Description
Aims:
The module aims to introduce and familiarise students with logical and mathematical inference. Students learn a number of logical inference methods for classical logics and for non-classical logics.
Intended learning outcomes:
On successful completion of the module, a student will be able to:
- Understand how axiomatic systems can be used for propositional and predicate logic.
- Understand the notions of soundness and completeness.
- Understand how propositional and predicate tableaus work.
- Have familiarity with other logics, including modal and temporal logics.
- Analyse algebras of relations.
Indicative content:Ìý
The following are indicative of the topics the module will typically cover:Ìý
Propositional logic, Predicate logic, Modal Logic and Temporal Logic:
- Review of syntax and semantics.
- Deduction and Inference.
- Truth tables.
- Decidability of propositional logic.
Mathematical proofs:
- Proof by contradiction.
- Induction and structured induction.
- Hilbert systems.
- Axioms and inference rules for propositional logic.
- Axioms and inference rules for predicate logic.
- Axioms and inference rules for modal and temporal logics.
- Tableau construction for propositional logic, predicate logic, modal logics.
- Soundness and completeness theorems for first order logic.
- Semi-decidability of first order logic.
- Undecidability of arithmetic.
Algebras of Relations:
- Algebras of binary relations
- Kleene Algebra
- Relation Algebra
- Other Algebras of Relations.
Requisites:
To be eligible to select this module as optional or elective, a student must: ​(1) be registered on a programme and year of study for which it is a formally available; (2) have taken Theory of Computation (COMP0003) and Algorithms (COMP0005); and (3) have some programming experience (as the assessment will require them to implement a program in C).
Module deliveries for 2024/25 academic year
Last updated
This module description was last updated on 19th August 2024.
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