Logic Tensor Networks (LTN)

Installation

Clone the LTN repository and install it using pip install -e <local project path>.

Following are the dependencies we used for development (similar versions should run fine):

• python 3.8
• tensorflow >= 2.2 (for running the core system)
• numpy >= 1.18 (for examples)
• matplotlib >= 3.2 (for examples)

Repository structure

• logictensornetworks/core.py -- core system for defining constants, variables, predicates, functions and formulas,
• logictensornetworks/fuzzy_ops.py -- a collection of fuzzy logic operators defined using Tensorflow primitives,
• logictensornetworks/utils.py -- a collection of useful functions,
• tutorials/ -- tutorials to start with LTN,
• examples/ -- various problems approached using LTN,
• tests/ -- tests.

Getting Started

Tutorials

tutorials/ contains a walk-through of LTN. In order, the tutorials cover the following topics:

1. Grounding in LTN part 1: Real Logic, constants, predicates, functions, variables,
2. Grounding in LTN part 2: connectives and quantifiers (+ complement: choosing appropriate operators for learning),
3. Learning in LTN: using satisfiability of LTN formulas as a training objective,
4. Reasoning in LTN: measuring if a formula is the logical consequence of a knowledgebase.

The tutorials are implemented using jupyter notebooks.

Examples

examples/ contains a series of experiments. Their objective is to show how the language of Real Logic can be used to specify a number of tasks that involve learning from data and reasoning about logical knowledge. Examples of such tasks are: classification (binary_classification, multiclass_classification, mnist), regression, clustering, link prediction (smokes_friends_cancer, parent_ancestor).

The examples are presented with both jupyter notebooks and Python scripts.

License

This project is licensed under the MIT License - see the LICENSE file for details.

Acknowledgements

LTN has been developed thanks to active contributions and discussions with the following people (in alphabetical order):

• Alessandro Daniele (FBK)
• Artur d’Avila Garces (City)
• Benedikt Wagner (City)
• Emile van Krieken (VU Amsterdam)
• Francesco Giannini (UniSiena)
• Giuseppe Marra (UniSiena)
• Ivan Donadello (FBK)
• Lucas Brukberger (UniOsnabruck)
• Luciano Serafini (FBK)
• Marco Gori (UniSiena)
• Michael Spranger (Sony AI)
• Michelangelo Diligenti (UniSiena)
• Samy Badreddine (Sony AI)