# Human Reasoning and Computational Logic

# Human Reasoning and Computational Logic

##### Course with SWS 2/2/0 (lecture/exercise/practical) in WS 2016

**Lecturer**

**SWS**

- 2/2/0

**Modules**

**Examination method**

- Oral exam

- There will be a workshop on Human Reasoning and Computational Logic on the 9th and 10th of February. You are welcome to come along!
- The slides from the last lecture and a draft version from the paper "A Core Method for the Weak Completion Semantics with Skeptical Abduction" are online!

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, 5.DS (14:50 - 16:20, starting on 12.10.2016)
- the tutorial will take place on Friday, delayed 4.DS (13:15 - 14:45, starting on 21.10.2016)

### Lecture Slides

The lecture slides can be found here (updated on 02.02.2017). the user name is *student* and the password will be given during the lecture.

### Exercises

- Exercise 1 (21.10.16)
- Exercise 2 (28.10.16)
- Exercise 3 (04.11.16)
- Exercise 4 (11.11.16)
- Exercise 5 (18.11.16)
- Exercise 6 (25.11.16)
- Exercise 7 (02.12.16)
- Exercise 8 (09.12.16)
- Exercise 9 (16.12.16)
- Exercise 10 (06.1.17)
- Exercise 11 (03.2.17)

### 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

### Practical Assignment

- Assignment
- Java implementation of Syllogistic Reasoning Task
- The original paper with the participants conclusions about the 64 syllogistic premises can be found here (pp. 22-23)

### 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