# Blog for IBM Neuro-Symbolic AI Summer School 2022 (8-9 August 2022)

## IBM Neuro-Symbolic AI Summer School 2022 - Playback

## Agenda & Registration

The 2022 IBM Neuro-Symbolic AI Summer School was held on 8 and 9 August 2022 (https://ibm.biz/nsss2022) as a virtual event. The summer school had talks from over 25 IBMers in various areas of theory and the application of neuro-symbolic AI. Invited speaker and luminary in the field, **Artur d’Avila Garcez** - (City University of London), presented an overview of the broad topic in a talk entitled “Neurosymbolic AI: The Third Wave”.

The agenda for the summer school was set to be a balance of educational content on neuro-symbolic AI, and a discussion of recent results. We are glad that the Neuro-symbolic AI community, and in particular and broad AI community, showed a great interest in the event. Over 6,000 people registered for the event and we had over 2,500 attendees. As of 24 Aug 2022, over 1,500 have accessed the recordings of the event.

In order not to miss any future events organized by us, please register at https://ibm.biz/nsss2022. You can also get a **free** digital badge for “Neuro-Symbolic AI Essentials” at https://www.credly.com/org/ibm/badge/neuro-symbolic-ai-essentials.

## Day 1 Session 1: Opening

### Agenda

**Opening 20 minutes**- Welcome (Alexander Gray - IBM)
- Motivation and Objective (Francesca Rossi - IBM)
- Summer School Overview (Jon Lenchner - IBM)
- Neuro-Symbolic AI Essentials Badge (Asim Munawar - IBM)

**Neurosymbolic AI: The Third Wave (Artur d’Avila Garcez - City University of London)**1 hour**Neuro-Symbolic AI Open Problems and IBM Progress (Alexander Gray - IBM)**40 minutes

## Day 1 Session 2: Knowledge

### Agenda

**Tutorial: Knowledge Foundations for AI Applications (Maria Chang - IBM)**1 hour- Symbolic Knowledge Representations
- Semantic Web
- AI applications using knowledge

**IBM Research Overview: Knowledge**- Part 1: Universal Logic Knowledge Base (Rosario Uceda-Sosa - IBM) 25 minutes
- Interlinked KBs for broad encyclopedic, linguistic, and commonsense knowledge
- Supporting foundation for neuro-symbolic reasoning

- Part 2: ULKB Logic Language (Guilherme Lima - IBM) 25 minutes
- Higher order logic and simple type theory
- The ULKB Logic Language and its Python API

- Part 3: Deep linguistic processing (Alexandre Rademaker - IBM) 10 minutes
- Minimal recursive semantics and abstract meaning representation
- Open source tooling

- Part 1: Universal Logic Knowledge Base (Rosario Uceda-Sosa - IBM) 25 minutes

### Summary

The Knowledge Foundations tutorial was divided into three parts:

- a brief introduction to symbolic knowledge representations and why they are useful in AI
- Examples of existing knowledge resources, including the Semantic Web ecosystem and the distinction between ontologic knowledge sources (knowledge about the world, commonsense knowledge) and lexical knowledge sources (knowledge about language); knowledge induction and acquisition
- How knowledge is used in AI applications, e.g. Google knowledge graph, COVID-19 knowledge graphs

The research overview was divided into three parts:

- In part 2, we presented the ULKB Logic Language, which is the language interface to the ULKB knowledge graph. We briefly discussed the foundations and syntax of the ULKB Logic Language, and provided a quick tour through its Python API using code examples to illustrate its main features.
- In part 3, we compared two popular semantic representations for sentences: AMR and MRS. We sketched our approach to combining the MRS obtained from DELPH-IN opensource tools (ERG Grammar, ACE parser, and PyDelphin library) with AMR produced by the in-house AMR Parser to create rich semantic representation from sentences and transform it into the ULKB logic.

