Undergraduate Course: Automated Reasoning (INFR09042)
|School||School of Informatics
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 9 (Year 3 Undergraduate)
||Availability||Available to all students
|Summary||The overall aim of the course is to describe how reasoning can be modelled using computers. Its more specific aim is to provide a route into more advanced uses of theorem proving in order to solve problems in mathematics and formal verification.
Major emphases are on: how knowledge can be represented using propositional, first-order and higher-order logic; how these representations can be used as the basis for reasoning, and how these reasoning processes can be guided to a successful conclusion through a variety of means ranging from fully-automated to interactive ones. Students will develop a thorough understanding of modern, interactive theorem proving via lectures and a practical assignment.
The course starts with an introduction to higher order logic, theorem provers and, more specifically, Isabelle/HOL. This will set the context for the rest of the course in which Isabelle will be the framework for getting hands-on experience about the application of various theoretical concepts.
Through the lectures and weekly exercises that incorporate practical aspects the students will gain the skills needed to get started with Isabelle and progress to more complex concepts involving both representation and reasoning.
The second part will look at representation/modelling of concepts in (higher order) logic in details. Axiomatic versus conservative extensions of theories will be covered and mechanisms such as Isabelle locales will be introduced and used. Recursive definitions and inductive notions will be covered too.
The third part of the course will focus on fundamental notions such as unification and rewriting, within both a first and higher order context. It will look at notions such as termination and use Isabelle's simplifier as the tool for understanding many of the concepts. It will also look at the interplay between (fully) automatic and interactive proofs.
The fourth part will introduce declarative/structured proofs and using the Isar language of Isabelle show how proofs resembling pencil and paper ones can be formalized.
Finally the various strands will be brought together through the discussion of a non-trivial case study.
This may involve either formalized mathematics (e.g. looking at a geometric theory) or a formal verification example.
The assignment will be a combination of basic to intermediate representation and reasoning in Isabelle (up to 40%), more advanced proof tackling one particular domain or example (up to 40%) and a final part which, if completed successfully, will clearly demonstrate that the student has a good grasp of the challenges that advanced interactive theorem proving entails.
Entry Requirements (not applicable to Visiting Students)
|| Students MUST have passed:
Informatics 2D - Reasoning and Agents (INFR08010)
||Other requirements|| This course is open to all Informatics students including those on joint degrees. External students should seek special permission from the course organiser. Prior familiarity with propositional and predicate logic is recommended.
Information for Visiting Students
|Pre-requisites||Prior familiarity with propositional and predicate logic is recommended.
|High Demand Course?
Course Delivery Information
|Academic year 2021/22, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
Lecture Hours 16,
Supervised Practical/Workshop/Studio Hours 16,
Feedback/Feedforward Hours 1,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
||The course will consist of 1 practical exercise (40%), assessing learning objectives 1 to 3. Students may be asked to represent and reason about particular domains e.g. geometry or inductive proofs in the Isabelle theorem prover. There will be a formative part to the assessment that will involve the students carrying out Natural Deduction proofs in Isabelle and receiving early feedback on their effort during lab sessions.
For the summative part, the students will submit their files, usually in the form of mechanized theories, electronically for marking.
The examination (60%) will concentrate on assessing learning outcomes 4 and 5, which mainly involve theoretical aspects (e.g. important algorithms and techniques), representation issues, problem solving (e.g. proofs using natural deduction) and discussing broader aspects such as the capabilities and limitations of various proof techniques.
This course is open to full year Visiting Students only, as the course is delivered in Semester 1 and examined at the end of Semester 2.
||The students will receive feedback on a weekly task via the mailing list/AR class forum and during the labs. The tasks will include both pen-and-paper and Isabelle-based exercises. Full solutions will be made available in Learn at the end of each week.
A marking guide, with extensive notes, will be released after the marks for the assignment have been returned. This will provide a breakdown of how marks were allocated, especially for the more challenging parts of the formalization. Common pitfalls will be highlighted and advice provided on how these should have been tackled.
The automated reasoning mailing list will be used (as is currently the case) to provide general feedback and any advice deemed appropriate during the course and before the exams.
||Hours & Minutes
|Main Exam Diet S2 (April/May)||3:00|
On completion of this course, the student will be able to:
- Use sophisticated mechanisms available in theorem provers to represent problem.
- Write interactive proof in procedural and declarative styles.
- Use interactive and automated methods to carry out proofs in the theorem prover.
- Represent and reason about mathematical and other less formal knowledge using logic.
- Understand and compare automated reasoning techniques and apply them using pen-and-paper.
|Recommended reading list:|
1. John Harrison. Handbook of Practical Logic and Automated Reasoning, CUP, 2009.
2. Tobias Nipkow and Gerwin Klein. Concrete Semantics with Isabelle/HOL, Springer, 2014.
3. T. Nipkow, L. C. Paulson, and M. Wenzel. Isabelle/HOL: A Proof Assistant for Higher- Order Logic , Springer, 2002.
4. M.Huth and M.Ryan. Logic in Computer Science, Modelling and and Reasoning about Systems, CUP, 2nd Edition, 2004.
The students will also be asked to read various papers and given links to presentations and
websites with materials pertaining to various theorem proving projects and repositories
(e.g. The Archive of Formal Proof).
|Graduate Attributes and Skills
|Keywords||Automated Reasoning,Theorem Proving,Formal proof
|Course organiser||Dr Jacques Fleuriot
Tel: (0131 6)50 9342
|Course secretary||Mrs Michelle Bain
Tel: (0131 6)51 7607