# Human Reasoning and Computational Logic

# Human Reasoning and Computational Logic

##### Course with SWS 4/2/0 (lecture/exercise/practical) in WS 2017

**Lecturer**

**SWS**

- 4/2/0

**Modules**

**Examination method**

- Oral exam

- Note that all slides from the lecture are online now.

- There will be a workshop on Human Reasoning and Computational Logic from the 10th to the 12th of April. You are welcome to come along!

In the lecture *Human Reasoning and Computational Logic* we present a new cognitive theory — the weak completion semantics — for selected human reasoning tasks. The weak completion semantics is based on logic programs, the three-valued Łukasiewicz logic, an appropriate fixed point operator, abduction and revision. It can be mapped onto an artificial neural network based on the core method. The networks can be trained by (deep) learning.

The language of instruction is English. If, however, only German speaking students are in the lecture hall, then the language of instruction is German. The slides will be in English. The literature is usually in English.

Contents

1. Logic Programs

2. Three-valued Łukasiewicz Logic

3. Abduction and Revision

4. Relation to Stable Model Semantics and Well-Founded Semantics

5. Selected Human Reasoning Tasks: Suppression Task, Selection Task, Syllogisms, Belief Bias, Spatial Reasoning, Reasoning about Conditionals

6. Artificial Neural Networks

7. The Core Method

8. Learning

### Schedule

- the lecture and the tutorial will take place in room E05
- the lecture will take place on Wednesday, 3.DS (11:10 - 12:40, starting on 11.10.2017) and on Thursday, 5.DS (14:50 - 16:20)
- the tutorial will take place on Wednesday, delayed 4.DS (13:15 - 14:45, starting on 18.10.2017)

### Lecture Slides

The lecture slides can be found here (updated on 04.02.2018). the user name is *student* and the password will be given during the lecture.

You can find an overview paper on neural-symbolic learning and reasoning here.

### Exercises

During the tutorial we will only discuss your solutions to the exercises. That means that you are supposed to solve the exercises by yourself beforehand.

- Exercise 1 (18.10.17)
- Exercise 2 (25.10.17)
- Exercise 3 (1.11.17)
- Exercise 4 (8.11.17)
- Exercise 5 (29.11.17)
- Exercise 6 (6.12.17)
- Exercise 7 (20.12.17)

### Practical Assignment

You can find more information and ideas in the following papers:

M. Ragni, I. Kola, and P. Johnson-Laird. The wason selection task: A meta-analysis. In G. Gunzelmann, A. Howes, T. Tenbrink, and E. Davelaar, editors, Proceedings of the 39th Annual Conference of the Cognitive Science Society, (CogSci 2017), pages 980–985. Austin, TX: Cognitive Science Society, 2017

M. Ragni, E.-A. Dietz, I. Kola, and S. Hölldobler. Two-valued logic is not sufficient to model human reasoning, but three-valued logic is: A formal analysis. In C. Schon and U. Furbach, editors, Proceedings of the Workshop on Bridging the Gap between Human and Automated Reasoning co-located with 25th International Joint Conference on Artificial Intelligence (IJCAI 2016), New York, USA, vol. 1651 of CEUR Workshop Proceedings, pages 61–73. CEUR-WS.org, 2016

- 3 (Figure 1 and Figure 2)

P. Johnson-Laird and P. Wason. A theoretical analysis of insight into a reasoning task. 1:134–148, 05 1970.

### Software

To compute the least fixed point of the SvL operator, you can use the following implementations:

- SvL Operator with graphical user interface (edit the environment path of your computer to run swipl from command line)
- Prolog files

### Additional material

Most of the proofs discussed in the exercises can be found here:

Der erste Teil der Vorlesung basiert auf die folgenden Bücher:

S. Hölldober. Logik und Logikprogrammierung, volume 1: Grundlagen. Synchron Publishers GmbH, Heidelberg, 2009.

J. W. Lloyd. Foundations of Logic Programming. Springer-Verlag New York, Inc., New York, NY, USA, 1984.

S. Hölldober. Weak Completion Semantics and its Applications in Human Reasoning. In Claudia Schon Ulrich Furbach, editor, Proceedings of the Workshop on Bridging the Gap between Human and Automated Reasoning on the 25th International Conference on Automated Deduction (CADE-25), pages 2–16. CEUR-WS.org, 2015.

Pascal Hitzler, Steffen Hölldobler, Anthony Karel Seda, Logic programs and connectionist networks. Journal of Applied Logic, Volume 2, Issue 3, 2004, Pages 245-272