### References

- https://github.com/delph-in/docs/wiki
- http://erg.delph-in.net/logon and http://delph-in.github.io/delphin-viz/demo/
- https://en.wikipedia.org/wiki/Minimal_recursion_semantics
- Ontolex: https://www.w3.org/2019/09/lexicog/
- Propbank: https://propbank.github.io/
- Verbnet: https://verbs.colorado.edu/verbnet/
- Semlink: https://verbs.colorado.edu/semlink/
- Unified verb index: https://uvi.colorado.edu/
- https://schema.org/
- https://diff.wikimedia.org/event/%E2%99%BB%EF%B8%8F-adding-and-subtracting-wikidata-for-linguistic-analysis-in-specialized-domains%EF%BF%BC/
- Noy, N., Gao, Y., Jain, A., Narayanan, A., Patterson, A., & Taylor, J. (2019). Industry-scale Knowledge Graphs: Lessons and Challenges: Five diverse technology companies show how it’s done. Queue, 17(2), 48-75.
- Wang, X. et al (2020a). Comprehensive named entity recognition on cord-19 with distant or weak supervision. arXiv preprint arXiv:2003.12218.
- Wang, Q. et al. (2020b). COVID-19 literature knowledge graph construction and drug repurposing report generation. arXiv preprint arXiv:2007.00576.
- Pestryakova, S., Vollmers, D., Sherif, M.A. et al. COVIDPUBGRAPH: A FAIR Knowledge Graph of COVID-19 Publications. Sci Data 9, 389 (2022).
- Reese, J. T. et al (2021). KG-COVID-19: a framework to produce customized knowledge graphs for COVID-19 response. Patterns, 2(1), 100155.

## Day 1 Session 3: Reasoning

## Agenda

**Tutorial: A Very Brief Introduction to Logic and Reasoning (Achille Fokoue - IBM)**1 hour- First order logic (FOL) syntax and model theoretic semantics
- FOL reasoning and deductive systems
- FOL Extensions

**IBM Research Overview: Learnable Reasoning (Ndivhuwo Makondo - IBM, Hima Karanam - IBM)**1 hour- Overview of Learning to Reason (e.g., neural theorem provers, MLNs, LTNs, etc)
- Introduction to LNNs - our framework for Learnable Reasoning
- Applications of LNNS

### Summary

In the tutorial session, after introducing the syntax and model theoretic semantics of First Order Logic (FOL), we presented the core reasoning tasks involved in FOL and the key desired properties (e.g., soundness, completeness) of deductive systems capable of performing those tasks. In particular, we described a simple and concrete deductive system for FOL based on Resolution. Finally, we discussed important limitations of FOL and presented standard extensions to address them.

In the IBM Research Overview session, we covered a brief literature survey on various approaches for Learnable Reasoning and then introduced two of IBM’s approaches, Logical Neural Networks (LNNs) and TRAIL (Trail Reasonder for AI that Learns). LNNs are a new representation for learning and reasoning which is both neural and symbolic at the same time. Core LNN concepts along with the way in which inference/reasoning and training are performed in LNNs were covered. Then TRAIL was briefly introduced, which is an RL based proof guidance system for learning reasoning strategies for various underlying reasoners. We described TRAIIL’s state-of-the-art results on several known theorem proving benchmarks. Finally, a set of example application use cases where LNNs have been used was described at a high level, which included a neuro-symbolic AI question answering system and a neuro-symbolic AI reinforcement learning agent for textworld interactive games.

### Reference

- Ronald Brachman and Hector Levesque. Knowledge Representation and Reasoning
- Riegel, et al 2020. Logical Neural Networks
- Fagin, Riegel, and Gray, 2020. Foundations of Reasoning with Uncertainty via Real-valued Logic
- Hang Jiang, et al 2021. LNN-EL: A Neuro-Symbolic Approach to Short-text Entity Linking
- Prithviraj Sen, et al. 2021 Neuro-Symbolic Inductive Logic Programming with Logical Neural Networks
- Songtao Lu, et al 2021. Training Logical Neural Networks by Primal-Dual Methods for Neuro-Symbolic Reasoning
- Pavan Kapanipathi et al. 2021. Leveraging Abstract Meaning Representation for Knowledge Base Question Answering
- Kimura, et al., 2020. Reinforcement Learning with External Knowledge by using Logical Neural Networks
- Lebese, et al., 2021. Proof Extraction for Logical Neural Networks
- Crouse, et al., 2021. A Deep Reinforcement Learning Approach to First-Order Logic Theorem Proving
- Abdelaziz, et al. 2022. Learning to Guide a Saturation-Based Theorem Prover
- Qian, et al., 2020, Logical Credal Networks
- Kautz, 2020 The Third AI Summer
- Garcez and Lamb 2020. Neurosymbolic AI: The 3rd Wave

