tankEngine greenFrog overwhelmingDispair
| And | |||||
| Wine | |||||
| Fills :Color red | |||||
| AtLeast 2 :GrapeType | |||||
| And | |||||
| Company | |||||
| AtLeast 7 :Director | |||||
| All | |||||
| :Manager | |||||
| And | |||||
| Woman | |||||
| Fills :Degree phD | |||||
| Fills :MinSalary $24.00/hour | |||||
| ProgressiveCompany \(\doteq\) | |||||
| And | |||||
| Company | |||||
| AtLeast 7 :Director | |||||
| All | |||||
| :Manager | |||||
| And | |||||
| Woman | |||||
| Fills :Degree phD | |||||
| Fills :MinSalary $24.00/hour | |||||
\(\mathcal I(\)Universe\() = \mathcal D\). \(\mathcal I(\)All\(\;r\; d) =\) \( \{ x \in \mathcal D \;|\; (x, y) \in \mathcal I(r)\) for \(y \in \mathcal I(d) \}\). \(\mathcal I(\)AtLeast\(\;n\; r) =\) \(\{ x \in \mathcal D \;|\; \#\{ (x, y) \in \mathcal I(r) \} \geq n \}\). \(\mathcal I(\)Fills\(\;r\;c) = \{ x \in \mathcal D \;|\; (x, \mathcal I(c)) \in \mathcal I(r) \}\). \(\mathcal I(\)And\(\;d_1 \ldots d_n) = \mathcal I(d_1) \cap \cdots \cap \mathcal I(d_n)\). 
\(I \models \) c \(\rightarrow\) d iff \(\mathcal I(\)c\() \in \mathcal I(\)d\()\) \(I \models \) d \(\sqsubseteq\) e iff \(\mathcal I(\)d\() \subseteq \mathcal I(\)e\()\) \(I \models \) d \(\doteq\) e iff \(\mathcal I(\)d\() \doteq \mathcal I(\)e\()\) 
KB \(\models\) c \(\rightarrow\) d or does c satisfy d? KB \(\models\) d \(\sqsubseteq\) d\('\) does d\('\) subsume d? 
john \(\rightarrow\) Universe
And Doctor Woman \(\sqsubseteq\) Doctor
KB \(\models\) And Surgeon Woman \(\sqsubseteq\) Doctor (*)
Surgeon \(\doteq\) And Doctor (Fills :Specialty surgery) 
then
d: All atomicConcept Fills r c1 AtLeast 2 c2 
e: All atomicConcept Fills r c1 AtLeast 3 c2 
KB \(\models\) e \(\sqsubseteq\) d and
KB \(\not\models\) e \(\sqsubseteq\) d
And a1 … an (Fills r1 c1) … (Fills rf cf) (AtLeast n1 r1) … (AtLeast nl rl) (All d1 d2) … (All da da) 
All d1 … dn
fred \(\rightarrow\) Fills :ManagedBy joe
fred \(\rightarrow\) All :ManagedBy Managers
Empty \(\doteq\) AtLeast 2 :ManagedBy
Managers \(\sqsubseteq\) Canadians
| This page last modified on 2011 December 14. |