheckingconsistency
verification ladder T0 review T1 audit T2 compute T3 formal
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We define LE-ALC, a generalization of the description logic ALC based on the propositional logic of general (i.e. not necessarily distributive) lattices, and semantically interpreted on relational structures based on formal contexts from Formal Concept Analysis (FCA). The description logic LE-ALC allows us to formally describe databases with objects, features, and formal concepts, represented according to FCA as Galois-stable sets of objects and features. We describe ABoxes and TBoxes in LE-ALC, provide a tableaux algorithm for checking the consistency of LE-ALC knowledge bases with acyclic TBoxes, and show its termination, soundness and completeness. Interestingly, consistency checking for LE-ALC is in PTIME for acyclic and completely unravelled TBoxes, while the analogous problem in the classical ALC setting is PSPACE-complete.

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  1. Fuzzy Lattice-based Description Logic

    cs.LO 2025-06 conditional novelty 6.0 of 10

    LE-FALC is a fuzzy lattice-based description logic with a sound and complete polynomial-time tableaux algorithm for ABox consistency, and an exponential-time procedure for acyclic TBoxes via unraveling.

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