# Neurosymbolic Learning and Reasoning

## Introduction

Neural-symbolic Learning and Reasoning: A Survey and Interpretation by Tarek R. Besold, Artur S. d'Avila Garcez, Sebastian Bader, Howard Bowman, Pedro Domingos, Pascal Hitzler, Kai-Uwe Kühnberger, Luis C. Lamb, Daniel Lowd, Priscila M. V. Lima, Leo de Penning, Gadi Pinkas, Hoifung Poon and Gerson Zaverucha, Dimensions of Neural-symbolic Integration - A Structured Survey by Sebastian Bader and Pascal Hitzler, Computational Architectures Integrating Neural and Symbolic Processes: A Perspective on the State of the Art edited by Ron Sun and Lawrence A. Bookman, Connectionist-symbolic Integration: From Unified to Hybrid Approaches by Ron Sun and Frederic Alexandre, Hybrid Neural Systems edited by Ron Sun and Stefan Wermter, Neural-symbolic Cognitive Reasoning by Artur S. d'Avila Garcez, Luis C. Lamb and Dov M. Gabbay, Perspectives of Neural-symbolic Integration edited by Barbara Hammer and Pascal Hitzler, Neural-symbolic Learning Systems: Foundations and Applications by Artur S. d'Avila Garcez, Krysia B. Broda and Dov M. Gabbay and What Can Neural Networks Reason About? by Keyulu Xu, Jingling Li, Mozhi Zhang, Simon S. Du, Ken-ichi Kawarabayashi and Stefanie Jegelka.

## Knowledge Representation

Cognitive Algorithms and Systems: Reasoning and Knowledge Representation by Artur S. d'Avila Garcez and Luis C. Lamb, Reconciling Deep Learning with Symbolic Artificial Intelligence: Representing Objects and Relations by Marta Garnelo and Murray Shanahan, A Model for Structured Information Representation in Neural Networks by Michael G. Müller, Christos H. Papadimitriou, Wolfgang Maass and Robert Legenstein, Learning Task-general Representations with Generative Neuro-symbolic Modeling by Reuben Feinman and Brenden M. Lake and Generating New Concepts with Hybrid Neuro-symbolic Models by Reuben Feinman and Brenden M. Lake.

## Logic

Logic Programs and Connectionist Networks by Pascal Hitzler, Steffen Hölldobler and Anthony K. Seda, Approximating the Semantics of Logic Programs by Recurrent Neural Networks by Steffen Hölldobler, Yvonne Kalinke and Hans-Peter Störr, The Connectionist Inductive Learning and Logic Programming System by Artur S. d'Avila Garcez and Gerson Zaverucha, A Connectionist Model of Unification by Andreas Stolcke, Unification as Constraint Satisfaction in Structured Connectionist Networks by Andreas Stolcke, Unification in Prolog by Connectionist Models by Volker Weber, A Structured Connectionist Unification Algorithm by Steffen Hölldobler, Connectionist Variable Binding by Antony Browne and Ron Sun, DeepLogic: Towards End-to-end Differentiable Logical Reasoning by Nuri Cingillioglu and Alessandra Russo, DeepProbLog: Neural Probabilistic Logic Programming by Robin Manhaeve, Sebastijan Dumancic, Angelika Kimmig, Thomas Demeester and Luc de Raedt, Logic Programs with Uncertainty: Neural Computations and Automated Reasoning by Ekaterina Komendantskaya and Anthony K. Seda, Neural-symbolic Intuitionistic Reasoning by Artur S. d'Avila Garcez, Luis C. Lamb and Dov M. Gabbay, Connectionist Modal Logic: Representing Modalities in Neural Networks by Artur S. d'Avila Garcez, Luis C. Lamb and Dov M. Gabbay, Advances in Neural-symbolic Learning Systems: Modal and Temporal Reasoning by Artur S. d'Avila Garcez, Connectionist Inference Models by Antony Browne and Ron Sun, Connectionist Representation of Multi-valued Logic Programs by Ekaterina Komendantskaya, Máire Lane and Anthony K. Seda, Connectionist Model Generation: A First-order Approach by Sebastian Bader, Pascal Hitzler and Steffen Hölldobler, Neural Logic Machines by Honghua Dong, Jiayuan Mao, Tian Lin, Chong Wang, Lihong Li and Denny Zhou, Integrating Learning and Reasoning with Deep Logic Models by Giuseppe Marra, Francesco Giannini, Michelangelo Diligenti and Marco Gori, Extracting Reduced Logic Programs from Artificial Neural Networks by Jens Lehmann, Sebastian Bader and Pascal Hitzler, A Neural Network Model of Causality by Ron Sun, Abductive Reasoning in Neural-symbolic Systems by Artur S. d'Avila Garcez, Dov M. Gabbay, Oliver Ray and John Woods and A Neural Network Approach for First-order Abductive Inference by Oliver Ray and Bruno Golénia.