## Day 1 Session 4: Theory of Reasoning

### Agenda

**Tutorial: Theory of Reasoning**- Foundations of Reasoning with Classical Logic (Marco Carmosino - IBM) 30 minutes
- Desiderata: what is a logic, and what makes a logic “good”?
- Example: First-Order Logic on finite graphs.
- Game-based semantics for First-Order Logic

- Computational Complexity (Jon Lenchner - IBM) 30 minutes
- Time and Space Complexity: P vs. NP and Related Questions
- Descriptive Complexity
- Bridging from Descriptive Complexity to Time and Space Complexity via Games

- Foundations of Reasoning with Classical Logic (Marco Carmosino - IBM) 30 minutes
**IBM Research Overview: Complexity**- Part I: Theory of Real-Valued Logics (Ron Fagin - IBM) 30 minutes
- Allowing sentences to take values other than “true” or “false”
- A rich class of real-valued logic sentences
- A sound and complete axiomatization

- Part II: Games and Complexity Classes (Rik Sengupta - IBM) 30 minutes
- From Ehrenfecht-Fraisse Games to Multi-Structural Games
- From Multi-Structural Games to Syntactic Games
- Open Questions

- Part I: Theory of Real-Valued Logics (Ron Fagin - IBM) 30 minutes

### Summary

In the two-part **Tutorial**, we gave a broad introduction to theoretical reasoning and computational complexity. **First,** we introduced logics *in general* by discussing the ingredients (syntax, semantics, deduction system) that make up a logic, and design considerations for developing a logic. We developed an example logic that formalizes the properties of finite graphs. We concluded part one by presenting a two-player zero-sum game that characterizes the semantics of classical First Order Logic: two players argue about whether a formula is true or false “inside” a given struture. **Second,** we gave a broad introduction to computational complexity: questions about the minimum resources (such as time and memory) required to solve algorithmic problems. The most fundamental question in this area is P vs. NP: can every search problem with efficiently checkable solutions be efficiently solved? We stated and discussed the P vs. NP question, and explained that this question is *equivalent* to questions about the expressive power of certain logics. We concluded part one by presenting a two-player zero-sum game that characterizes the expressive power of classical logics.

In the two-part **Research Overview,** we presented ongoing work about moving beyond classical logic by admitting semantic values besides “True” and “False”, and a separate project that develops new game-theoretic tools for analyzing the expressive power of logics. **First,** Ron Fagin presented a new family of logics whose sentences take truth values between 0 and 1. This logic reasons about what information can be inferred about the *combinations* of real values of a collection of formulas. Despite the richness of this logic, we presented a sound and complete axiomatization see (Fagin, Riegel, Gray, below). **Second,** Rik Sengupta gave an overview of our active research on games that characterize the expressive power of classical logics. The Multi-Sturctural game captures number of quantifiers (exists, for-all) required to define properties. The Syntactic Games generalize this to any “reasonable” complexity measure of logical formulas. Rik concluded our session by presenting many open problems related to logic, complexity, and games.

**Keywords**: computational complexity, logical expressibility, real-valued logic, strongly complete axiomatization

### Reference

**Tutorial**- Textbook: Uwe Schöning, Logic for Computer Scientists
- Textbook: Christos H. Papadimitriou, Computational Complexity
- Textbook: Neil Immerman, Descriptive Complexity

**Research**- Ronald Fagin, Ryan Riegel, and Alexander Gray: Foundations of Reasoning with Uncertainty via Real-valued Logics.
- Ronald Fagin, Jonathan Lenchner, Kenneth W. Regan, Nikhil Vyas: Multi-Structural Games and Number of Quantifiers.
- Ronald Fagin, Jonathan Lenchner, Nikhil Vyas and Ryan Williams: On the Number of Quantifiers as a Complexity Measure.

