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 attribute-value pairs (slots). PSOA RuleML 1.0 specifies 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 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 data and knowledge representation where a slot attribute can have different values depending on the predicate. PSOA thus extends object-oriented multi-membership and multiple inheritance. Based on objectification, PSOA laws are given: Besides unscoping and centralization, the semantic restriction and transformation of describution permits 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 metamodel and a Grailog visualization, PSOA's 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 interpretation functions for dependent descriptors. The open PSOATransRun system since Version 1.3 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.