## Question Answering

Scalable Neural Methods for Reasoning with a Symbolic Knowledge Base by William W. Cohen, Haitian Sun, R. Alex Hofer and Matthew Siegler, End-to-end Entity Resolution and Question Answering Using Differentiable Knowledge Graphs by Armin Oliya, Amir Saffari, Priyanka Sen and Tom Ayoola and Expanding End-to-end Question Answering on Differentiable Knowledge Graphs with Intersection by Priyanka Sen, Amir Saffari and Armin Oliya.

## Mathematics

Analysing Mathematical Reasoning Abilities of Neural Models by David Saxton, Edward Grefenstette, Felix Hill and Pushmeet Kohli, End-to-end Differentiable Proving by Tim Rocktäschel and Sebastian Riedel, Learning Reasoning Strategies in End-to-end Differentiable Proving by Pasquale Minervini, Sebastian Riedel, Pontus Stenetorp, Edward Grefenstette and Tim Rocktäschel, Deep Learning for Symbolic Mathematics by Guillaume Lample and François Charton and Solving Quantitative Reasoning Problems with Language Models by Aitor Lewkowycz, Anders Andreassen, David Dohan, Ethan Dyer, Henryk Michalewski, Vinay Ramasesh, Ambrose Slone, Cem Anil, Imanol Schlag, Theo Gutman-Solo, Yuhuai Wu, Behnam Neyshabur, Guy Gur-Ari and Vedant Misra.

## Argumentation

Argumentation Neural Networks by Artur S. d'Avila Garcez, Dov M. Gabbay and Luís C. Lamb, Argumentation Frameworks as Neural Networks by Artur S. d'Avila Garcez, Luís C. Lamb and Dov M. Gabbay and Fibring Argumentation Frames by Dov M. Gabbay.

## Constraint Satisfaction

Model Agnostic Solution of CSPs via Deep Learning: A Preliminary Study by Andrea Galassi, Michele Lombardi, Paola Mello and Michela Milano, Towards Effective Deep Learning for Constraint Satisfaction Problems by Hong Xu, Sven Koenig and T. K. Satish Kumar and PDP: A General Neural Framework for Learning Constraint Satisfaction Solvers by Saeed Amizadeh, Sergiy Matusevych and Markus Weimer.

## Algorithmic Reasoning

Neural Execution of Graph Algorithms by Petar Veličković, Rex Ying, Matilde Padovano, Raia Hadsell and Charles Blundell and Neural Algorithmic Reasoning by Petar Veličković and Charles Blundell.

## Program Synthesis

Neural Programmer-interpreters by Scott Reed and Nando de Freitas, Neuro-symbolic Program Synthesis by Emilio Parisotto, Abdel-rahman Mohamed, Rishabh Singh, Lihong Li, Dengyong Zhou and Pushmeet Kohli, DeepCoder: Learning to Write Programs by Matej Balog, Alexander L. Gaunt, Marc Brockschmidt, Sebastian Nowozin and Daniel Tarlow, Neural Program Search: Solving Programming Tasks from Description and Examples by Illia Polosukhin and Alexander Skidanov and Program Synthesis from Natural Language Using Recurrent Neural Networks by Xi V. Lin, Chenglong Wang, Deric Pang, Kevin Vu and Michael D. Ernst.

## Fibring

Fibring Neural Networks by Artur S. d'Avila Garcez and Dov M. Gabbay, Computing First-order Logic Programs by Fibring Artificial Neural Networks by Sebastian Bader, Artur S. d'Avila Garcez and Pascal Hitzler and Computation of Normal Logic Programs by Fibring Neural Networks by Vladimir Komendantsky and Anthony K. Seda.

## Modularity

Modular Neural Networks: A Survey by Gasser Auda and Mohamed Kamel, Design and Evolution of Modular Neural Network Architectures by Bart L. M. Happel and Jacob M. J. Murre, Biologically Inspired Modular Neural Networks by Farooq Azam and A Review of Modularization Techniques in Artificial Neural Networks by Mohammed Amer and Tomás Maul.