AI has long pursued the goal of having systems reason over *explicitly provided* knowledge, but building suitable representations has proved challenging. Here we explore whether transformers can similarly learn to reason (or emulate reasoning), but using rules expressed in language, thus bypassing a formal representation. We provide the first demonstration that this is possible, and characterize the extent of this capability. To do this, we use a collection of synthetic datasets that test increasing levels of reasoning complexity (number of rules, presence of negation, and depth of chaining). We find transformers appear to learn rule-based reasoning with high (99%) accuracy on these datasets, and in a way that generalizes to test data requiring substantially deeper chaining than in the training data (95%+ scores). We also demonstrate that the models transfer well to two hand-authored rulebases, and to rulebases paraphrased into more natural language. These findings are significant as it suggests a new role for transformers, namely as a limited "soft theorem prover" operating over explicit theories in language. This in turn suggests new possibilities for explainability, correctability, and counterfactual reasoning in question-answering. All datasets and a live demo are available at http://rule-reasoning.apps.allenai.org/

Deep Learning (DL) techniques for Natural Language Processing have been evolving remarkably fast. Recently, the DL advances in language modeling, machine translation and paragraph understanding are so prominent that the potential of DL in Software Engineering cannot be overlooked, especially in the field of program learning. To facilitate further research and applications of DL in this field, we provide a comprehensive review to categorize and investigate existing DL methods for source code modeling and generation. To address the limitations of the traditional source code models, we formulate common program learning tasks under an encoder-decoder framework. After that, we introduce recent DL mechanisms suitable to solve such problems. Then, we present the state-of-the-art practices and discuss their challenges with some recommendations for practitioners and researchers as well.

We describe an implementation of gradient boosting and neural guidance of saturation-style automated theorem provers that does not depend on consistent symbol names across problems. For the gradient-boosting guidance, we manually create abstracted features by considering arity-based encodings of formulas. For the neural guidance, we use symbol-independent graph neural networks and their embedding of the terms and clauses. The two methods are efficiently implemented in the E prover and its ENIGMA learning-guided framework and evaluated on the MPTP large-theory benchmark. Both methods are shown to achieve comparable real-time performance to state-of-the-art symbol-based methods.

The Diproche system, an automated proof checker for natural language proofs specifically adapted to the context of exercises for beginner's students similar to the Naproche system by Koepke, Schröder, Cramer and others, uses a modification of an automated theorem prover which uses common formal fallacies intead of sound deduction rules for mistake diagnosis. We briefly describe the concept of such an'Anti-ATP' and explain the basic techniques used in its implementation. Learning how to prove is one major obstacle of the introductory phase of university education in mathematics. It requires practice, i.e. exercises, which need to be corrected, which is both an expensive and time-consuming task. This limits the way in which corrections can usually enter into the process of solving proof exercises as feedback.

We address the problem of learning human-interpretable descriptions of a complex system from a finite set of positive and negative examples of its behavior. In contrast to most of the recent work in this area, which focuses on descriptions expressed in Linear Temporal Logic (LTL), we develop a learning algorithm for formulas in the IEEE standard temporal logic PSL (Property Specification Language). Our work is motivated by the fact that many natural properties, such as an event happening at every n-th point in time, cannot be expressed in LTL, whereas it is easy to express such properties in PSL. Moreover, formulas in PSL can be more succinct and easier to interpret (due to the use of regular expressions in PSL formulas) than formulas in LTL. Our learning algorithm builds on top of an existing algorithm for learning LTL formulas. Roughly speaking, our algorithm reduces the learning task to a constraint satisfaction problem in propositional logic and then uses a SAT solver to search for a solution in an incremental fashion. We have implemented our algorithm and performed a comparative study between the proposed method and the existing LTL learning algorithm. Our results illustrate the effectiveness of the proposed approach to provide succinct human-interpretable descriptions from examples.

The problem of human speech modeling has been solved more than once, but each time it faced paradoxes and contradictions. The scientific approach was initiated by Boolean algebra, which transgressed into logic of predicates. The human speech is more complicated than the predicate logic, but at the same time it is free of paradoxes, which occur at the first or higher orders. This article is an attempt to solve certain problems by introducing special restrictions. Speech analysis will be done in some consecutive stages. We should create automata, which can work over context-sensitive grammer, at first. This grammer will be defined in section 2. This definition based on concept of mask, which is responsible to symbol from ingress aphabet. The automata's transition function devides on some parts, which has specific logic operations over its. The main difference with previous studies is the specific function Φ, which can represent any class as data and some data as the class.

Implementing enterprise process automation often requires significant technical expertise and engineering effort. It would be beneficial for non-technical users to be able to describe a business process in natural language and have an intelligent system generate the workflow that can be automatically executed. A building block of process automations are If-Then programs. In the consumer space, sites like IFTTT and Zapier allow users to create automations by defining If-Then programs using a graphical interface. We explore the efficacy of modeling If-Then programs as a sequence learning task. We find Seq2Seq approaches have high potential (performing strongly on the Zapier recipes) and can serve as a promising approach to more complex program synthesis challenges.

Programming-by-example (PBE) is a synthesis paradigm that allows users to generate functions by simply providing input-output examples. While a promising interaction paradigm, synthesis is still too slow for realtime interaction and more widespread adoption. Existing approaches to PBE synthesis have used automated reasoning tools, such as SMT solvers, as well as works applying machine learning techniques. At its core, the automated reasoning approach relies on highly domain specific knowledge of programming languages. On the other hand, the machine learning approaches utilize the fact that when working with program code, it is possible to generate arbitrarily large training datasets. In this work, we propose a system for using machine learning in tandem with automated reasoning techniques to solve Syntax Guided Synthesis (SyGuS) style PBE problems. By preprocessing SyGuS PBE problems with a neural network, we can use a data driven approach to reduce the size of the search space, then allow automated reasoning-based solvers to more quickly find a solution analytically. Our system is able to run atop existing SyGuS PBE synthesis tools, decreasing the runtime of the winner of the 2019 SyGuS Competition for the PBE Strings track by 47.65% to outperform all of the competing tools.

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.

We discuss an agent-based approach to proof design and implementation, which we call {\it Lemma Flow Diagram} (LFD). This approach is based on the multicut rule with $shared$ cuts. This approach is modular and easy to use, read and automate. Thus, we consider LFD an appealing alternative to `flow proof' which is popular in mathematical education. Some examples are provided.