Dynamic, Automatic, First-Order Ontology repair by Diagnosis of Failed Plan Execution

ion and Refinement The reasons that ontologies are altered are very often concerned with the fact that too much or, more often, too little detail has been included in the ontology. This creates the need to remove detail performing an abstraction of the ontology, or add detail performing a refinement. Notions of abstractions are often quite vague, but the theory of abstracting first-order ontologies was formalised by Walsh and Giunchilgia (Giunchiglia & Walsh, 1990), who created a theory of abstraction through observing and categorising large numbers of examples of abstraction. Since abstractions should change the theory and not the logic (except in the case of reducing a unary predicate to a nullary predicate, which could be seen as reducing first-order logic to propositional logic), DYNAMIC, AUTOMATIC, FIRST-ORDER ONTOLOGY REPAIR BY DIAGNOSIS OF FAILED PLAN EXECUTION 7 the problem of building abstractions can be reduced to the problem of deciding on a suitable matching of atomic formulae. They developed four categories into which abstractions of objects in first-order ontologies can fall: 1. Predicate abstractions matching predicate names in some uniform way:e.g., (Bottle ?X), (Cup ?X) map onto (Container ?X). 2. Domain abstractions matching constants and function symbols in some uniform way: e.g., (Prime 3), (Prime 5) map onto (Prime Oddnumber). 3. Propositional abstractions dropping some or all of the arguments to predicates: e.g., (Abelian GroupA), (Abelian GroupB) map onto (Abelian). 4. Precondition abstractions matching some of the atomic formulae onto true or false: e.g., (Has Ticket Me) → (Can-Travel Me) maps onto (Can-Travel Me) We have developed corresponding refinement categories through inverting these abstraction categories: 1. Predicate refinement A single predicate is split into one or more subtype predicates, e.g.,: (Money ?Amount) maps onto (Dollars ?Amount), (Euros ?Amount), (Sterling ?Amount), etc. 2. Domain refinement The type of an argument is divided into one or more subtypes, e.g.,: (Money ?Amount European) maps onto (Money ?Amount Euros), (Money ?Amount Sterling), (Money ?Amount Krona), etc. 3. Propositional refinement The arity of a predicate is increased, e.g.,: (Money ?Amount) maps onto (Money ?Amount Dollars), (Money ?Amount Sterling), etc.. 4. Precondition refinement A precondition is added to a rule, e.g.,: (Has Money ?Agent) → (Has Item ?Agent) maps onto (Has Money ?Agent) ∧ (InStock Item Shop) → (Has Item ?Agent) Naturally, not all possible mismatches in first-order techniques are concerned with abstraction or refinements, but these categories describe a large number of mismatches that are encountered and provide a basis for developing a full theory of the space of possible mismatches between first-order ontological objects.