By Krauss und Comp.
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1 suffice to establish two central properties of relaxed abduction, namely conservativeness and weak optimality. The fact that relaxed abduction conservatively extends standard logic-based abduction guarantees that, under natural conditions, our extended approach reproduces all solutions to the corresponding standard abduction problem. Intuitively, this means that no “perfect” solution explaining all observations is lost when applying the relaxation. 1 (Conservativeness of the relaxation) Let RAP = (T , A, O, A , O ) be a relaxed abduction problem, with the corresponding preferential abduction problem PrefAP = (T , A, O, A ).
This idea can be formally grounded within the notion of Pareto-optimality from the theory of economics. 1: Pareto-optimality and Dominance (i. e. either incomparable or worse), the strong notion demands a component being strictly better. 1 visualizes the different notions for total orders. In this example, the points A and B are both weakly and strongly Pareto-optimal, whereas C is weakly Pareto-optimal, but not strongly. Point D is said to be dominated by A (A is smaller than D in all dimensions).
Representing Diagnostic Knowledge Causal Modelling. Diagnostic knowledge represented causally is captured in an ontology Mcaus of axioms that have the form Sysi ∃ Rinfi . (∃ operatesIn . Fault ) j ∃ shows . 3: A hierarchy of diagnostic ontologies where C , r denote variables that range over concepts and roles respectively, Sysi is some system, Symi,j are concrete symptoms, and Rinfi is a relation expressing that one system influences another. We moreover require that Msys ∪ Mcust |= { Fault FaultMode, Symi,j Symptom, Rinfi isInfluencedBy}.