1. A frame is a concept or an instance.
Notes: Each concept or instance is represented in a single frame. Therefore, there are no complex concepts. If we want to allow complex concepts, a number of the following axioms will have to be revised and augmented (apart from significant changes to tools and the semantic analyzer).
2. Every concept except ALL must have another concept that is its IS-A.
Notes: There are no disjoint parts in the ontology. Each hierarchy must ultimately attach to the top-level classification of concepts. This guarantees that a search in the ontology for checking selectional constraints will always succeed. Also, a concept may have multiple parents. It is the responsibility of the ontology acquirer or the semantic analyst to make sure that there are no conflicts in inheritance between such multiple parents.
3. No concept is an INSTANCE-OF anything.
Notes: We do not allow frames that are both instances and concepts. Allowing such frames may be desirable for representing such things in the world as the Great Lakes (which have five instances but are not really concepts). See also #6 below.
4. If a concept X IS-A Y, then X is in the SUBCLASSES of Y.
Notes: Taxonomic links are bi-directional.
5. Every instance must have a concept that is its INSTANCE-OF.
Notes: It is, however, possible for an instance to have more than one concept as its INSTANCE-OF. It is the responsibility of the ontology acquirer or the semantic analyst to make sure that there are no conflicts in inheritance between such multiple parents.
6. No instance is an IS-A of anything.
Notes: See #3 above.
7. If an instance X is an INSTANCE-OF a concept Y, then X is in the INSTANCES of Y.
Notes: Links between the ontology and the onomasticon are also bidirectional.
8. Instances do not have instances or subclasses.
9. If Y is an ancestor of X, then X and Y are concepts and either X = Y, or X IS-A Y, or X IS-A some Z and Y is an ancestor of Z.
Notes: Note that this is just taxonomic ancestry, not subsumption. A descendant may not share all of the properties of one of its ancestors (due to nonmonotonic inheritance; see #27 and #28 below).
10. A concept is either ALL or has one of OBJECT, EVENT, and PROPERTY as an ancestor.
Notes: The topmost classification is into OBJECT, EVENT, and PROPERTY. There are no states in the ontology.
11. No concept has more than one of OBJECT, EVENT, and PROPERTY as ancestors.
Notes: The topmost classification defines three non-overlapping partitions. Although there are dualities between OBJECTs and EVENTs (etc.) in the world, the same concept may not have a dual status in the ontology.
12. Every frame has a DEFINITION slot filled by a string and a TIME-STAMP slot also filled by a string.
13. If Y is a slot in an OBJECT or EVENT X with a filler Z, then either Y is a property or it is one of IS-A, SUBCLASSES, INSTANCE-OF, INSTANCES, DEFINITION, and TIME-STAMP.
Notes: This allows the topmost concepts among PROPERTYs such as PROPERTY, RELATION, or ATTRIBUTE themselves to be slots in other concepts. This feature must of course be used only when there is no further information to indicate a more specific (and meaningful) slot.
14. Only OBJECTs and EVENTs can have PROPERTYs as slots. A PROPERTY cannot have other PROPERTYs as slots.
Notes: This does not preclude reification. However, it does not permit nesting of slots or adding other slots to reified properties within the ontology. Such a thing may be necessary and permissible in Text Meaning Representations.
15. Every PROPERTY is either a RELATION or an ATTRIBUTE. No PROPERTY is both.
Notes: Once again, this classification is exclusive. No slot may take concepts as fillers at one time and literal or numerical values at other times. This is a limitation in meaning representation since there are often properties that are ``n-place'' and link a concept to other concepts as well as add numerical or literal values to the link.
16. Only RELATIONs have an INVERSE slot.
Notes: Inverse slots are used to keep links bidirectional in the ontology. Since attributes map concepts to numbers or literals which are not defined as concepts in the ontology, it does not make sense to have an inverse link from them back to concepts.
17. Fillers of INVERSE slots are always RELATIONs.
18. Every RELATION (other than RELATION itself) has an INVERSE slot filled by another RELATION.
Notes: It is possible for a RELATION to be its own inverse. There are many such reflexive RELATIONs in the world (and in the ontology).
