We propose Logic Tensor Networks: a uniform framework for integrating automatic learning and reasoning. A logic formalism called Real Logic is defined on a first-order language whereby formulas have truth-value in the interval [0,1] and semantics defined concretely on the domain of real numbers. Logical constants are interpreted as feature vectors of real numbers. Real Logic promotes a well-founded integration of deductive reasoning on a knowledge-base and efficient data-driven relational machine learning. We show how Real Logic can be implemented in deep Tensor Neural Networks with the use of Google's tensorflow primitives. The paper concludes with experiments applying Logic Tensor Networks on a simple but representative example of knowledge completion.
Logical relations widely exist in human activities. Human use them for making judgement and decision according to various conditions, which are embodied in the form of \emph{if-then} rules. As an important kind of cognitive intelligence, it is prerequisite of representing and storing logical relations rightly into computer systems so as to make automatic judgement and decision, especially for high-risk domains like medical diagnosis. However, current numeric ANN (Artificial Neural Network) models are good at perceptual intelligence such as image recognition while they are not good at cognitive…
Logical reasoning is essential in a variety of human activities. A representative example of a logical task is mathematics. Recent large-scale models trained on large datasets have been successful in various fields, but their reasoning ability in arithmetic tasks is limited, which we reproduce experimentally. Here, we recast this limitation as not unique to mathematics but common to tasks that require logical operations. We then propose a new set of tasks, termed logical tasks, which will be the next challenge to address. This higher point of view helps the development of inductive biases that…
Logical Structure as Knowledge: Enhancing LLM Reasoning via Structured Logical Knowledge Density Estimation
Huzhou University（湖州大学）；Zhejiang Key Laboratory of Intelligent Education Technology and Application（浙江智能教育技术与应用重点实验室）；Banbu AI Foundation（Banbu AI基金会）；Baichuan Inc（白川公司）；University of Edinburgh（爱丁堡大学）；Zhejiang University（浙江大学）
Max Planck Institute（马克斯·普朗克研究所）；ETH Zürich（苏黎世联邦理工学院）；BITS Pilani（博拉理工学院）；IIT Kharagpur（印度理工学院克勒格布尔分校）；Saarland Informatics Campus（萨尔兰信息学园区）；University of Michigan（密歇根大学）；University of Hong Kong（香港大学）
Reasoning is central to human intelligence. However, fallacious arguments are common, and some exacerbate problems such as spreading misinformation about climate change. In this paper, we propose the task of logical fallacy detection, and provide a new dataset (Logic) of logical fallacies generally found in text, together with an additional challenge set for detecting logical fallacies in climate change claims (LogicClimate). Detecting logical fallacies is a hard problem as the model must understand the underlying logical structure of the argument. We find that existing pretrained large langua…
National and Kapodistrian University of Athens（雅典国立卡波迪斯特里安大学）；University of Ioannina（约阿尼纳大学）
Logic Programs with Ordered Disjunction (LPODs) extend classical logic programs with the capability of expressing preferential disjunctions in the heads of program rules. The initial semantics of LPODs, although simple and quite intuitive, is not purely model-theoretic. A consequence of this is that certain properties of programs appear non-trivial to formalize in purely logical terms. An example of this state of affairs is the characterization of the notion of strong equivalence for LPODs. Although the results of Faber et al. (2008) are accurately developed, they fall short of characterizing …
We examine the recently proposed language of Logical Credal Networks, in particular investigating the consequences of various Markov conditions. We introduce the notion of structure for a Logical Credal Network and show that a structure without directed cycles leads to a well-known factorization result. For networks with directed cycles, we analyze the differences between Markov conditions, factorization results, and specification requirements.
Machine learning models such as Transformers or LSTMs struggle with tasks that are compositional in nature such as those involving reasoning/inference. Although many datasets exist to evaluate compositional generalization, when it comes to evaluating inference abilities, options are more limited. This paper presents LogicInference, a new dataset to evaluate the ability of models to perform logical inference. The dataset focuses on inference using propositional logic and a small subset of first-order logic, represented both in semi-formal logical notation, as well as in natural language. We als…
Zhejiang University（浙江大学）；Shanghai Institute for Advanced Study of Zhejiang University（浙江大学上海高等研究院）；Shanghai AI Laboratory（上海人工智能实验室）
The aim of Logic2Text is to generate controllable and faithful texts conditioned on tables and logical forms, which not only requires a deep understanding of the tables and logical forms, but also warrants symbolic reasoning over the tables. State-of-the-art methods based on pre-trained models have achieved remarkable performance on the standard test dataset. However, we question whether these methods really learn how to perform logical reasoning, rather than just relying on the spurious correlations between the headers of the tables and operators of the logical form. To verify this hypothesis…
