Abstract
Abductive inference derives explanations for encountered anomalies and thus embodies a natural approach for diagnostic reasoning. Yet its computational complexity, which is inherent to the expressiveness of the underlying theory, remains a disadvantage. Even when restricting the representation to Horn formulae the problem is NP-complete. Hence, finding procedures that can efficiently solve abductive diagnosis problems is of particular interest from a research as well as practical point of view. In this paper, we aim at providing guidance on choosing an algorithm or tool when confronted with the issue of computing explanations in propositional logic-based abduction. Our focus lies on Horn representations, which provide a suitable language to describe most diagnostic scenarios. We illustrate abduction via two contrasting problem formulations: direct proof methods and conflict-driven techniques. While the former is based on determining logical consequences, the later searches for suitable refutations involving possible causes. To reveal runtime performance trends we conducted a case study, in which we compared publicly available general purpose tools, established Horn reasoning engines, as well as new variations of known methods as a means for abduction.
Highlights
Within the last decades, an extensive number of approaches and tools for abductive reasoning have been developed within the Artificial Intelligence community
For restricted to bijunctive Horn clauses [27, 28] and on the general propositional theories or models in clausal form other hand, we have developed a meta-approach that has abductive reasoning is located in the second level of the been evaluated in regard to different abduction algorithms polynomial hierarchy, while for Horn theories the problem
All algorithms and tools are implemented in Java, except clingo, which is a C++ Answer Set Programming (ASP) solver
Summary
An extensive number of approaches and tools for abductive reasoning have been developed within the Artificial Intelligence community These methods are tailored to various underlying artifacts and diverse domains, such as plan recognition [4], test case generation [36], ontology debugging [50], or human behavior interpretation [19]. Logic-based abduction is defined as the search for a set of consistent abducible propositions that together with a background theory entail the observations. Additional restrictions, such as minimality, are often placed on the solutions. Besides being a suitable representation for diagnostic models, the complexity results for this subset of logic are less daunting; that is, abduction for general theories is located on the second level in the polynomial hierarchy, while for Horn models the complexity is lowered by one level [10]
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