Embedding words in vector space is a fundamental first step in state-of-the-art natural language processing (NLP). Typical NLP solutions employ pre-defined vector representations to improve generalization by co-locating similar words in vector space. For instance, Word2Vec is a self-supervised predictive model that captures the context of words using a neural network. Similarly, GLoVe is a popular unsupervised model incorporating corpus-wide word co-occurrence statistics. Such word embedding has significantly boosted important NLP tasks, including sentiment analysis, document classification, and machine translation. However, the embeddings are dense floating-point vectors, making them expensive to compute and difficult to interpret. In this paper, we instead propose to represent the semantics of words with a few defining words that are related using propositional logic. To produce such logical embeddings, we introduce a Tsetlin Machine-based autoencoder that learns logical clauses self-supervised. The clauses consist of contextual words like "black," "cup," and "hot" to define other words like "coffee," thus being human-understandable. We evaluate our embedding approach on several intrinsic and extrinsic benchmarks, outperforming GLoVe on six classification tasks. Furthermore, we investigate the interpretability of our embedding using the logical representations acquired during training. We also visualize word clusters in vector space, demonstrating how our logical embedding co-locate similar words.

Tsetlin Machine (TM) has been gaining popularity as an inherently interpretable machine leaning method that is able to achieve promising performance with low computational complexity on a variety of applications. The interpretability and the low computational complexity of the TM are inherited from the Boolean expressions for representing various sub-patterns. Although possessing favorable properties, TM has not been the go-to method for AI applications, mainly due to its conceptual and theoretical differences compared with perceptrons and neural networks, which are more widely known and well understood. In this paper, we provide detailed insights for the operational concept of the TM, and try to bridge the gap in the theoretical understanding between the perceptron and the TM. More specifically, we study the operational concept of the TM following the analytical structure of perceptrons, showing the resemblance between the perceptrons and the TM. Through the analysis, we indicated that the TM's weight update can be considered as a special case of the gradient weight update. We also perform an empirical analysis of TM by showing the flexibility in determining the clause length, visualization of decision boundaries and obtaining interpretable boolean expressions from TM. In addition, we also discuss the advantages of TM in terms of its structure and its ability to solve more complex problems.

由于需要确保安全可靠的人工智能（AI），因此在过去几年中，机器伦理学受到了越来越多的关注。这两种在机器伦理中使用的主要理论是道义和功利主义伦理。另一方面，美德伦理经常被称为另一种伦理理论。尽管这种有趣的方法比流行的道德理论具有一定的优势，但由于其形式化，编纂和解决道德困境以训练良性剂的挑战，工程人工贤惠的媒介几乎没有努力。我们建议通过使用充满道德困境的角色扮演游戏来弥合这一差距。有几种这样的游戏，例如论文，生活很奇怪，主要角色遇到的情况必须通过放弃对他们所珍视的其他东西来选择正确的行动方案。我们从此类游戏中汲取灵感，以展示如何设计系统的角色扮演游戏来发展人造代理中的美德。使用现代的AI技术，例如基于亲和力的强化学习和可解释的AI，我们激励了扮演这种角色扮演游戏的良性代理，以及通过美德道德镜头对他们的决策进行检查。这种代理和环境的发展是朝着实际上正式化和证明美德伦理在伦理代理发展的价值的第一步。

The Tsetlin Machine (TM) is a novel machine-learning algorithm based on propositional logic, which has obtained state-of-the-art performance on several pattern recognition problems. In previous studies, the convergence properties of TM for 1-bit operation and XOR operation have been analyzed. To make the analyses for the basic digital operations complete, in this article, we analyze the convergence when input training samples follow AND and OR operators respectively. Our analyses reveal that the TM can converge almost surely to reproduce AND and OR operators, which are learnt from training data over an infinite time horizon. The analyses on AND and OR operators, together with the previously analysed 1-bit and XOR operations, complete the convergence analyses on basic operators in Boolean algebra.