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.

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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.

Deduction is the one of the major forms of inferences and commonly used in formal logic. This kind of inference has the feature of monotonicity, which can be problematic. There are different types of inferences that are not monotonic, e.g. abductive inferences. The debate between advocates and critics of abduction as a useful instrument can be reconstructed along the issue, how an abductive inference warrants to pick out one hypothesis as the best one. But how can the goodness of an inference be assessed? Material inferences express good inferences based on the principle of material incompatibility. Material inferences are based on modal vocabulary, which enriches the logical expressivity of the inferential relations. This leads also to certain limits in the application of labeling in machine learning. I propose a modal interpretation of implications to express conceptual relations.

Abduction is a form of inference that seeks the best explanation for the given observation. Because it provides a reasoning process based on background knowledge, it is used in applications that need convincing explanations. In this study, we consider weighted abduction, which is one of the commonly used mathematical models for abduction. The main difficulty associated with applying weighted abduction to real problems is its computational complexity. A state-of-the-art method formulates weighted abduction as an integer linear programming (ILP) problem and solves it using efficient ILP solvers; however, it is still limited to solving problems that include at most 100 rules of background knowledge and observations. In this study, we first formulate the weighted abduction problem as a Max-SAT problem whose hard clauses are mostly Horn clauses. Then, we propose to solve the problem using modern Max-SAT solvers. In our experiments, the proposed method solved the problems much faster than the state-of-the-art ILP-based weighted abduction.

Mathematical proofs are both paradigms of certainty and some of the most explicitly-justified arguments that we have in the cultural record. Their very explicitness, however, leads to a paradox, because their probability of error grows exponentially as the argument expands. Here we show that under a cognitively-plausible belief formation mechanism that combines deductive and abductive reasoning, mathematical arguments can undergo what we call an epistemic phase transition: a dramatic and rapidly-propagating jump from uncertainty to near-complete confidence at reasonable levels of claim-to-claim error rates. To show this, we analyze an unusual dataset of forty-eight machine-aided proofs from the formalized reasoning system Coq, including major theorems ranging from ancient to 21st Century mathematics, along with four hand-constructed cases from Euclid, Apollonius, Spinoza, and Andrew Wiles. Our results bear both on recent work in the history and philosophy of mathematics, and on a question, basic to cognitive science, of how we form beliefs, and justify them to others.

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.

We demonstrate the need and potential of systematically integrated vision and semantics} solutions for visual sensemaking (in the backdrop of autonomous driving). A general method for online visual sensemaking using answer set programming is systematically formalised and fully implemented. The method integrates state of the art in (deep learning based) visual computing, and is developed as a modular framework usable within hybrid architectures for perception & control. We evaluate and demo with community established benchmarks KITTIMOD and MOT. As use-case, we focus on the significance of human-centred visual sensemaking ---e.g., semantic representation and explainability, question-answering, commonsense interpolation--- in safety-critical autonomous driving situations.

Abductive reasoning generates explanatory hypotheses for new observations using prior knowledge. This paper investigates the use of forgetting, also known as uniform interpolation, to perform ABox abduction in description logic (ALC) ontologies. Non-abducibles are specified by a forgetting signature which can contain concept, but not role, symbols. The resulting hypotheses are semantically minimal and each consist of a set of disjuncts. These disjuncts are each independent explanations, and are not redundant with respect to the background ontology or the other disjuncts, representing a form of hypothesis space. The observations and hypotheses handled by the method can contain both atomic or complex ALC concepts, excluding role assertions, and are not restricted to Horn clauses. Two approaches to redundancy elimination are explored for practical use: full and approximate. Using a prototype implementation, experiments were performed over a corpus of real world ontologies to investigate the practicality of both approaches across several settings.

Dr. Christine Blasey Ford responds to a question from Sen. Dianne Feinstein during testimony before the Senate Judiciary Committee on her sexual assault allegations against Supreme Court nominee Brett Kavanaugh. Christine Blasey Ford gave a detailed scientific explanation for her memory of the alleged incident involving Supreme Court nominee Judge Brett Kavanaugh at her highly anticipated Senate testimony Thursday. Senate Judiciary Committee Ranking Member Dianne Feinstein, D-Calif., pressed Ford over her level of certainty that it was, in fact, Kavanaugh who allegedly pinned her down 36 years ago, while in high school, and attempted to remove her clothing. "How are you so sure that it was he?" Feinstein asked. Ford, a California-based psychology professor, laid out a detailed scientific explanation.