How the multiple statements on Extenstial restrictions and universal restriction interpreted in protege

Question

I am new to Protégé . I have a question that is related with the use of existential restrictions and universal restriction in the Protégé . I am taking an example from the Protégé Pizza ontology guide. As per the notes in the guide

when multiple restrictions are used the total description is taken to be the intersection of individual restrictions

therfore let us say:

hasTopping some CheeseTopping
hasTopping some VegetableTopping

should be interpreted as

hasTopping some (CheeseTopping and VegetableTopping)

and

hasTopping only CheeseTopping
hasTopping only VegetableTopping

should be interpreted as

hasTopping only (CheeseTopping and VegetableTopping)

Now from the above understanding because the CheeseTopping and VegetableTopping classes are Disjoint therefore, both of the statements should be logically in correct. But why in the above statement protege give error for Universal restriction statement :

hasTopping only CheeseTopping
hasTopping only VegetableTopping

while for the Existential restriction the below statemets are correct ?

hasTopping some CheeseTopping
hasTopping some VegetableTopping

Please help me in clarifying this query.

Thanks in advance

@Artemis, Thanks for the clarification. As per my understanding on your final comment, in case if i am taking "some" restriction, due to open world assumption this statement is treated as true by protege reasoner. however if i read my above example lines in which if the intersection of the 2 toppings occur, ie hasTopping some (CheeseTopping and VegetableTopping), logically this will be incorrect as both the classes are Disjoint, but due to fact that there can some leeway, this statement is trated True by protege reasoner. Whereas the only restriction is Hard restriction which doesn't quantify any leeway thus resulting into error by protege reasoner. But i feel this is quite confusing situation to deal with "some" restriction in case if the ontology is very large.

Answer 1

Logically an Universal quantifier mentions that:

A restriction containing an owl:allValuesFrom constraint is used to describe a class of all individuals for which all values of the property under consideration are either members of the class extension of the class description or are data values within the specified data range. In other words, it defines a class of individuals x for which holds that if the pair (x,y) is an instance of P (the property concerned), then y should be an instance of the class description or a value in the data range, respectively.

However, the Existential quantifier mentions that:

A restriction containing an owl:someValuesFrom constraint describes a class of all individuals for which at least one value of the property concerned is an instance of the class description or a data value in the data range. In other words, it defines a class of individuals x for which there is at least one y (either an instance of the class description or value of the data range) such that the pair (x,y) is an instance of P. This does not exclude that there are other instances (x,y') of P for which y' does not belong to the class description or data range.

That is the reason the reasoner doesn't accept one of the definitions. So the reasoner assumes that hasTopping only (CheeseTopping and VegetableTopping) is true for all the members of this class, which is obviously not true.

Basically only is a hard restriction. some means that it must have at least one individual of the class x, but can have others of other classes. Using only , you're saying that every individual that is a range of this property must be an individual of the class X. Therefore, when an intersection is used, there is a leeway when dealing with some that unless you have individuals that contradict this rule, this situation might not occur. But in the case of only , regardless of what is in the ontology, this rule is always contradicted.