@article{murfet_logic_2019,
title = {Logic and the \$2\$-{Simplicial} {Transformer}},
url = {http://arxiv.org/abs/1909.00668},
abstract = {We introduce the \$2\$-simplicial Transformer, an extension of the Transformer which includes a form of higher-dimensional attention generalising the dot-product attention, and uses this attention to update entity representations with tensor products of value vectors. We show that this architecture is a useful inductive bias for logical reasoning in the context of deep reinforcement learning.},
urldate = {2019-11-21},
journal = {arXiv:1909.00668 [cs, stat]},
author = {Murfet, Daniel and Clift, James and Doryn, Dmitry and Wallbridge, James},
month = sep,
year = {2019},
note = {ZSCC: 0000000
arXiv: 1909.00668
version: 1},
keywords = {Abstract machines, Algebra, Machine learning, Semantics}
}
@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}
}
@article{murfet_derivatives_2019,
title = {Derivatives of {Turing} machines in {Linear} {Logic}},
url = {http://arxiv.org/abs/1805.11813},
abstract = {We calculate denotations under the Sweedler semantics of the Ehrhard-Regnier derivatives of various encodings of Turing machines into linear logic. We show that these derivatives calculate the rate of change of probabilities naturally arising in the Sweedler semantics of linear logic proofs. The resulting theory is applied to the problem of synthesising Turing machines by gradient descent.},
urldate = {2019-11-21},
journal = {arXiv:1805.11813 [math]},
author = {Murfet, Daniel and Clift, James},
month = jan,
year = {2019},
note = {ZSCC: NoCitationData[s0]
arXiv: 1805.11813},
keywords = {Abstract machines, Categorical ML, Differentiation, Linear logic, Machine learning}
}
@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{graves_neural_2014,
title = {Neural {Turing} {Machines}},
url = {http://arxiv.org/abs/1410.5401},
abstract = {We extend the capabilities of neural networks by coupling them to external memory resources, which they can interact with by attentional processes. The combined system is analogous to a Turing Machine or Von Neumann architecture but is differentiable end-to-end, allowing it to be efficiently trained with gradient descent. Preliminary results demonstrate that Neural Turing Machines can infer simple algorithms such as copying, sorting, and associative recall from input and output examples.},
urldate = {2019-11-21},
journal = {arXiv:1410.5401 [cs]},
author = {Graves, Alex and Wayne, Greg and Danihelka, Ivo},
month = dec,
year = {2014},
note = {ZSCC: 0001222
arXiv: 1410.5401},
keywords = {Abstract machines, Classical ML, Machine learning}
}
@article{fages_biocham:_2006,
title = {{BIOCHAM}: an environment for modeling biological systems and formalizing experimental knowledge},
volume = {22},
issn = {1367-4803, 1460-2059},
shorttitle = {{BIOCHAM}},
url = {https://academic.oup.com/bioinformatics/article-lookup/doi/10.1093/bioinformatics/btl172},
doi = {10/dfv},
language = {en},
number = {14},
urldate = {2019-11-23},
journal = {Bioinformatics},
author = {Fages, F. and Calzone, L. and Soliman, S.},
month = jul,
year = {2006},
note = {ZSCC: 0000264},
keywords = {Abstract machines, Biology, Implementation, Rewriting theory, Symbolic logic, Systems biology},
pages = {1805--1807}
}