We introduce an extension of Hoare logic for call-by-value higher-order functions with ML-like local reference generation. Local references may be generated dynamically and exported outside their scope, may store higher-order functions and may be used to construct complex mutable data structures. This primitive is captured logically using a predicate asserting reachability of a reference name from a possibly higher-order datum and quantifiers over hidden references. We explore the logic's descriptive and reasoning power with non-trivial programming examples combining higher-order procedures and dynamically generated local state. Axioms for reachability and local invariant play a central role for reasoning about the examples.
Transformers have been shown to be able to perform deductive reasoning on a logical rulebase containing rules and statements written in English natural language. While the progress is promising, it is currently unclear if these models indeed perform logical reasoning by understanding the underlying logical semantics in the language. To this end, we propose RobustLR, a suite of evaluation datasets that evaluate the robustness of these models to minimal logical edits in rulebases and some standard logical equivalence conditions. In our experiments with RoBERTa and T5, we find that the models tra…
Sun Yat-sen University（中山大学）；Tencent AI Lab（腾讯人工智能实验室）；Tsinghua University（清华大学）；Pengcheng Laboratory（鹏城实验室）
In this paper, we propose a comprehensive benchmark to investigate models' logical reasoning capabilities in complex real-life scenarios. Current explanation datasets often employ synthetic data with simple reasoning structures. Therefore, it cannot express more complex reasoning processes, such as the rebuttal to a reasoning step and the degree of certainty of the evidence. To this end, we propose a comprehensive logical reasoning explanation form. Based on the multi-hop chain of reasoning, the explanation form includes three main components: (1) The condition of rebuttal that the reasoning n…
Logical frameworks and meta-languages form a common substrate for representing, implementing and reasoning about a wide variety of deductive systems of interest in logic and computer science. Their design, implementation and their use in reasoning tasks, ranging from the correctness of software to the properties of formal systems, have been the focus of considerable research over the last two decades. This workshop brings together designers, implementors and practitioners to discuss various aspects impinging on the structure and utility of logical frameworks, including the treatment of variabl…
Ensemble trees are a popular machine learning model which often yields high prediction performance when analysing structured data. Although individual small decision trees are deemed explainable by nature, an ensemble of large trees is often difficult to understand. In this work, we propose an approach called optimised explanation (OptExplain) that faithfully extracts global explanations of ensemble trees using a combination of logical reasoning, sampling and optimisation. Building on top of this, we propose a method called the profile of equivalent classes (ProClass), which uses MAX-SAT to si…
This volume contains a selection of papers presented at LFMTP 2019, the 14th International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice (LFMTP), held on June 22, 2019, in Vancouver, Canada. The workshop was affiliated with the Thirty-Fourth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). Logical frameworks and meta-languages form a common substrate for representing, implementing and reasoning about a wide variety of deductive systems of interest in logic and computer science. Their design, implementation and their use in reasoning tasks, ranging from th…
This volume contains a selection of papers presented at LFMTP 2020, the 15th International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice (LFMTP), held the 29-30th of June, 2019, using the Zoom video conferencing tool due to COVID restrictions. Officially the workshop was held in Paris, France, and it was affiliated with IJCAR 2020, FSCD 2020 and many other satellite events. Logical frameworks and meta-languages form a common substrate for representing, implementing and reasoning about a wide variety of deductive systems of interest in logic and computer science. Their …
Fudan University（复旦大学）；Australian National University（澳大利亚国立大学）；University of New South Wales（新南威尔士大学）
The classical view of epistemic logic is that an agent knows all the logical consequences of their knowledge base. This assumption of logical omniscience is often unrealistic and makes reasoning computationally intractable. One approach to avoid logical omniscience is to limit reasoning to a certain belief level, which intuitively measures the reasoning "depth." This paper investigates the computational complexity of reasoning with belief levels. First we show that while reasoning remains tractable if the level is constant, the complexity jumps to PSPACE-complete -- that is, beyond classical r…
Combining machine learning with logic-based expert systems in order to get the best of both worlds are becoming increasingly popular. However, to what extent machine learning can already learn to reason over rule-based knowledge is still an open problem. In this paper, we explore how symbolic logic, defined as logic programs at a character level, is learned to be represented in a high-dimensional vector space using RNN-based iterative neural networks to perform reasoning. We create a new dataset that defines 12 classes of logic programs exemplifying increased level of complexity of logical rea…
University of Genova（热那亚大学）；Ministry of Justice（司法部）
On May 12th, 2020, during the course entitled Artificial Intelligence and Jurisdiction Practice organized by the Italian School of Magistracy, more than 70 magistrates followed our demonstration of a Prolog logical judge reasoning on an armed robbery case. Although the implemented logical judge is just an exercise of knowledge representation and simple deductive reasoning, a practical demonstration of an automated reasoning tool to such a large audience of potential end-users represents a first and unique attempt in Italy and, to the best of our knowledge, in the international panorama. In thi…
Recent years have witnessed the success of deep neural networks in many research areas. The fundamental idea behind the design of most neural networks is to learn similarity patterns from data for prediction and inference, which lacks the ability of cognitive reasoning. However, the concrete ability of reasoning is critical to many theoretical and practical problems. On the other hand, traditional symbolic reasoning methods do well in making logical inference, but they are mostly hard rule-based reasoning, which limits their generalization ability to different tasks since difference tasks may …
