1. Copyright © 2002 Cycorp Errors with Constants, Variables, and Reliance on NL Errors with Specialization, Generalization, and Rules Other Errors Errors in Representing Knowledge

2. Copyright © 2002 Cycorp #$equiv usually isn’t Is it? (#$equiv (#$and (#$parents ?PERSON ?PARENT) (#$brothers ?PARENT ?UNCLE)) (#$uncles ?PERSON ?UNCLE)) Better to use implies twice, and convince yourself that both directions really hold.

3. Copyright © 2002 Cycorp Definable Collections E.g., #$WhiteCat Completely definable in terms of other constants; nothing new to say. Anytime one wishes to write (#$isa ?X #$WhiteCat) one could write this instead: (#$and (#$isa ?X #$Cat) (#$mainColorOfObject ?X #$WhiteColor)

4. Copyright © 2002 Cycorp Tedious Hand-Reification E.g., #$Kilometer, #$Kilogram, #$Kiloliter ( #$Centimeter, #$Millimeter, #$Nanometer, etc) What must we say about, e.g., Kilogram? (#$isa #$Kilogram #$UnitOfMeasure) (#$resultIsa #$Kilogram #$Mass) (#$unitMultiplicationFactor #$Kilogram #$Gram 1000)

5. Copyright © 2002 Cycorp Avoiding Tedious Hand-Reification Better: Constant : MetricUnitPrefix isa : RelationshipType genls : ReifiableFunction UnaryFunction Constant : Kilo isa : MetricUnitPrefix arg1Isa : UnitOfMeasureNoPrefix resultIsa : UnitOfMeasureWithPrefix E.g., 1km = ((#$Kilo #$Meter) 1)

6. Copyright © 2002 Cycorp Avoiding Tedious Hand-Reification Now rules can enforce consistent definitions: (#$unitMultiplicationFactor (#$Kilo ?UNIT) ?UNIT 1000) (#$implies (#$and (#$isa ?PREFIX #$MetricUnitPrefix) (#$natFunction ?METRIC-UOM ?PREFIX) (#$resultIsa ?UOM ?COL) (#$natArgument ?METRIC-UOM 1 ?UOM)) (#$resultIsa ?METRIC-UOM ?COL)) Therefore, (#$unitMultiplicationFactor (#$Kilo #$Meter) #$Meter 1000) (#$resultIsa (#$Kilo #$Meter) #$Distance)

7. Copyright © 2002 Cycorp Gratuitous High-arity Predicates: Lumping independent properties together Bad: (#$inventionInfo #$Telephone #$AlexanderGrahamBell (#$YearFn 1876)) State independently instead: (#$inventors #$Telephone #$AlexanderGrahamBell) (#$inventionDate #$Telephone (#$YearFn 1876))

8. Copyright © 2002 Cycorp Gratuitous High-arity Predicates: Hiding concepts inside assertions Bad: (#$teamLineup #$DallasCowboys-1998 #$TroyAikman #$EmmittSmith #$MichaelErvin...) Reify the positions: (#$hasPositionIn #$TroyAikman #$DallasCowboys-1998 #$Quarterback) (#$hasPositionIn #$EmmittSmith #$DallasCowboys-1998 #$RunningBack)...

9. Copyright © 2002 Cycorp Summary #$equiv usually isn’t Definable Collections Tedious Hand-Reification Gratuitous High-arity Predicates –Lumping independent properties together –Hiding concepts inside assertions