An inference engine for RDF - Agfa

An inference engine for RDF
Appendix 5. A theory of graph resolution
5.1. Introduction
In this section I present the complete series of definitions and lemmas.
5.2. Definitions
A triple consists of two labeled nodes and a labeled arc.
A tripleset is a set of triples.
A graph is represented by a set of triplesets.
A rule consists of antecedents and a consequent. The antecedents are a tripleset;
the consequent is a triple.
Applying a rule r to a graph G in the closure process is the process of unifying
the antecedents with all possible triples of the graph G while propagating the
substitutions. For each successful unification the consequents of the rule is
added to the graph with its variables substituted.
Applying a rule r to a subgraph g in the resolution process is the process of
unifying the consequents with all possible triples of g while propagating the
substitutions. For each successful unification the antecedents of the rule are
added to the goallist of the resolution process (see the explanation of the
resolution process).
A rule r is valid with respect to the graph G if its closure G’ with respect to the
graph G is a valid graph.
A graph G is valid if all the elements of its representation are triples.
The graph G entails the graph T using the rule R if T is a subgraph of the closure
G’ of the graph G with respect to the rule R.
The closure G’ of a graph G with respect to a ruleset R is the result of the
application of the rules of the ruleset R to the graph G giving intermediate
graphs Gi till no more new triples can be generated. A graph may not contain
duplicate triples.
149