## Day 2 Session 1: Machine Learning

### Agenda

**Tutorial: What can Transformers do? (Mark Wegman - IBM, Hans Florian - IBM)**1 hour 30 minutes- Computational power of transformers
- What limits their power and what means there are around those limits?
- Theoretical power of a transformer and the relation to their behavior in practice

**IBM Research**- Inductive Logic Programming with LNN (Prithviraj Sen - IBM, Sanjeeb Dash - IBM) 20 minutes
- Introduction to Inductive Logic Programming (ILP)
- Understanding LNN Output Semantics
- Generating LNNs for ILP
- Experimental Results: Knowledge Base Completion (KBC)

- NS architecture zoo (Tengfei Ma - IBM, Ronny Luss - IBM) 10 minutes
- LNN for Times Series
- LNN for Mixed Models

- Inductive Logic Programming with LNN (Prithviraj Sen - IBM, Sanjeeb Dash - IBM) 20 minutes

### Summary

In the tutorial part of the session we recaped for those that understand them, and introduced for those that don’t, the basics of transformers and showed why they are used as a basis for much of modern deep learning topologies. We gave some hints about domains they can be applied in and some of the more common variations. We then described the theoretical power of transformers and what they might be able to do with better than currently known training algorithms — they can in the extreme do anything a Turing machine can. However, current transformer systems can’t reach that level because there are theoretical limits that apply. However, there are ways to attempt to get around those theoretical limits and those work arounds have some very interesting practical impacts.

This IBM Research session was divided into two parts:

In the first IBM Research session on Inductive Logic Programming with LNN, we looked at how to learn rules in first-order logic from labeled data using logical neural networks. While inductive logic programming has for long pursued this goal, LNNs offer the advantage of being differentiable. Thus we can use gradient-based optimization to learn rules while ensuring that said rules adhere closely to first-order logic’s semantics. We demonstrated LNN’s effectiveness by reporting experimental results on real-world applications.

In the second IBM Research session on the Neuro-Symbilic Architecture Zoo, we considered different architectures that make use of LNNs. We first demonstrated an architecture that uses LNN for time series, offering interpretability beyond other time series models, and applied this to biological data regarding wound healing. Next we demonstrated how different modalities can be incorporated into LNN models using additional neural network layers. An example using MNIST images was shown.

### Reference

- Prithviraj Sen, Breno W. S. R. de Carvalho, Ryan Riegel, and Alexander Gray. Neuro-Symbolic Inductive Logic Programming with Logical Neural Networks in Proceedings of the AAAI Conference on Artificial Intelligence, 36(8), 8212-8219, Vancouver, Canada, 2022.
- Ruixuan Yan; Agung Julius; Maria Chang; Achille Fokoue; Tengfei Ma; Rosario Uceda-Sosa. STONE: Signal Temporal Logic Neural Network for Time Series Classification. In 2021 International Conference on Data Mining Workshops (ICDMW)

## Day 2 Session 2: NLP via Logic

### Agenda

- Tutorial: NLP via Logic
- Deep Semantic Parsing with Abstract Meaning Representation (Ramon Astudillo - IBM) 30 minutes
- AMR as Deep Semantic Representation
- AMR parsing and AMR-to-text machine learning approaches
- Incorporating structure to Large Language Models for AMR parsing

- Entity Linking (Dinesh Garg - IBM) 30 minutes
- Setup: What do we mean by entity, mention, and linking
- Linking over knowledge graphs
- Linking over relational databases

- Deep Semantic Parsing with Abstract Meaning Representation (Ramon Astudillo - IBM) 30 minutes
**Challenges and Approaches for Reliable Reasoning with Foundation Models: An Abstractive Summarization Use-case (Pavan Kapanipathi - IBM, Hans Florian - IBM)**1 hour- Reliable Reasoning with Foundation Models
- Abstractive Summarization: Reasoning and Factuality in Summarization
- Challenges and Neuro-Symbolic Approaches

### Summary

### Reference

- https://github.com/IBM/transition-amr-parser
- Zhou J, Naseem T, Astudillo RF, Lee YS, Florian R, Roukos S. Structure-aware Fine-tuning of Sequence-to-sequence Transformers for Transition-based AMR Parsing. InProceedings of the 2021 Conference on Empirical Methods in Natural Language Processing 2021 Nov (pp. 6279-6290).

