Perspectival Knowledge in PSOA RuleML: Representation, Model Theory, and Translation

In Positional-Slotted Object-Applicative (PSOA) RuleML, a predicate application (atom) can have an Object IDentifier (OID) and descriptors that may be positional arguments (tuples) or attributevalue pairs (slots). PSOA RuleML 1.0 extends earlier versions by explicitly specifying for each descriptor whether it is to be interpreted under the perspective of the predicate in whose scope it occurs. This perspectivity dimension refines the design space between oidless, positional atoms (relationships) and oidful, slotted atoms (frames): While relationships use only a predicate-scope-sensitive (predicate-dependent) tuple and frames use only predicate-scope-insensitive (predicate-independent) slots, PSOA RuleML 1.0 uses a systematics of orthogonal constructs also permitting atoms with (predicate-)independent tuples and atoms with (predicate-)dependent slots. This supports advanced data and knowledge representation where, e.g., a slot attribute can have different values depending on the predicate. PSOA thus extends classical objectoriented multi-membership and multiple inheritance. Based on objectification, PSOA laws are explicated: Besides unscoping and centralization, the semantic restriction and implemented transformation of describution permits the rescoping of one atom’s independent descriptors to another atom with the same OID but a different predicate. For inheritance, default descriptors are realized by rules. On top of a basic metamodel and a new Grailog visualization, PSOA’s use of the atom systematics for facts, queries, and rules is explained. The presentation and (XML-)serialization syntaxes of PSOA RuleML 1.0 are introduced. Its model-theoretic semantics is formalized by extending the earlier interpretation functions to accommodate dependent descriptors. The open-source PSOATransRun 1.3 system realizes PSOA RuleML 1.0 by a translator to runtime predicates, including for dependent tuples (prdtupterm) and slots (prdsloterm). Our tests show efficiency advantages of dependent and tupled modeling.