Logic-based Abduction Research Articles

The Parameterized Complexity of Abduction

Abduction belongs to the most fundamental reasoning methods. It is a method for reverse inference, this means one is interested in explaining observed behavior by finding appropriate causes. We study logic-based abduction, where knowledge is represented by propositional formulas. The computational complexity of this problem is highly intractable in many interesting settings. In this work we therefore present an extensive parameterized complexity analysis of abduction within various fragments of propositional logic together with (combinations of) natural parameters.

Faster horn diagnosis - a performance comparison of abductive reasoning algorithms

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.

The complexity of handling minimal solutions in logic-based abduction

Logic-based abduction is an important reasoning method with many applications in Artificial Intelligence including diagnosis, planning, and configuration. The goal of an abduction problem is to find a ‘solution’, i.e., an explanation for some observed symptoms. Usually, many solutions exist, and one is often interested in minimal ones only. Previous definitions of ‘solutions’ to an abduction problem tacitly made an open-world assumption. However, as far as minimality is concerned, this assumption may not always lead to the desired behaviour. To overcome this problem, we propose a new definition of solutions based on a closed-world approach. Moreover, we also introduce a new variant of minimality where only a part of the hypotheses is subject to minimization. A thorough complexity analysis reveals the close relationship between these two new notions as well as the differences compared with previous notions of solutions.

An Analysis of Abductive Reasoning on the Inquiry of Scientists and Elementary School Gifted Children in Science

The purpose of this study was to analyze abductive reasoning on the inquiry of scientists and elementary school gifted children in science. Subjects for this study were eight scientists and eight elementary school gifted children in science studying in the Academy of Gifted Child Education in Science affiliated with Seoul National University of Education. As a result, abductive reasoning on the scientific inquiry of scientists and gifted children showed the three stages of generating hypotheses, designing the experiments, and interpreting the results. The abductive reasoning in each stage characterized the five types as complex abduction, analogical abduction, observation-based abduction, logic-based abduction, selective abduction. The sub-reasoning process of the abductive reasoning of gifted children in science differed in some ways from that of scientists. First, for most scientists, representing a method or representing a casual explican appeared after searching for the characteristics of variables but for gifted children in science, searching for the characteristics of variables appeared after representing a method. Second, scientists tend to rely on logic-based abduction but gifted children in science tend to rely on observationbased abduction. Third, scientists reason by the similar rate in three steps: generating the hypothesis, designing the experience, interpreting the results. On the other hand, most gifted children in science reason about designing the experience.

Bounded treewidth as a key to tractability of knowledge representation and reasoning

Several forms of reasoning in AI – like abduction, closed world reasoning, circumscription, and disjunctive logic programming – are well known to be intractable. In fact, many of the relevant problems are on the second or third level of the polynomial hierarchy. In this paper, we show how the notion of treewidth can be fruitfully applied to this area. In particular, we show that all these problems become tractable (actually, even solvable in linear time), if the treewidth of the involved formulae or programs is bounded by some constant. Clearly, these theoretical tractability results as such do not immediately yield feasible algorithms. However, we have recently established a new method based on monadic datalog which allowed us to design an efficient algorithm for a related problem in the database area. In this work, we exploit the monadic datalog approach to construct new algorithms for logic-based abduction.

Tractable database design and datalog abduction through bounded treewidth

Given that most elementary problems in database design are NP-hard, the currently used database design algorithms produce suboptimal results. For example, the current 3NF decomposition algorithms may continue further decomposing a relation even though it is already in 3NF. In this paper we study database design problems whose sets of functional dependencies have bounded treewidth. For such sets, we develop polynomial-time and highly parallelizable algorithms for a number of central database design problems such as: • primality of an attribute; • 3NF-test for a relational schema or subschema; • BCNF-test for a subschema. In order to define the treewidth of a relational schema, we shall associate a hypergraph with it. Note that there are two main possibilities of defining the treewidth of a hypergraph H : One is via the primal graph of H and one is via the incidence graph of H . Our algorithms apply to the case where the primal graph is considered. However, we also show that the tractability results still hold when the incidence graph is considered instead. It turns out that our results have interesting applications to logic-based abduction. By the well-known relationship with the primality problem in database design and the relevance problem in propositional abduction, our new algorithms and tractability results can be easily carried over from the former field to the latter. Moreover, we show how these tractability results can be further extended from propositional abduction to abductive diagnosis based on non-ground datalog.

New Polynomial Classes for Logic-Based Abduction

We address the problem of propositional logic-based abduction, i.e., the problem of searching for a best explanation for a given propositional observation according to a given propositional knowledge base. We give a general algorithm, based on the notion of projection; then we study restrictions over the representations of the knowledge base and of the query, and find new polynomial classes of abduction problems.

The complexity of logic-based abduction

Abduction is an important form of nonmonotonic reasoning allowing one to find explanations for certain symptoms or manifestations. When the application domain is described by a logical theory, we speak about logic-based abduction . Candidates for abductive explanations are usually subjected to minimality criteria such as subset-minimality, minimal cardinality, minimal weight, or minimality under prioritization of individual hypotheses. This paper presents a comprehensive complexity analysis of relevant decision and search problems related to abduction on propositional theories. Our results indicate that abduction is harder than deduction. In particular, we show that with the most basic forms of abduction the relevant decision problems are complete for complexity classes at the second level of the polynomial hierarchy, while the use of prioritization raises the complexity to the third level in certain cases.