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I am new to ontology axioms and DL Syntax and trying to understand what exactly the axioms in the image mean. I have also given the reference from where I took the image paper. Kindly help me to understand these axioms.
https://dl.acm.org/doi/pdf/10.1145/3102254.3102277

fairyjee
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    those are all subclass axioms. some with existential restrictions (`owl:someValuesFrom`), some with additionally inverse relations (`owl:inverse`) in subclass or superclass position. But honestly, even the Wikipedia article would explain the meaning of those symbols: https://en.wikipedia.org/wiki/Description_logic – UninformedUser Apr 17 '21 at 08:20
  • The `∃r` concept constructor (without subsequent `.c`) is an abbreviation for `∃r.⊤`, where `⊤` is an universal concept aka `owl:Thing`. The `C` near `⊑` means that this is a concept inclusion (and not e.g. role inclusion). – Stanislav Kralin Apr 17 '21 at 09:36
  • @UninformedUser If i understood it correctly isn't the 3-8 axioms are domain axioms? – fairyjee Apr 21 '21 at 13:28
  • they are still subclass axioms in DL syntax. and yes, for 3-5 the property domain is basically the idea behind those axioms. 6-8 as well but this is for the inverse of the properties – UninformedUser Apr 21 '21 at 15:14
  • @UninformedUser One thing that is confusing for me is the existential quantifier on the left side of axiom 4,5,7,8. so, how can I interpret it as a range axiom because I thought they could be GCI (maybe i am wrong). could you kindly give me example in simple English a possible use case that can be used for 4,5,7,8 axiom? Like for 3rd axiom i can say "worksFor" has domain "organization". – fairyjee Apr 23 '21 at 08:44
  • it's not a range axiom. Any axiom with an existential quantifier (and top concept as role filler which is the case if there is no role filler at all) on the left side can be seen as a domain axiom for `r`. – UninformedUser Apr 23 '21 at 17:43
  • Your example is quite confusing. "worksFor" has domain "organization" wouldn't make sense, it might have as range "organization", but the domain should be "person" or "employee" or whatever. A complex domain could be for example for the property `goldMedalsWon` something like `∃ hasProfession.Athlete` which means anything that has a gold medal won has as profession being an athlete of any kind – UninformedUser Apr 23 '21 at 17:47
  • @UninformedUser (6) axiom ∃r^-.⊤ ⊑ c is described as a range in this https://aic.ai.wu.ac.at/~polleres/teaching/SemWebTech_2012/20120606lecture6.pdf which makes me wonder 7 and 8 axiom then will be the complex range. I am just trying to understand the notational differences for domain and range. – fairyjee Apr 24 '21 at 11:46

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