@article{serafini_logic_2016,
title = {Logic {Tensor} {Networks}: {Deep} {Learning} and {Logical} {Reasoning} from {Data} and {Knowledge}},
shorttitle = {Logic {Tensor} {Networks}},
url = {http://arxiv.org/abs/1606.04422},
abstract = {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.},
urldate = {2019-11-24},
journal = {arXiv:1606.04422 [cs]},
author = {Serafini, Luciano and Garcez, Artur d'Avila},
month = jul,
year = {2016},
note = {ZSCC: 0000057
arXiv: 1606.04422},
keywords = {Abstract machines, Machine learning, Symbolic logic}
}
@article{dong_neural_2019,
title = {Neural {Logic} {Machines}},
url = {http://arxiv.org/abs/1904.11694},
abstract = {We propose the Neural Logic Machine (NLM), a neural-symbolic architecture for both inductive learning and logic reasoning. NLMs exploit the power of both neural networks---as function approximators, and logic programming---as a symbolic processor for objects with properties, relations, logic connectives, and quantifiers. After being trained on small-scale tasks (such as sorting short arrays), NLMs can recover lifted rules, and generalize to large-scale tasks (such as sorting longer arrays). In our experiments, NLMs achieve perfect generalization in a number of tasks, from relational reasoning tasks on the family tree and general graphs, to decision making tasks including sorting arrays, finding shortest paths, and playing the blocks world. Most of these tasks are hard to accomplish for neural networks or inductive logic programming alone.},
urldate = {2019-11-24},
journal = {arXiv:1904.11694 [cs, stat]},
author = {Dong, Honghua and Mao, Jiayuan and Lin, Tian and Wang, Chong and Li, Lihong and Zhou, Denny},
month = apr,
year = {2019},
note = {ZSCC: 0000008
arXiv: 1904.11694},
keywords = {Abstract machines, Machine learning, Symbolic logic}
}