## Day 2 Session 3: Sequential Decision Making

### Agenda

**Tutorial: SDM**- Theory and practice of RL (Miao Liu - IBM) 30 minutes
- Core elements in RL
- Computational approaches and RL tools
- Important mechanisms - Hierarchical RL and Multiagent RL

- Theory and practice of AI Planning (Michael Katz - IBM) 30 minutes
- What is planning and why is it hard
- Computational approaches to classical planning
- Planners and planning tools

- Theory and practice of RL (Miao Liu - IBM) 30 minutes
**IBM Research Overview: SDM**- Integrating Planning and RL (Junkyu Lee - IBM) 30 minutes
- Introduction to integrating planning and RL
- AI Planning as annotation of RL
- Demonstration of libraries for planning annotated RL tasks

- Logical optimal actions (Don Joven - IBM, Maxwell Crouse - IBM) 30 minutes
- Text-based games as an application environment
- LNN rule induction for learning world models
- The situation calculus and theorem proving applied to planning

- Integrating Planning and RL (Junkyu Lee - IBM) 30 minutes

### Summary

The section on sequential decision making consisted of two parts. First, turorials on the two major approaches to sequential decision making were given, introducing the audience to reinforcement learning (RL) and AI planning. Then, two presentations on IBM research contributions that integrate the two approaches to sequential decision making were presented. Planning annotated RL (PaRL) allows for efficient sequential decision making in complex combinatorial domains, by performing high-level decision making with planning and low-level with RL. Logical optimal action (LOA) focuses on learning action models for planning and ways to exploit the knowledge.

