https://www.dagstuhl.de/19361

### 01. – 06. September 2019, Dagstuhl-Seminar 19361

# Logic and Learning

## Organisatoren

Michael Benedikt (University of Oxford, GB)

Kristian Kersting (TU Darmstadt, DE)

Phokion G. Kolaitis (University of California – Santa Cruz & IBM Almaden Research Center – San Jose, US)

Daniel Neider (MPI-SWS – Kaiserslautern, DE)

## Auskunft zu diesem Dagstuhl-Seminar erteilt

## Dokumente

Dagstuhl Report, Volume 9, Issue 9

Motivationstext

Teilnehmerliste

Gemeinsame Dokumente

Dagstuhl's Impact: Dokumente verfügbar

Programm des Dagstuhl-Seminars [pdf]

## Summary

### Motivation

Logic and learning are central to Computer Science, and in particular to AI research and allied areas. Alan Turing envisioned, in his paper "Computing Machinery and Intelligence" [1], a combination of statistical (*ab initio*) machine learning and an "unemotional" symbolic language such as logic. However, currently, the interaction between research in logic and research in learning is far too limited; in fact, they are often perceived as being completely distinct or even opposing approaches.

While there has been interest in using machine learning methods within many application areas of logic, the investigation of these interactions has usually been carried out within the confines of a single problem area. We believe that an interaction involving a broader perspective is needed. It would be fruitful to look for common techniques in applying learning to logic-related tasks, which requires looking across a wide spectrum of applications. It is also important to consider the ways that logic and learning, deduction and induction, can work together.

### Design of the Seminar

The main aim of this Dagstuhl Seminar was to address the above problems by bring researchers from the logic and learning communities together and to create bridges between the two fields via the exchange of ideas ranging between the (seemingly) polar possibilities of the injection of declarative methods in machine learning and the use and applications of learning technologies in logical contexts. This included creating an understanding of the work in different applications, an increased understanding of the formal connections between these applications, and the development of a more unified view of the current attempts to organically reconcile deductive and inductive approaches. In order to structure these explorations, the focal points of the seminar were the following three distinct strands of interaction between logic and learning:

*Machine Learning for Logic*, including the learning of logical artifacts, such as formulas, logic programs, database queries and integrity constraints, as well as the application of learning to tune deductive systems.*Logic for Machine Learning*, including the role of logics in delineating the boundary between tractable and intractable learning problems, the construction of formalisms that allow learning systems to take advantage of specified logical rules, and the use of logic as a declarative framework for expressing machine learning constructs.-
*Logic vs. Machine Learning*, including the study of problems that can be solved using either logic-based techniques or via machine learning, an exploration of the trade-offs between these techniques, and the development of benchmarks for comparing these methods.

### Summary of seminar activities

The seminar was attended by 41 researchers across various communities including logic, databases, Inductive Logic Programming (ILP), formal verification, machine learning, deep learning, and theorem proving. The membership consisted of senior and junior researchers, including graduate students, post-doctoral researchers, and industry experts. The seminar was conducted through talks and breakout sessions, with breaks for discussion between the attendees. There were three long talks, 21 short talks, and three breakout sessions on the discussion of open problems in logic and learning.

The talks consisted of: (i) presentation of recent advances in research questions and methodologies relating to the motivations discussed above; (ii) surveys of the state of research on various problems requiring the combination of deductive and inductive reasoning as well as methodologies developed to address fundamental hurdles in this space; (iii) new perspectives on the organic combination of logical formulations and methods with machine learning in specific application domains; (iv) theoretical formulations and results on problems in learning logical representations; (v) demonstrations of state-of-the art tools combining logic and learning for applications such as theorem proving or entity resolution; (vi) presentation of research on challenge problems for the field of AI and intelligent reasoning.

The breakout sessions were conducted in three continuing parts, each spanning one session. The first part involved all the participants in a discussion of the current (small and large) open problems in AI, challenge problems for the field of intelligent systems, and research questions about defining specific goals representing a successful combination of inductive and deductive reasoning. This involved a deliberation of what problems were relevant, which problems could be potentially related to or dependent upon each other, and various suggestions to formalise commonly desired research goals. This session resulted in the choice of three broad areas for further specific discussion: (i) Explainable AI (ii) Injecting symbolic knowledge or constraints into neural networks, and (iii) Learning of logical formulae (first-order logic) from satisfaction on structures in a differentiable manner. The second part consisted of parallel thematic sessions on these three areas. Each thematic session was conducted in the form of a round-table discussion and was led by one or two participants who championed the theme. The third session brought all the participants together again to conclude with a summary of the ideas exchanged during the parallel sessions.

### Conclusion

We consider the seminar a success. There is a growing need to enable the disparate communities of logic and learning to interact with each other, and we noted from the seminar that researchers from each community appreciated the perspective offered by the other, often identified techniques used by the other community that could be imported into their own, and, interestingly, were in agreement about the relevant and important problems of the day. The format of the seminar including ample time for discussions and breakout sessions received positive feedback from the participants.

### References

- A. M. Turing, “Computing machinery and intelligence”, Mind, vol. LIX, pp. 433–460, October 1950

**Summary text license**

Creative Commons BY 3.0 Unported license

Michael Benedikt, Kristian Kersting, Phokion G. Kolaitis, Adithya Murali, and Daniel Neider

## Classification

- Artificial Intelligence / Robotics
- Data Bases / Information Retrieval
- Verification / Logic

## Keywords

- Machine learning
- Logic
- Databases
- Verification
- Computational complexity