Logical Neural Networks
- URL: http://arxiv.org/abs/2006.13155v1
- Date: Tue, 23 Jun 2020 16:55:45 GMT
- Title: Logical Neural Networks
- Authors: Ryan Riegel, Alexander Gray, Francois Luus, Naweed Khan, Ndivhuwo
Makondo, Ismail Yunus Akhalwaya, Haifeng Qian, Ronald Fagin, Francisco
Barahona, Udit Sharma, Shajith Ikbal, Hima Karanam, Sumit Neelam, Ankita
Likhyani, Santosh Srivastava
- Abstract summary: We propose a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning)
Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a highly intepretable disentangled representation.
Inference is omni rather than focused on predefined target variables, and corresponds to logical reasoning.
- Score: 51.46602187496816
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We propose a novel framework seamlessly providing key properties of both
neural nets (learning) and symbolic logic (knowledge and reasoning). Every
neuron has a meaning as a component of a formula in a weighted real-valued
logic, yielding a highly intepretable disentangled representation. Inference is
omnidirectional rather than focused on predefined target variables, and
corresponds to logical reasoning, including classical first-order logic theorem
proving as a special case. The model is end-to-end differentiable, and learning
minimizes a novel loss function capturing logical contradiction, yielding
resilience to inconsistent knowledge. It also enables the open-world assumption
by maintaining bounds on truth values which can have probabilistic semantics,
yielding resilience to incomplete knowledge.
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