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School of Information Engineering Knowledge Engineering 2012–13 Solutions of Test 3 – 9th September 2013 1!5!pt!List!the!eleven!types!of!expressions!that!can!be!used!in!SROIQ!to!specify!a!complex)class.!For!each!such!type!of!expression!describe!the!DL!syntax!and!specify!the!formal!semantics!(i.e.,!define!the!set!of!objects!corresponding!to!the!class!in!the!interpretation).!Let!C!and!D!be!any!class!(either!atomic!or!complex)!and!R!a!property:!the!eleven!types!of!expressions!specifying!complex!classes,!together!with!the!respective!formal!semantics,!are!:!!!!!!(¬C)I!=!!Δ!\!CI!!(C!⊓!D)I!=!CI!∩!DI!!!(C!⊔!D)I!=!CI!∪!DI!!(∀R.C)I!=!{x∈Δ!|!for!all!y∈Δ:!if!<x,y>∈RI,!then!y∈CI)!!(∃R!.C)I!=!{x∈Δ!|!for!some!y∈CI:!〈x,y〉∈RI}!!(R∍a)I!=!{x∈Δ!|!〈x,aI〉∈RI}!!(∃R!.Self)I!=!{x∈Δ!|!〈x,x〉∈RI}!!(≤nR!.C)I!=!{x∈Δ!|!#{y∈CI!|!〈x,y〉∈RI}!≤!n}!!(≥nR.C)I!=!{x∈Δ!|!#{y∈CI!|!〈x,y〉∈RI}!≥!n}!!(=nR!.C)I!=!{x∈Δ!|!#{y∈CI!|!〈x,y〉∈RI}!=!n}!!({a})I!=!{aI}!1!15!pt) An!organisation!is!structured!in!teams!with!certain!requirements!reported!below.!Please!read!carefully:!• Translate!the!requirements!into!OWL!2!DL!using!the!DL!notation,!specifying!the!domain!and!range!of!every!property!(in!the!R:!C!,→!D!form).!• In!case!a!requirement!cannot!be!specified!in!OWL!2!DL!explain!why,!and!if!possible!provide!an!OWL!2!DL!approximation.!• Avoid!redundancies!(i.e.,!do!not!state!again!what!can!be!derived!by!reasoning).!•…