50009

Symbolic Reasoning

Module aims

This module covers the foundations of symbolic reasoning:  logic programming, answer set programming, and non-monotonic reasoning. It equips you with the practical skills necessary to use to solve real-world problems in symbolic artificial intelligence. It also provides the theoretical background for more advanced modules in these areas.    

Learning outcomes

Upon successful completion of this module you will be able to:
- explain the theoretical foundations of logic programming
- apply resolution as an inference system for logic programming
- encode problems using Answer Set Programming (ASP) and solve them using state-of-the-art ASP solvers 
- explain the main ideas behind non-monotonic reasoning 
- realise non-monotonic reasoning in different formal systems 
- encode problems using different modes of non-monotonic reasoning

Module syllabus

The module is divided into four parts:
1. Theoretical foundation of knowledge representation and reasoning in AI:
- Logic programming syntax 
- Definite logic programs semantics: herbrand models, minimal models,  immediate consequent operator
- Normal logic programs semantics: stratification, iterative fixed point, stable models, answer set semantics
2. Methods and approaches for knowledge-driven inference:
- Inference systems: SLD resolution and SLDNF resolution 
- Answer set programming: syntax, choice rules, aggregation, optimization statements, hard constraints and weak constraints     
3. Theoretical foundations of non-monotonic reasoning in AI: 
- monotonic vs non-monotonic reasoning 
- logic programming and answer set programming as non-monotonic reasoning 
- other formalisms for non-monotonic reasoning: abductive logic programming, default logic 
4. A unifying theory of non-monotonic reasoning: abstract argumentation frameworks 
- assumption-based argumentation 
- different semantics (stable, preferred, grounded) 
- instantiations in logic programming

Teaching methods

The material will be taught through lectures, backed up by formative exercises designed to reinforce the material as it is taught. Approximately one third of the timetabled activities will be dedicated to problem solving, using selected formative exercises as examples. Some of these will be in the form of small-group laboratory exercises, in order to encourage group discussions and group problem solving. These exercises wil reinforce the practical aspect of the material through application to real-word problems.

An online service will be used as a discussion forum for the module. 

Assessments

There will be two assessed coursework exercises that, combined, contribute 20% of the mark for the module. There will be a final written exam, which counts for the remaining 80% of the marks.

Detailed verbal feedback will be given on the exercises covered in the tutorial/lab sessions. Written feedback will be given on assessed work.

Reading list

Module leaders

Dr Dalal Alrajeh
Professor Francesca Toni