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Non-ground Abductive Logic Programming with Probabilistic Integrity Constraints

arXiv.org Artificial Intelligence

Uncertain information is being taken into account in an increasing number of application fields. In the meantime, abduction has been proved a powerful tool for handling hypothetical reasoning and incomplete knowledge. Probabilistic logical models are a suitable framework to handle uncertain information, and in the last decade many probabilistic logical languages have been proposed, as well as inference and learning systems for them. In the realm of Abductive Logic Programming (ALP), a variety of proof procedures have been defined as well. In this paper, we consider a richer logic language, coping with probabilistic abduction with variables. In particular, we consider an ALP program enriched with integrity constraints `a la IFF, possibly annotated with a probability value. We first present the overall abductive language, and its semantics according to the Distribution Semantics. We then introduce a proof procedure, obtained by extending one previously presented, and prove its soundness and completeness.


Abductive Knowledge Induction From Raw Data

arXiv.org Artificial Intelligence

For many reasoning-heavy tasks, it is challenging to find an appropriate end-to-end differentiable approximation to domain-specific inference mechanisms. Neural-Symbolic (NeSy) AI divides the end-to-end pipeline into neural perception and symbolic reasoning, which can directly exploit general domain knowledge such as algorithms and logic rules. However, it suffers from the exponential computational complexity caused by the interface between the two components, where the neural model lacks direct supervision, and the symbolic model lacks accurate input facts. As a result, they usually focus on learning the neural model with a sound and complete symbolic knowledge base while avoiding a crucial problem: where does the knowledge come from? In this paper, we present Abductive Meta-Interpretive Learning ($Meta_{Abd}$), which unites abduction and induction to learn perceptual neural network and first-order logic theories simultaneously from raw data. Given the same amount of domain knowledge, we demonstrate that $Meta_{Abd}$ not only outperforms the compared end-to-end models in predictive accuracy and data efficiency but also induces logic programs that can be re-used as background knowledge in subsequent learning tasks. To the best of our knowledge, $Meta_{Abd}$ is the first system that can jointly learn neural networks and recursive first-order logic theories with predicate invention.


Tabling Optimization for Contextual Abduction

arXiv.org Artificial Intelligence

The requirement for artificial intelligence (AI) to provide explanations in making critical decision becomes increasingly important due to concerns of accountability, trust, as well as ethics. Such an explainable AI is expected to be capable of providing justifications that are human-understandable. A form of reasoning for providing explanations to an observation, known as abduction, has been well studied in AI, particularly in knowledge representation and reasoning. It extends to logic programming, dubbed abductive logic programming [3], and it has a wide variety of usage, e.g., in planning, scheduling, reasoning of rational agents, security protocols verification, biological systems, and machine ethics.


Machine Reasoning Explainability

arXiv.org Artificial Intelligence

As a field of AI, Machine Reasoning (MR) uses largely symbolic means to formalize and emulate abstract reasoning. Studies in early MR have notably started inquiries into Explainable AI (XAI) -- arguably one of the biggest concerns today for the AI community. Work on explainable MR as well as on MR approaches to explainability in other areas of AI has continued ever since. It is especially potent in modern MR branches, such as argumentation, constraint and logic programming, planning. We hereby aim to provide a selective overview of MR explainability techniques and studies in hopes that insights from this long track of research will complement well the current XAI landscape. This document reports our work in-progress on MR explainability.


Signature-Based Abduction for Expressive Description Logics -- Technical Report

arXiv.org Artificial Intelligence

Signature-based abduction aims at building hypotheses over a specified set of names, the signature, that explain an observation relative to some background knowledge. This type of abduction is useful for tasks such as diagnosis, where the vocabulary used for observed symptoms differs from the vocabulary expected to explain those symptoms. We present the first complete method solving signature-based abduction for observations expressed in the expressive description logic ALC, which can include TBox and ABox axioms, thereby solving the knowledge base abduction problem. The method is guaranteed to compute a finite and complete set of hypotheses, and is evaluated on a set of realistic knowledge bases.


Reasoning-Driven Question-Answering for Natural Language Understanding

arXiv.org Artificial Intelligence

Natural language understanding (NLU) of text is a fundamental challenge in AI, and it has received significant attention throughout the history of NLP research. This primary goal has been studied under different tasks, such as Question Answering (QA) and Textual Entailment (TE). In this thesis, we investigate the NLU problem through the QA task and focus on the aspects that make it a challenge for the current state-of-the-art technology. This thesis is organized into three main parts: In the first part, we explore multiple formalisms to improve existing machine comprehension systems. We propose a formulation for abductive reasoning in natural language and show its effectiveness, especially in domains with limited training data. Additionally, to help reasoning systems cope with irrelevant or redundant information, we create a supervised approach to learn and detect the essential terms in questions. In the second part, we propose two new challenge datasets. In particular, we create two datasets of natural language questions where (i) the first one requires reasoning over multiple sentences; (ii) the second one requires temporal common sense reasoning. We hope that the two proposed datasets will motivate the field to address more complex problems. In the final part, we present the first formal framework for multi-step reasoning algorithms, in the presence of a few important properties of language use, such as incompleteness, ambiguity, etc. We apply this framework to prove fundamental limitations for reasoning algorithms. These theoretical results provide extra intuition into the existing empirical evidence in the field.


Abduction-Based Explanations for Machine Learning Models

arXiv.org Artificial Intelligence

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.


Modeling Variations of First-Order Horn Abduction in Answer Set Programming

arXiv.org Artificial Intelligence

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.


Causes for Query Answers from Databases: Datalog Abduction, View-Updates, and Integrity Constraints

arXiv.org Artificial Intelligence

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.


An Improved Algorithm for Learning to Perform Exception-Tolerant Abduction

AAAI Conferences

Inference from an observed or hypothesized condition to a plausible cause or explanation for this condition is known as abduction. For many tasks, the acquisition of the necessary knowledge by machine learning has been widely found to be highly effective. However, the semantics of learned knowledge are weaker than the usual classical semantics, and this necessitates new formulations of many tasks. We focus on a recently introduced formulation of the abductive inference task that is thus adapted to the semantics of machine learning. A key problem is that we cannot expect that our causes or explanations will be perfect, and they must tolerate some error due to the world being more complicated than our formalization allows. This is a version of the qualification problem, and in machine learning, this is known as agnostic learning. In the work by Juba that introduced the task of learning to make abductive inferences, an algorithm is given for producing k-DNF explanations that tolerates such exceptions: if the best possible k-DNF explanation fails to justify the condition with probability ε, then the algorithm is promised to find a k-DNF explanation that fails to justify the condition with probability at most O(nkε), where n is the number of propositional attributes used to describe the domain. Here, we present an improved algorithm for this task. When the best k- DNF fails with probability ε, our algorithm finds a k-DNF that fails with probability at most O ̃(nk/2ε) (i.e., suppressing logarithmic factors in n and 1/ε). We also examine the empirical advantage of this new algorithm over the previous algorithm in two test domains, one of explaining conditions generated by a “noisy” k-DNF rule, and another of explaining conditions that are actually generated by a linear threshold rule.