Our work extends Juba’s formulation of learning abductive reasoning from examples, in which both the relative plausibility of various explanations, as well as which explanations are valid, are learned directly from data. We extend the formulation to consider partially observed examples, along with declarative background knowledge about the missing data. We show that it is possible to use implicitly learned rules together with the explicitly given declarative knowledge to support hypotheses in the course of abduction. We observe that when a small explanation exists, it is possible to obtain a much-improved guarantee in the challenging exception-tolerant setting.

Juba recently proposed a formulation of learning abductive reasoning from examples, in which both the relative plausibility of various explanations, as well as which explanations are valid, are learned directly from data. The main shortcoming of this formulation of the task is that it assumes access to full-information (i.e., fully specified) examples; relatedly, it offers no role for declarative background knowledge, as such knowledge is rendered redundant in the abduction task by complete information. In this work we extend the formulation to utilize such partially specified examples, along with declarative background knowledge about the missing data. We show that it is possible to use implicitly learned rules together with the explicitly given declarative knowledge to support hypotheses in the course of abduction. We also show how to use knowledge in the form of graphical causal models to refine the proposed hypotheses. Finally, we observe that when a small explanation exists, it is possible to obtain a much-improved guarantee in the challenging exception-tolerant setting. Such small, human-understandable explanations are of particular interest for potential applications of the task.

We study abduction in First Order Horn logic theories where all atoms can be abduced and we are looking for preferred solutions with respect to three objective functions: cardinality minimality, coherence, and weighted abduction. We represent this reasoning problem in Answer Set Programming (ASP), in order to obtain a flexible framework for experimenting with global constraints and objective functions, and to test the boundaries of what is possible with ASP. Realizing this problem in ASP is challenging as it requires value invention and equivalence between certain constants, because the Unique Names Assumption does not hold in general. To permit reasoning in cyclic theories, we formally describe fine-grained variations of limiting Skolemization. We identify term equivalence as a main instantiation bottleneck, and improve the efficiency of our approach with on-demand constraints that were used to eliminate the same bottleneck in state-of-the-art solvers. We evaluate our approach experimentally on the ACCEL benchmark for plan recognition in Natural Language Understanding. Our encodings are publicly available, modular, and our approach is more efficient than state-of-the-art solvers on the ACCEL benchmark.

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The work described in my Ph.D. dissertation (Fischer 1991) It is the outcome of seven years of research focusing on abductive explanation generation and involving the departments of computer and information science, industrial and systems engineering, pathology, and allied medical professions at The Ohio State University. In the first phase of my work, I characterized abductive problem solving and performed a comparative analysis of two abductive problem solvers (Smith and Fischer 1990). Thus, I implemented two cognitively plausible heuristics to tackle the complexity of abductive reasoning and successfully experimented with them. This work, originally applied to the domain of alloantibody identification, was generalized to domain-independent abductive problem solving. Abduction, that is, inference to a hypothesis that best explains a set of data, appears to be ubiquitous in cognition.

There are however, a variety of different approaches that claim to capture the true nature of this concept. One reason for this diversity lies in the fact that abductive reasoning occurs in a multitude of contexts. It concerns cases that cover the simplest selection of already existing hypotheses to the generation of new concepts in science. It also concerns cases where the observation is puzzling because it is novel versus cases in which the surprise concerns an anomalous observation. For example, if we wake up, and the lawn is wet, we might explain this observation by assuming that it must have rained or that the sprinklers have been on.

Time series interpretation aims to provide an explanation of what is observed in terms of its underlying processes. The present work is based on the assumption that common classification-based approaches to time series interpretation suffer from a set of inherent weaknesses whose ultimate cause lies in the monotonic nature of the deductive reasoning paradigm. In this document we propose a new approach to this problem based on the initial hypothesis that abductive reasoning properly accounts for the human ability to identify and characterize patterns appearing in a time series. The result of the interpretation is a set of conjectures in the form of observations, organized into an abstraction hierarchy, and explaining what has been observed. A knowledge-based framework and a set of algorithms for the interpretation task are provided, implementing a hypothesize-and-test cycle guided by an attentional mechanism. As a representative application domain, the interpretation of the electrocardiogram allows us to highlight the strengths of the proposed approach in comparison with traditional classification-based approaches.

Causality has been recently introduced in databases, to model, characterize, and possibly compute causes for query answers. Connections between QA-causality and consistency-based diagnosis and database repairs (wrt. integrity constraint violations) have already been established. In this work we establish precise connections between QA-causality and both abductive diagnosis and the view-update problem in databases, allowing us to obtain new algorithmic and complexity results for QA-causality. We also obtain new results on the complexity of view-conditioned causality, and investigate the notion of QA-causality in the presence of integrity constraints, obtaining complexity results from a connection with view-conditioned causality. The abduction connection under integrity constraints allows us to obtain algorithmic tools for QA-causality.

State estimation is the task of estimating the state of a partially observable dynamical system given a sequence of executed actions and observations. In logical settings, state estimation can be realized via logical filtering, which is exact but can be intractable. We propose logical smoothing, a form of backwards reasoning that works in concert with approximated logical filtering to refine past beliefs in light of new observations.  We characterize the notion of logical smoothing together with an algorithm for backwards-forwards state estimation.  We also present an approximation of our smoothing algorithm that is space efficient. We prove properties of our algorithms, and experimentally demonstrate their behaviour, contrasting them with state estimation methods for planning. Smoothing and backwards-forwards reasoning are important techniques for reasoning about partially observable dynamical systems, introducing the logical analogue of effective techniques from control theory and dynamic programming.

In many real tasks there are human knowledge expressed in logic formulae as well as data samples described by raw features (e.g., pixels, strings). It is popular to apply SRL or PILPtechniques to exploit human knowledge through learning of symbolic data, or statistical learning techniques to learn from the raw data samples; however, it is often desired to directly exploit these logic formulae on raw data processing, like human beings utilizing knowledge to guide perception. In this paper, we propose an approach, LASIN, which combines Logical Abduction and Statistical Induction. The LASIN approach generates candidate hypotheses based on the abduction of first-order formulae, and then, the hypotheses are exploited as constraints for statistical induction. We apply theLASIN approach to the learning of representation of written primitives, where a primitive is a basic component in human writing. Our results show that the discovered primitives are reasonable for human perception, and these primitives, if used in learning tasks such as classification and domain adaptation, lead to better performances than simply applying feature learning based on raw data only.