19. If Y is the INVERSE of X, then X is the INVERSE of Y.
Notes: Inverse links between relations are always reciprocal. The inverse ``relation'' (as in mathematics) partitions all RELATIONs in the ontology into a set of pairs.
20. There is only one INVERSE for every RELATION.
21. Every PROPERTY has a DOMAIN slot and a RANGE slot.
Notes: There must be ontological constraints on the domains and ranges of PROPERTYs.
22. Fillers of DOMAIN slots must be frames.
Notes: They must in fact be OBJECTs or EVENTs.
23. Fillers of RANGE slots of RELATIONs must be a frame or the special symbol *nothing* used to block inheritance. Those of ATTRIBUTEs must not be frames.
Notes: The special symbol *nothing* makes inheritance nonmonotonic. A child concept that uses this symbol may not have a property that its parent has.
24. If X has a slot Y that is a PROPERTY, then X must have an ancestor W that is in the DOMAIN slot of the concept Y.
Notes: A concept cannot have a PROPERTY unless it falls in the domain of the PROPERTY.
25. If X has a slot Y that is a RELATION filled by Z, then Z must have an ancestor W that is in the RANGE of the concept Y or Z must be the special symbol *NOTHING* used to block inheritance.
Notes: The filler of a RELATION slot must fall within the range of the RELATION (or be the special symbol *nothing*).
26. Every slot has an inverse slot as follows. The inverse slot is not necessarily direct; it may be inherited from higher up. Thus, If X has a slot Y that is a RELATION filled by Z, then Z has a slot U filled by V where V is an ancestor of X and Y has an INVERSE W that is an ancestor of U. If it is not even inherited, then V may be present implicitly in the RANGE slot of the INVERSE of Y.
Notes: In most cases, U and W are in fact identical. However, we do want to allow for the possibility that Z has a more general or more specific slot U where U and W have an ancestor relationship between them. This allows more flexibility in representing inverse links. It must be noted here that inverse links are not always directly reciprocal in the ontology; they may be inherited or implicit in complex ways as per the above axioms.
27. Inheritance of RELATION slots: If X has a RELATION Y as a slot filled by Z and X is an ancestor of W, then W also has a slot Y that is filled by a U that has Z as one of its ancestors or is the special symbol *NOTHING* used to block inheritance.
Notes: Note that only SEM facets are inherited. Note also that these axioms do not take into account any conflicts that may arise when there are multiple parents, nor do they specify any ordering of multiple parents or a particular inheritance method such as depth-first or breadth-first.
28. Inheritance of ATTRIBUTE slots: If X has an ATTRIBUTE Y as a slot filled by Z and X is a ancestor of W, then W also has a slot Y that is filled by a U that is either equal to Z or is a subset of Z or is the special symbol *NOTHING* used to block inheritance.
Notes: The same observations as in #27 above apply here.
29. Inheritance to instances: an instance has all the slots that its parent concept does. The fillers in the instance are more specific than those in the concept. The instance is allowed to have a SEM facet only when the slot has the same value as in the concept.
Notes: Instances always use VALUE facets. The only exception is when a SEM facet is inherited from a parent concept without a further narrowing of the constraint. Note also that this axiom does not allow an instance in the onomasticon to have a filler that is outside the constraint specified in the parent concept. This ensures that the ontology and the onomasticon are always consistent with each other. Nevertheless, it may be desirable and possible to have fillers outside the ontologically specified constraints in an instance that is part of a (lexical or text) meaning representation.
30. Every slot has at least one of VALUE, SEM, and DEFAULT facets.
31. No slot can have both a VALUE and a SEM facet.
32. Some slots only have VALUE facets.
33. Concepts only have SEM or DEFAULT facets in their PROPERTY slots.
34. Every ATTRIBUTE is either a SCALAR-ATTRIBUTE or a LITERAL-ATTRIBUTE. No ATTRIBUTE is both.
Notes: This partitioning is again a simplification. It is often desirable to have attributes that take scalar and literal values at different times. Such ambiguity is not permitted in the ontology to enable us to specify constraints on attribute fillers precisely.
35. The RANGE of a SCALAR-ATTRIBUTE can only be filled by a scalar.
36. The RANGE of a LITERAL-ATTRIBUTE can only be filled by a literal symbol.
Kavi Mahesh