# Human Reasoning and Computational Logic

# Human Reasoning and Computational Logic

##### Course with SWS 2/2/0 (lecture/exercise/practical) in WS 2019

**Lecturer**

**SWS**

- 2/2/0

**Modules**

**Examination method**

- Oral exam

The slides are updated (31.1.2020).

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 lectures will take place on Wednesday, 4.DS (13:00 - 14:30) starting on 16.10.2019
- the tutorials will take place on Wednesday, 5.DS (14:50 - 16:20) starting on 23.10.2019

### Lecture Slides

The lecture slides can be found here and here. The manuscript can be found here.

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

- Human Reasoning and Abduction by Tobias Philipp (Bachelor thesis)
- Logic Programs and Three-Valued Consequence Operators by Carroline Dewi Puspa Kencana Ramli (Master thesis)

### Exercises

Old exercises can be found here.

- In the tutorials, we will discuss exercises that are written on the lecture slides or here:

- Syllogistic Reasoning Challenge

### Software

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

- http://olb.computational-logic.org/processing/svl.php
- SvL Operator with graphical user interface (edit the environment path of your computer to run swipl from command line)
- Prolog files

### Book draft

Here you can find a draft of the book that Steffen Hölldobler is writing about the topic of this course (the password for this PDF file is provided to participants of the course).The first part of the lecture is based on the following books:

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