All GFL semantic constructs reflect respective F-Logic constructs. For instance the logical operators OR, AND, NOT introduced in previous section reflect respective operators in F-Logic and thus they are different from operations AND, OR, NOT encountered in ontology languages based on the Description Logic. In Description Logic operator AND has set theoretical semantic and denotes the intersection of two or more concepts. In DL the operation AND is applied to the concepts to fetch a concept with the denotation set equal to the intersection of the denotation sets of the two concepts. Say the concept (ecologist AND modeler) would denote the set of instances which are ecologist and modeler at the same time. Operator OR fetch the union of denotation sets , and NOT fetch the set theoretical complement.
GFL has elegant framework for graphic extensions (see section 4) which allows introducing new symbols with a complex meaning. This framework allows to introduce external operators which emulate AND, OR, NOT operations of Description Logic. In this section, we shall only illustrate the graphic representation and describe the meaning of these symbols . Their precise semantics will be described in the section 5.2 (link). Since we have already reserved AND, OR, NOT for native F-Logic constructs we shall use different names for respective Description logic operations. We shall use Intersect for AND, Union for OR, and Complement for NOT, besides that we will use DUnion (Disjoint Union) for XOR. The introduction of Complement involves some additional requirements so we postpone it till the section 5.2.
Examples:
The following diagram define an ecomodeler as someone who is both ecologist and modeler. Operator Intersection takes two concepts/classes as input and outputs the concept/class which contains all the instances that belong to both the input concepts/classes.
The following diagram define a commodity as something which is either a good or service . The Operator Union takes two concepts/classes as inputs and output the concept/class which contain all the instances that belong to at least one of those input concepts/classes.
The following diagram suggests that all the organisms fall under one of the five categories: animalia, plantae, fungi, protista, monera. The Operator DUnion takes two , three or more concepts/classes as input and outputs the concept/class containing all the instances belonging to at least one of those classes. It also demands that there should be no intersection between the input concept/classes.
Modern ontology editors, such as OntoEdit from Ontoprise allow to convert DAML+OIL ontologies into F-Logic. During such conversion native Description Logic operations AND, OR, NOT find their expression in the form of rules. We must note however that conversion of DAML+OIL or OWL ontologies is a complex problem which has not been discussed in literature so far. The working paper by B. Grosof and I. Horrocks . describes the conversion of DAML+OIL ontologies to RuleML , but it touches merely the tip of the iceberg.
C 2003 S. Krivov Send your comments to skrivov@zoo.uvm.edu