Explainable artificial intelligence has rapidly emerged since lawmakers have started requiring interpretable models for safety-critical domains. Concept-based neural networks have arisen as explainable-by-design methods as they leverage human-understandable symbols (i.e. concepts) to predict class memberships. However, most of these approaches focus on the identification of the most relevant concepts but do not provide concise, formal explanations of how such concepts are leveraged by the classifier to make predictions. In this paper, we propose a novel end-to-end differentiable approach enabling the extraction of logic explanations from neural networks using the formalism of First-Order Logic. The method relies on an entropy-based criterion which automatically identifies the most relevant concepts. We consider four different case studies to demonstrate that: (i) this entropy-based criterion enables the distillation of concise logic explanations in safety-critical domains from clinical data to computer vision; (ii) the proposed approach outperforms state-of-the-art white-box models in terms of classification accuracy and matches black box performances.
Logical Expressivity and Explanations for Monotonic GNNs with Scoring Functions
Department of Compute Science, University of Oxford（牛津大学计算机科学系）；Department of Computer Science, Royal Holloway, University of London（伦敦大学皇家霍洛威学院计算机科学系）
In this paper, we consider the problem of lifted inference in the context of Prism-like probabilistic logic programming languages. Traditional inference in such languages involves the construction of an explanation graph for the query and computing probabilities over this graph. When evaluating queries over probabilistic logic programs with a large number of instances of random variables, traditional methods treat each instance separately. For many programs and queries, we observe that explanations can be summarized into substantially more compact structures, which we call lifted explanation g…
We introduce a lazy approach to the explanation-based approximation of probabilistic logic programs. It uses only the most significant part of the program when searching for explanations. The result is a fast and anytime approximate inference algorithm which returns hard lower and upper bounds on the exact probability. We experimentally show that this method outperforms state-of-the-art approximate inference.
Japan Advanced Institute of Science and Technology（日本北陆先端科学技术大学院大学）
Bayesian reasoning plays a significant role both in human rationality and in machine learning. In this paper, we introduce transfinite modal logic, which combines modal logic with ordinal arithmetic, in order to formalize Bayesian reasoning semi-quantitatively. Technically, we first investigate some nontrivial properties of ordinal arithmetic, which then enable us to expand normal modal logic's semantics naturally and elegantly onto the novel transfinite modal logic, while still keeping the ordinary definition of Kripke models totally intact. Despite all the transfinite mathematical definition…
Dipartimento di Informatica e Sistemistica, Universita di Roma "La Sapienza"（罗马大学信息与系统系）
This paper is directed towards combining Pearl's structural-model approach to causal reasoning with high-level formalisms for reasoning about actions. More precisely, we present a combination of Pearl's structural-model approach with Poole's independent choice logic. We show how probabilistic theories in the independent choice logic can be mapped to probabilistic causal models. This mapping provides the independent choice logic with appealing concepts of causality and explanation from the structural-model approach. We illustrate this along Halpern and Pearl's sophisticated notions of actual ca…
University of Manchester（曼彻斯特大学）；Idiap Research Institute（IDIAP研究所）
An emerging line of research in Explainable NLP is the creation of datasets enriched with human-annotated explanations and rationales, used to build and evaluate models with step-wise inference and explanation generation capabilities. While human-annotated explanations are used as ground-truth for the inference, there is a lack of systematic assessment of their consistency and rigour. In an attempt to provide a critical quality assessment of Explanation Gold Standards (XGSs) for NLI, we propose a systematic annotation methodology, named Explanation Entailment Verification (EEV), to quantify th…
In recent research, human-understandable explanations of machine learning models have received a lot of attention. Often explanations are given in form of model simplifications or visualizations. However, as shown in cognitive science as well as in early AI research, concept understanding can also be improved by the alignment of a given instance for a concept with a similar counterexample. Contrasting a given instance with a structurally similar example which does not belong to the concept highlights what characteristics are necessary for concept membership. Such near misses have been proposed…