### Reference

- AI Planning tutorial at AAAI 2022
- AI Planning Service
- ForbidIterative planners suite
- PRL Workshop – Bridging the Gap Between AI Planning and Reinforcement Learning
- M. Katz, S. Sohrabi, O. Udrea, D. Winterer, A Novel Iterative Approach to Top-k Planning, in Proceedings of The 28th International Conference on Automated Planning and Scheduling (ICAPS), Delft, Netherlands, 2018.
- M. Katz, S. Sohrabi, Reshaping Diverse Planning, in Proceedings of The 34th AAAI Conference on Artificial Intelligence (AAAI), New York, NY, USA, 2020.
- M. Katz, S. Sohrabi, O. Udrea, Top-Quality Planning: Finding Practically Useful Sets of Best Plans, in Proceedings of The 34th AAAI Conference on Artificial Intelligence (AAAI), New York, NY, USA, 2020.
- M. Katz, S. Sohrabi, O. Udrea, Bounding Quality in Diverse Planning, in Proceedings of The 36th AAAI Conference on Artificial Intelligence (AAAI), Virtual, 2022.
- M. Katz and S. Sohrabi, Who Needs These Operators Anyway: Top Quality Planning with Operator Subset Criteria, in Proceedings of The 32nd International Conference on Automated Planning and Scheduling (ICAPS), Virtual, 2022.
- S. Sievers, M. Katz, S. Sohrabi, H. Samulowitz, P. Ferber, Deep learning for cost-optimal planning: Task-dependent planner selection, in Proceedings of The 33rd AAAI Conference on Artificial Intelligence (AAAI), Honolulu, HI, USA, 2019.
- D. Speck, M. Katz, Symbolic Search for Oversubscription Planning, in Proceedings of The 35th AAAI Conference on Artificial Intelligence (AAAI), Virtual, 2021.
- M. Katz, E. Keyder, A* Search and Bound-Sensitive Heuristics for Oversubscription Planning, in Proceedings of The 36th AAAI Conference on Artificial Intelligence (AAAI), Virtual, 2022.
- M. Katz, P. Ram, S. Sohrabi, O. Udrea, Exploring Context-Free Languages via Planning: The Case for Automating Machine Learning, in Proceedings of The 30th International Conference on Automated Planning and Scheduling (ICAPS), Nancy, France, 2020.
- J. Lee, M. Katz, D. J. Agravante, M. Liu, T. Klinger, M. Campbell, S. Sohrabi and G. Tesauro, AI Planning Annotation in Reinforcement Learning: Options and Beyond, in ICAPS 2021 Workshop on Bridging the Gap Between AI Planning and Reinforcement Learning (PRL), Virtual, 2021.
- M. Abdulhai, D. K. Kim, M. Riemer, M. Liu, G. Tesauro, J. P. How. Context-specific representation abstraction for deep option learning, In Proc. of The 36th AAAI Conference on Artificial Intelligence (AAAI), 2022
- D.K. Kim, M. Liu, M. Riemer, C.C. Sun, M. Abdulhai, G. Habibi, S. Lopez-Cot, G. Tesauro, and J.P. How. Learning Hierarchical Teaching Policies for Cooperative Agents., in Proc. of the 38th International Conference on Machine Learning (ICML), 2021
- D.K. Kim, M. Liu, S. Omidshafiei, S. Lopez-Cot, M. Riemer, G. Habibi, G. Tesauro, S. Mourad, M. Campbell and J.P. How. Learning Hierarchical Teaching Policies for Cooperative Agents. in Proc. of The 19th International Conference on Autonomous Agents and Multiagent Systems:(AAMAS), 2020
- M. Riemer, I. Cases, C. Rosenbaum, M. Liu, and G. Tesauro. On the Role of Weights Sharing. In Proc. of The 34th AAAI Conference on Artificial Intelligence (AAAI), 2020
- S. Omidshafiei, D.K. Kim, M. Liu, G. Tesauro, M. Riemer, C. Amato, M. Campbell, and J.P.How. Learning to Teach in Cooperative Multiagent Reinforcement Learning. in the Proc. of The 33th AAAI Conference on Artificial Intelligence (AAAI), 2021
- M. Riemer,M. Liu and G. Tesauro. Learning Abstract Options. In The Proc. of Neural Information Processing Systems (Neurips), 2018
- M. Liu, K. Sivakumar, S. Omidshafiei, C. Amato and J. P. How. Learning for Multi-robot Cooperation in Partially Observable Stochastic Environments with Macro-actions, IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 2017
- Crouse, M., Abdelaziz, I., Makni, B., Whitehead, S., Cornelio, C., Kapanipathi, P., Srinivas, K., Thost, V., Witbrock, M. and Fokoue, A., 2021, May. A deep reinforcement learning approach to first-order logic theorem proving. In Proceedings of the AAAI Conference on Artificial Intelligence.
- Abdelaziz, I., Crouse, M., Makni, B., Austel, V., Cornelio, C., Ikbal, S., Kapanipathi, P., Makondo, N., Srinivas, K., Witbrock, M. and Fokoue, A., 2022. Learning to guide a saturation-based theorem prover. IEEE Transactions on Pattern Analysis and Machine Intelligence.
- D. Kimura, M. Ono, S. Chaudhury, R. Kohita, A. Wachi, D. J. Agravante, M. Tatsubori, A. Munawar, A. Gray, Neuro-Symbolic Reinforcement Learning with First-Order Logic, in Proceedings of the Conference on Empirical Methods in Natural Language Processing (EMNLP), Online and Punta Cana, Dominican Republic, 2021
- Example “Open-World” Environments: Malmo Platform, Minerl, ProcGen, ScienceWorld, NetHack LE, Interactive Fiction Games, TextWorld Commonsense

## Day 2 Session 4: Neuro-Symbolic AI toolkit/Closing

### Agenda

**Neuro-symbolic AI Toolkit (Naweed Khan - IBM)**45 minutes- Logical Neural Networks (LNN)
- Universal Logic Knowledge Base (ULKB)
- Additional NSTK Components

**Closing**15 minutes- Badge, Feedback (Asim Munawar - IBM)
- Closing Remarks (Alexander Gray - IBM)

### Summary

In this final session, we conclude the summer school by reiterating the goals of Neuro-Symbolic AI and reflecting on how complex problems can be approached using various components that have been presented on throughout the event. IBM Research remains commited to open-source collaboration and upskilling, which is reflected in the release of the Neuro-Symbolic AI Toolkit and the Neuro-Symbolic AI Essentials Badge. We hope that you enjoyed the summer school and that you will reach out to the various authors on their respective work. Let’s create.