On the Complexity of Finding Second-Best Abductive Explanations

While looking for abductive explanations of a given set of manifestations, an ordering between possible solutions is often assumed. The complexity of finding/verifying optimal solutions is already known. In this paper we consider the computational complexity of finding second-best solutions. We consider different orderings, and consider also different possible definitions of what a second-best solution is

More Than Storage of Information: What Working Memory Contributes to Visual Abductive Reasoning

Abductive reasoning is the process of finding the best explanation for a set of observations. As the number of possible observations and corresponding explanations may be very high, it is commonly accepted that working memory capacity is closely related to successful abductive reasoning. However, the precise relationship between abductive reasoning and working memory capacity remains largely opaque. In a reanalysis of two experiments (N = 59), we first investigated whether reasoning performance is associated with differences in working memory capacity. Second, using eye tracking, we explored the relationship between the facets of working memory and the process of visuospatial reasoning. We used working memory tests of both components (verbal-numerical/spatial) as well as an intelligence measure. Results showed a clear relationship between reasoning accuracy and spatial components as well as intelligence. Process measures suggested that working memory seems to be a limiting factor to reasoning and that looking-back to previously relevant areas is compensating for poor mental models rather than being a sign of a particularly elaborate one. Following, high working memory ability might lead to the use of strategies to optimize the content and complexity of the mental representation on which abductive reasoning is based

Abductive retrieval for multimedia information seeking

In this paper we discuss an approach to the retrieval of data annotated using the MPEG-7 multimedia description schema. In particular we describe a framework for the retrieval of annotated video samples that is based on principles from the area of abductive reasoning

Abduction-Based Explanations for Machine Learning Models

The growing range of applications of Machine Learning (ML) in a multitude of settings motivates the ability of computing small explanations for predictions made. Small explanations are generally accepted as easier for human decision makers to understand. Most earlier work on computing explanations is based on heuristic approaches, providing no guarantees of quality, in terms of how close such solutions are from cardinality- or subset-minimal explanations. This paper develops a constraint-agnostic solution for computing explanations for any ML model. The proposed solution exploits abductive reasoning, and imposes the requirement that the ML model can be represented as sets of constraints using some target constraint reasoning system for which the decision problem can be answered with some oracle. The experimental results, obtained on well-known datasets, validate the scalability of the proposed approach as well as the quality of the computed solutions

Compilability of Abduction

Abduction is one of the most important forms of reasoning; it has been successfully applied to several practical problems such as diagnosis. In this paper we investigate whether the computational complexity of abduction can be reduced by an appropriate use of preprocessing. This is motivated by the fact that part of the data of the problem (namely, the set of all possible assumptions and the theory relating assumptions and manifestations) are often known before the rest of the problem. In this paper, we show some complexity results about abduction when compilation is allowed