Postgraduate Course: Automated Reasoning (Level 11) (INFR11074)
Course Outline
School  School of Informatics 
College  College of Science and Engineering 
Course type  Standard 
Availability  Not available to visiting students 
Credit level (Normal year taken)  SCQF Level 11 (Postgraduate) 
Credits  10 
Home subject area  Informatics 
Other subject area  None 
Course website 
http://www.inf.ed.ac.uk/teaching/courses/ar 
Taught in Gaelic?  No 
Course description  The overall aim of the module is to describe how reasoning can be automated. Its more specific aim is to provide a route into more advanced uses of theorem proving in automated reasoning and in solving challenging problems if mathematics. Major emphases are on: how knowledge can be represented using logic; how these representations can be used as the basis for reasoning and how these reasoning processes can be guided to a successful conclusion. Students are encouraged to develop a deep understanding of automated reasoning from mathematical "first principles" via theorem proving. 
Entry Requirements (not applicable to Visiting Students)
Prerequisites 

Corequisites  
Prohibited Combinations  Students MUST NOT also be taking
Automated Reasoning (Level 10) (INFR10041)

Other requirements  For Informatics PG and final year MInf students only, or by special permission of the School. This course assumes prior mathematical knowledge of induction.

Additional Costs  None 
Course Delivery Information

Delivery period: 2011/12 Semester 1, Not available to visiting students (SS1)

WebCT enabled: No 
Quota: None 
Location 
Activity 
Description 
Weeks 
Monday 
Tuesday 
Wednesday 
Thursday 
Friday 
No Classes have been defined for this Course 
First Class 
Week 1, Monday, 16:10  17:00, Zone: Central. Chrystal Mac Building Sem Rm 5 
Exam Information 
Exam Diet 
Paper Name 
Hours:Minutes 


Main Exam Diet S2 (April/May)   2:00   
Summary of Intended Learning Outcomes
1  represent mathematical and other knowledge using logic.
2  analyze the behaviour of various reasoning techniques from "first principles" as theorem provign tasks.
3  formalize informal knowledge and reason rigorously about it, understanding the role of mathematical proof in this process.
4  compare precisely the tradeoffs between some rival techniques for the same reasoning task.
5  implement key reasoning techniques in a computer program/theorem prover.
6  know how to use more sophisticated reasoning techniques implemented in a computer program/theorem prover.
7  organize their own study to manage project development.
8  search and read the literature.
9  conduct exploratory experiments.
10  critically analyze and evaluate other people's work.
11  be broadly uptodate with current research in the field
12  be uptodate in detail with at least one significant, specific aspect of current research in the field 
Assessment Information
Written Examination 75
Assessed Assignments 25
Oral Presentations 0
The course consists of 2 practical exercises. Students may be asked to reason about particular domains (e.g. geometry) in a theorem prover such as Isabelle or Coq. They may also be asked to verify a program using the SPIN model checker. This version of the course differs from the level 10 one in requiring students to undertake practical exercises demanding deeper analysis of the mathematical theory behind the computational mechanisms. Some aspects of the exercises are thus likely to be openended in nature and the students will be expected to analyze various issues to do with their formalization and/or implementation. 
Special Arrangements
None 
Additional Information
Academic description 
Not entered 
Syllabus 
The module combines an exposition of theory with the analysis of particular computer programs for reasoning. Topics will be selected from the following list:
# First Order Logic and Higher Order Logic
* Syntax
* HOL: Types and terms, currying and binders
* Unification algorithm
* Natural Deduction
# Model Checking
* Computation Tree Logic: syntax and semantics
* A model checking algorithm
* Model checker: SMV or SPIN
* Fairness
* Alternatives and extensions of CTL: LTL, CTL*
# Interactive Theorem Proving
* Humanoriented methods
* Interactive provers and proof checkers
* LCF style theorem proving
* Proof styles
* Formalized Mathematics
# Decidable Problems and Automation
* Presburger arithmetic
* Geometry theorem proving
* Induction and recursion
* Simplification, proof planning, and rippling
# Program Verification
* Functional programs
* Case studies e.g. sorting algorithms
Relevant QAA Computing Curriculum Sections: Artificial Intelligence 
Transferable skills 
Not entered 
Reading list 
* A. Bundy et al. Rippling: Metalevel Guidance for Mathematical Reasoning, Cambridge Tracts in Theoretical Computer Science (No. 56), 2005
* T. Nipkow, L. C. Paulson, and M. Wenzel. Isabelle/HOL: A Proof Assistant for HigherOrder Logic , SpringerVerlag, 2002
* M. R. A. Ruth and M. D. Ryan. Logic in Computer Science, Cambridge University Press, Second Edition, 2004.
* Y. Bertot and P. Casteran. Interactive Theorem Proving and Program Development: Coq'Art: the Calculus of Inductive Constructions, 2004.

Study Abroad 
Not entered 
Study Pattern 
Lectures 20
Tutorials 0
Timetabled Laboratories 0
Nontimetabled assessed assignments 30
Private Study/Other 50
Total 100 
Keywords  Not entered 
Contacts
Course organiser  Dr Michael Rovatsos
Tel: (0131 6)51 3263
Email: mrovatso@inf.ed.ac.uk 
Course secretary  Miss Kate Weston
Tel: (0131 6)50 2701
Email: Kate.Weston@ed.ac.uk 