Free University of Bozen-Bolzano（博尔扎诺自由大学）；University of Osnabrück（奥斯纳布吕克大学）
A central question for knowledge representation is how to encode and handle uncertain knowledge adequately. We introduce the probabilistic description logic ALCP that is designed for representing context-dependent knowledge, where the actual context taking place is uncertain. ALCP allows the expression of logical dependencies on the domain and probabilistic dependencies on the possible contexts. In order to draw probabilistic conclusions, we employ the principle of maximum entropy. We provide reasoning algorithms for this logic, and show that it satisfies several desirable properties of probab…
When we say "I know why he was late", we know not only the fact that he was late, but also an explanation of this fact. We propose a logical framework of "knowing why" inspired by the existing formal studies on why-questions, scientific explanation, and justification logic. We introduce the Ky_i operator into the language of epistemic logic to express "agent i knows why phi" and propose a Kripke-style semantics of such expressions in terms of knowing an explanation of phi. We obtain two sound and complete axiomatizations w.r.t. two different model classes depending on different assumptions abo…
The last decade witnessed an ever-increasing stream of successes in Machine Learning (ML). These successes offer clear evidence that ML is bound to become pervasive in a wide range of practical uses, including many that directly affect humans. Unfortunately, the operation of the most successful ML models is incomprehensible for human decision makers. As a result, the use of ML models, especially in high-risk and safety-critical settings is not without concern. In recent years, there have been efforts on devising approaches for explaining ML models. Most of these efforts have focused on so-call…
This paper presents a five-valued representation of bifuzzy sets. This representation is related to a five-valued logic that uses the following values: true, false, inconsistent, incomplete and ambiguous. In the framework of five-valued representation, formulae for similarity, entropy and syntropy of bifuzzy sets are constructed.
KAIST（韩国科学技术院）；IBS（基础科学研究院）；Microsoft Research Asia（微软亚洲研究院）
We present SELOR, a framework for integrating self-explaining capabilities into a given deep model to achieve both high prediction performance and human precision. By "human precision", we refer to the degree to which humans agree with the reasons models provide for their predictions. Human precision affects user trust and allows users to collaborate closely with the model. We demonstrate that logic rule explanations naturally satisfy human precision with the expressive power required for good predictive performance. We then illustrate how to enable a deep model to predict and explain with log…
University of Texas at Austin（德克萨斯大学奥斯汀分校）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
We study the problem of synthesizing a policy that maximizes the entropy of a Markov decision process (MDP) subject to a temporal logic constraint. Such a policy minimizes the predictability of the paths it generates, or dually, maximizes the exploration of different paths in an MDP while ensuring the satisfaction of a temporal logic specification. We first show that the maximum entropy of an MDP can be finite, infinite or unbounded. We provide necessary and sufficient conditions under which the maximum entropy of an MDP is finite, infinite or unbounded. We then present an algorithm which is b…
Insight Centre for Data Analytics（洞察数据分析中心）；University College Cork（科克大学学院）
We present in this paper our solver for logic grid puzzles. The approach used by our algorithm mimics the way a human would try to solve the same problem. Every progress made during the solving process is accompanied by a detailed explanation of our program's reasoning. Since this reasoning is based on the same heuristics that a human would employ, the user can easily follow the given explanation.
Free University of Bozen-Bolzano（博尔扎诺-博岑自由大学）；Vienna University of Technology（维也纳工业大学）；University of Oxford（牛津大学）
In order to meet usability requirements, most logic-based applications provide explanation facilities for reasoning services. This holds also for Description Logics, where research has focused on the explanation of both TBox reasoning and, more recently, query answering. Besides explaining the presence of a tuple in a query answer, it is important to explain also why a given tuple is missing. We address the latter problem for instance and conjunctive query answering over DL-Lite ontologies by adopting abductive reasoning; that is, we look for additions to the ABox that force a given tuple to b…
The notion of Craig interpolant, used as a form of explanation in automated reasoning, is adapted from logical inference to statistical inference and used to explain inferences made by neural networks. The method produces explanations that are at the same time concise, understandable and precise.
