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The knowledge representation languages, in general (like Description logics, OWL, etc), provide only binary relations, in order to keep decidability. But I don't understant why providing ternary relations would make the language undecidable.

I would like some reference explaining this. I didn't find any interesting reference about the subject.

Zaratruta
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    who told you that Description Logics don't support n-ary relations to keep the language decidable? there are also DLs that support n-ary relations and are still decidable although it's clearly not the base for OWL 2 which in fact is SROIQ. You just have to remove some of the features like number restrictions, transitive roles etc. - it's always a tradeoff – UninformedUser Oct 28 '18 at 08:29
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    Can you provide references for these description logics that are decidable and have n-ary relations (with n greater than 2)? – Zaratruta Oct 29 '18 at 00:10
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    well, [`DLR`](https://iccl.inf.tu-dresden.de/web/LATPub148/en) for instance. Just search for "n-ary description logics" - there is at least some research by well known people in the field of description logics. – UninformedUser Oct 29 '18 at 06:25
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    *Very* speculative: limiting number of variables to 2 makes FOL decidable; and it does not make much sense to use ternary predicates having two variables only. Although, omitting that limitation doesn't make a FOL fragment undecidable, because there are other ways to make a FOL fragment decidable... Related: https://pdfs.semanticscholar.org/5d76/79990085800e901143e2c134b713043316cb.pdf – Stanislav Kralin Nov 01 '18 at 11:40

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