About Cardinality Restrictions In OWL

bader asks about the meaning of cardinality restrictions in OWL, in the discussion of Level 2 Known Issues

Regarding the comment: Compare CONTROLLED max 1 in catalysis with SHORT-NAME max 1 in entity. In the first case, all catalyses have a CONTROLLED, though we might not know what it is. In the second, there legitimately may or may not be a SHORT-NAME.

bader - Jan.3.2006 - true, but that doesn't affect the meaning of the BioPAX file if a property is not filled in - you don't know the information (for whatever reason). Partly, this is an issue of different types of 'unknown' - there are many possible types and we don't deal with any of them e.g. I don't know because I didn't check, I don't know because nobody knows, I don't know because I checked (some number of hours Googling) and couldn't find anything, I don't know but it doesn't matter because it can legitimately not exist, etc. I think this is a reasonable simplification. The other part is saying that some controlled exists, but I don't know the specific one - that is an issue of generics. For instance, you might know it's a biochemical reaction, then you could say some biochemical reaction exists which is a controlled
Also, what does "definitional" mean in "Cardinality restrictions are often used as a means to suggest which properties are required or optional, rather than being considered definitional."?
Alan Ruttenberg - Definitional means it forms the definition of what a thing means. All catalyses by definition have a CONTROLLED and a CONTROLLER. Even if we don't know what one is, we know there is one. Contrast this with SHORT-NAME. We may or may not choose to give an entity a SHORT-NAME. If one isn't mentioned, we have no basis to believe that one exists, though one might. So for example, the enterprise of pathway "hole-filling" would try to fill in empty CONTROLLERs, but wouldn't try to fill in empty SHORT-NAMES. In this sense, an empty SHORT-NAME and CONTROLLER have a different meaning. OWL provides even stronger tools for making definitions in the form of equivalentClass, something we haven't taken advantage of yet. JoanneLuciano discussed this an email. One way that these sorts of definitions can help (once we implement them properly) is in making our files more concise, as we will be able to say less, and have the reasoner conclude more. Hope this helps, Alan
bader - that helps, thanks, but I don't see how this could make our files more concise - could you provide an example? Also, do you know why min-cardinality is allowed to be specified in OWL?
Alan Ruttenberg re: conciseness, an existing example would be saying the PARTICIPANT is a super property of LEFT and RIGHT etc. By stating this definition of PARTICIPANT we don't have to state PARTICIPANT x if we state LEFT x, we can infer it - when we use an OWL reasoner. In general, the more definitions we make, the more a reasoner can infer, and the less we have to state explicitly.
Alan Ruttenberg - minCardinality and maxCardinality may have come before cardinality, and it is often the case that cardinality is translated, in the underlying representation, to a conjunction of a min and max, i.e. card=1 is the same as min=1 and max=1. minCardinality is allowed in order to make the language more expressive. An example might be in the definition of an approved credit transaction, where there is a property that records the forms of identification supplied, and it is stated that there needs to be at least 1. You could google "mincardinality filetype:owl" to see examples of how it is used. In BioPAX, for example, it would make sense to have complex COMPONENTS minCardinality 2, since we generally mean a complex to made of more than 1 components (even if we don't know what they are).
bader - but if components was mincard=2, why won't the OWL validator raise a warning if there are less than 2 components?
Alan Ruttenberg Because of the open world assumption. It may be that you know there needs to be 2, but you don't know what they are. However, if you had an instance in which you closed a property to say it has a single value, that would trigger an inconsistency, because your statement that there was only one would conflict with the requirement that there be at least two. See http://www.ksl.stanford.edu/people/dlm/webont/HowToDoIt/closingRoles.html