With the increasing number of deep learning applications, there is a growing demand for explanations. Visual explanations provide information about which parts of an image are relevant for a classifier's decision. However, highlighting of image parts (e.g., an eye) cannot capture the relevance of a specific feature value for a class (e.g., that the eye is wide open). Furthermore, highlighting cannot convey whether the classification depends on the mere presence of parts or on a specific spatial relation between them. Consequently, we present an approach that is capable of explaining a classifi…
In recent years, a number of artificial intelligent services have been developed such as defect detection system or diagnosis system for customer services. Unfortunately, the core in these services is a black-box in which human cannot understand the underlying decision making logic, even though the inspection of the logic is crucial before launching a commercial service. Our goal in this paper is to propose an analytic method of a model explanation that is applicable to general classification models. To this end, we introduce the concept of a contribution matrix and an explanation embedding in…
In this paper we propose a framework for combining Disjunctive Logic Programming and Poole's Probabilistic Horn Abduction. We use the concept of hypothesis to specify the probability structure. We consider the case in which probabilistic information is not available. Instead of using probability intervals, we allow for the specification of the probabilities of disjunctions. Because minimal models are used as characteristic models in disjunctive logic programming, we apply the principle of indifference on the set of minimal models to derive default probability values. We define the concepts of …
We propose neural-symbolic integration for abstract concept explanation and interactive learning. Neural-symbolic integration and explanation allow users and domain-experts to learn about the data-driven decision making process of large neural models. The models are queried using a symbolic logic language. Interaction with the user then confirms or rejects a revision of the neural model using logic-based constraints that can be distilled into the model architecture. The approach is illustrated using the Logic Tensor Network framework alongside Concept Activation Vectors and applied to a Convol…
Integrated Gradients (IG), one of the most popular explainability methods available, still remains ambiguous in the selection of baseline, which may seriously impair the credibility of the explanations. This study proposes a new uniform baseline, i.e., the Maximum Entropy Baseline, which is consistent with the "uninformative" property of baselines defined in IG. In addition, we propose an improved ablating evaluation approach incorporating the new baseline, where the information conservativeness is maintained. We explain the linear transformation invariance of IG baselines from an information …
University of Cambridge（剑桥大学）；Universita’ di Siena（锡耶纳大学）
"PyTorch, Explain!" is a Python module integrating a variety of state-of-the-art approaches to provide logic explanations from neural networks. This package focuses on bringing these methods to non-specialists. It has minimal dependencies and it is distributed under the Apache 2.0 licence allowing both academic and commercial use. Source code and documentation can be downloaded from the github repository: https://github.com/pietrobarbiero/pytorch_explain.
University of Alberta（阿尔伯塔大学）；Carnegie Mellon University（卡内基梅隆大学）
Natural language inference (NLI) aims to determine the logical relationship between two sentences, such as Entailment, Contradiction, and Neutral. In recent years, deep learning models have become a prevailing approach to NLI, but they lack interpretability and explainability. In this work, we address the explainability of NLI by weakly supervised logical reasoning, and propose an Explainable Phrasal Reasoning (EPR) approach. Our model first detects phrases as the semantic unit and aligns corresponding phrases in the two sentences. Then, the model predicts the NLI label for the aligned phrases…
Swansea University（斯旺西大学）；University of Utah（犹他大学）
The overarching goal of Explainable AI is to develop systems that not only exhibit intelligent behaviours, but also are able to explain their rationale and reveal insights. In explainable machine learning, methods that produce a high level of prediction accuracy as well as transparent explanations are valuable. In this work, we present an explainable classification method. Our method works by first constructing a symbolic Knowledge Base from the training data, and then performing probabilistic inferences on such Knowledge Base with linear programming. Our approach achieves a level of learning …
BACON: A fully explainable AI model with graded logic for decision making problems
Department of Information Systems University of Maryland, Baltimore County (UMBC)（信息系统系大学马里兰大学巴尔的摩县（UMBC））；Department of Computer Science San Francisco State University（计算机科学系旧金山州立大学）；Department of Information Systems UMBC（信息系统系大学马里兰大学巴尔的摩县（UMBC））
By their nature, the composition of black box models is opaque. This makes the ability to generate explanations for the response to stimuli challenging. The importance of explaining black box models has become increasingly important given the prevalence of AI and ML systems and the need to build legal and regulatory frameworks around them. Such explanations can also increase trust in these uncertain systems. In our paper we present RICE, a method for generating explanations of the behaviour of black box models by (1) probing a model to extract model output examples using sensitivity analysis; …
