Connectionist Inference Models

The performance of symbolic inference tasks has long been a challenge to connectionists. In this paper, we present an extended survey of this area. Existing connectionist inference systems are reviewed, with particular reference to how they perform variable binding and rule-based reasoning, and whether they involve distributed or localist representations. The benefits and disadvantages of different representations and systems are outlined, and conclusions drawn regarding the capabilities of connectionist inference systems when compared with symbolic inference systems or when used for cognitive modeling

Logic-based Technologies for Intelligent Systems: State of the Art and Perspectives

Together with the disruptive development of modern sub-symbolic approaches to artificial intelligence (AI), symbolic approaches to classical AI are re-gaining momentum, as more and more researchers exploit their potential to make AI more comprehensible, explainable, and therefore trustworthy. Since logic-based approaches lay at the core of symbolic AI, summarizing their state of the art is of paramount importance now more than ever, in order to identify trends, benefits, key features, gaps, and limitations of the techniques proposed so far, as well as to identify promising research perspectives. Along this line, this paper provides an overview of logic-based approaches and technologies by sketching their evolution and pointing out their main application areas. Future perspectives for exploitation of logic-based technologies are discussed as well, in order to identify those research fields that deserve more attention, considering the areas that already exploit logic-based approaches as well as those that are more likely to adopt logic-based approaches in the future

NLProlog: Reasoning with Weak Unification for Question Answering in Natural Language

Rule-based models are attractive for various tasks because they inherently lead to interpretable and explainable decisions and can easily incorporate prior knowledge. However, such systems are difficult to apply to problems involving natural language, due to its linguistic variability. In contrast, neural models can cope very well with ambiguity by learning distributed representations of words and their composition from data, but lead to models that are difficult to interpret. In this paper, we describe a model combining neural networks with logic programming in a novel manner for solving multi-hop reasoning tasks over natural language. Specifically, we propose to use a Prolog prover which we extend to utilize a similarity function over pretrained sentence encoders. We fine-tune the representations for the similarity function via backpropagation. This leads to a system that can apply rule-based reasoning to natural language, and induce domain-specific rules from training data. We evaluate the proposed system on two different question answering tasks, showing that it outperforms two baselines -- BIDAF (Seo et al., 2016a) and FAST QA (Weissenborn et al., 2017b) on a subset of the WikiHop corpus and achieves competitive results on the MedHop data set (Welbl et al., 2017).Comment: ACL 201

On the role of Computational Logic in Data Science: representing, learning, reasoning, and explaining knowledge

In this thesis we discuss in what ways computational logic (CL) and data science (DS) can jointly contribute to the management of knowledge within the scope of modern and future artificial intelligence (AI), and how technically-sound software technologies can be realised along the path. An agent-oriented mindset permeates the whole discussion, by stressing pivotal role of autonomous agents in exploiting both means to reach higher degrees of intelligence. Accordingly, the goals of this thesis are manifold. First, we elicit the analogies and differences among CL and DS, hence looking for possible synergies and complementarities along 4 major knowledge-related dimensions, namely representation, acquisition (a.k.a. learning), inference (a.k.a. reasoning), and explanation. In this regard, we propose a conceptual framework through which bridges these disciplines can be described and designed. We then survey the current state of the art of AI technologies, w.r.t. their capability to support bridging CL and DS in practice. After detecting lacks and opportunities, we propose the notion of logic ecosystem as the new conceptual, architectural, and technological solution supporting the incremental integration of symbolic and sub-symbolic AI. Finally, we discuss how our notion of logic ecosys- tem can be reified into actual software technology and extended towards many DS-related directions

Interpretable Narrative Explanation for ML Predictors with LP: A Case Study for XAI

In the era of digital revolution, individual lives are going to cross and interconnect ubiquitous online domains and offline reality based on smart technologies\u2014discovering, storing, processing, learning, analysing, and predicting from huge amounts of environment-collected data. Sub-symbolic techniques, such as deep learning, play a key role there, yet they are often built as black boxes, which are not inspectable, interpretable, explainable. New research efforts towards explainable artificial intelligence (XAI) are trying to address those issues, with the final purpose of building understandable, accountable, and trustable AI systems\u2014still, seemingly with a long way to go. Generally speaking, while we fully understand and appreciate the power of sub-symbolic approaches, we believe that symbolic approaches to machine intelligence, once properly combined with sub-symbolic ones, have a critical role to play in order to achieve key properties of XAI such as observability, interpretability, explainability, accountability, and trustability. In this paper we describe an example of integration of symbolic and sub-symbolic techniques. First, we sketch a general framework where symbolic and sub-symbolic approaches could fruitfully combine to produce intelligent behaviour in AI applications. Then, we focus in particular on the goal of building a narrative explanation for ML predictors: to this end, we exploit the logical knowledge obtained translating decision tree predictors into logical programs

Relational Neural Machines

Deep learning has been shown to achieve impressive results in several tasks where a large amount of training data is available. However, deep learning solely focuses on the accuracy of the predictions, neglecting the reasoning process leading to a decision, which is a major issue in life-critical applications. Probabilistic logic reasoning allows to exploit both statistical regularities and specific domain expertise to perform reasoning under uncertainty, but its scalability and brittle integration with the layers processing the sensory data have greatly limited its applications. For these reasons, combining deep architectures and probabilistic logic reasoning is a fundamental goal towards the development of intelligent agents operating in complex environments. This paper presents Relational Neural Machines, a novel framework allowing to jointly train the parameters of the learners and of a First--Order Logic based reasoner. A Relational Neural Machine is able to recover both classical learning from supervised data in case of pure sub-symbolic learning, and Markov Logic Networks in case of pure symbolic reasoning, while allowing to jointly train and perform inference in hybrid learning tasks. Proper algorithmic solutions are devised to make learning and inference tractable in large-scale problems. The experiments show promising results in different relational tasks

An overview of decision table literature 1982-1995.

This report gives an overview of the literature on decision tables over the past 15 years. As much as possible, for each reference, an author supplied abstract, a number of keywords and a classification are provided. In some cases own comments are added. The purpose of these comments is to show where, how and why decision tables are used. The literature is classified according to application area, theoretical versus practical character, year of publication, country or origin (not necessarily country of publication) and the language of the document. After a description of the scope of the interview, classification results and the classification by topic are presented. The main body of the paper is the ordered list of publications with abstract, classification and comments.

Neurosymbolic AI for Reasoning on Graph Structures: A Survey

Neurosymbolic AI is an increasingly active area of research which aims to combine symbolic reasoning methods with deep learning to generate models with both high predictive performance and some degree of human-level comprehensibility. As knowledge graphs are becoming a popular way to represent heterogeneous and multi-relational data, methods for reasoning on graph structures have attempted to follow this neurosymbolic paradigm. Traditionally, such approaches have utilized either rule-based inference or generated representative numerical embeddings from which patterns could be extracted. However, several recent studies have attempted to bridge this dichotomy in ways that facilitate interpretability, maintain performance, and integrate expert knowledge. Within this article, we survey a breadth of methods that perform neurosymbolic reasoning tasks on graph structures. To better compare the various methods, we propose a novel taxonomy by which we can classify them. Specifically, we propose three major categories: (1) logically-informed embedding approaches, (2) embedding approaches with logical constraints, and (3) rule-learning approaches. Alongside the taxonomy, we provide a tabular overview of the approaches and links to their source code, if available, for more direct comparison. Finally, we discuss the applications on which these methods were primarily used and propose several prospective directions toward which this new field of research could evolve.Comment: 21 pages, 8 figures, 1 table, currently under review. Corresponding GitHub page here: https://github.com/NeSymGraph