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The Syllabus gives an overview of what is covered in this course and outlines the assessment procedure if you wish to receive a statement of accomplishment.

Subject Aims

The overall aim of this course is to provide an introduction to modern propositional logic and its applications to Electronic Engineering, Philosophy, Linguistics, and Computer Science.

Subject Objectives

Upon successful completion of this course, you should be accomplished in core techniques of propositional logic, including

• Use formulas in the language of propositional logic to represent and analyse propositional logical structure.
• Translate natural language sentences into formulas of propositional logic; esp. varieties of implication: if, only if, unless, etc.
• Use truth tables to analyse formulas and collections of formulas, including to determine whether a formula is a tautology, a contradiction, a contingency, and to determine whether or not formulas are related by logical consequence or logical equivalence, or whether they are contradictory, contraries or subcontraries
• Use a proof tree to determine validity of argument form, or the status of formula.
• Understand the soundness and completeness of the tree proof method.

You should also have a number of skills in the interpretation and application of propositional logic, from among these:

• Use propositional logic to specify, analyse and simplify combinational digital systems.
• Understand a range of different ways to either interpret or revise two-valued classical logic in the presence of vagueness and borderline cases.
• Detect the difference between implicature and implication, and understand the way that implicatures are developed in co-operative dialogue.
• Apply propositional logic techniques in the representation of databases, and become skilled in the application of resolution proof techniques and the representation of databases in the logic programming language, Prolog.

Course outline

• Week 1 (Starting February 24, 2015), §1: Language and Models of Propositional Logic (Core)

This section covers the syntax and truth tables for propositional logic. You will learn how to distinguish sentences that express propositions from those that don't, translate in and out of the language of propositional logic, and use truth tables to analyse propositions.

Assessments for this section are due on Midnight 30th March PDT.

• Week 2 (Starting March 3, 2015), §2: Proof Trees for Propositional Logic (Core)

This section covers the use of truth trees to analyse propositions, including using proof trees to determine truth evaluations, and to detect satisfiability or unsatisfiability.

Assessments for this section are due on Midnight 30th March PDT.

• Week 3-5 (Starting March 10, 2015), §3-6: Applications of Propositional Logic

Assessments for the application section are due on Midnight 6th April PDT.

You will choose from among the following application areas:

§3: Combinational Digital Systems (Electronic Engineering)

This section covers the representation, analysis and simplification of combinational digital systems. We will use the K-map technique to find ways to simplify circuits.

§4: Vagueness (Philosophy)

This section covers the analysis of vagueness, including the sorties paradox, and responses to the paradox, including the development of fuzzy logic (Lukasiewicz's three valued logic and infinitely valued logic), and classical two-valued responses to vagueness, including supervaluations and epistemicism.

§5: Implication and Implicature (Linguistics)

This section covers the distinction between entailment and implicature, and introduces Grice's analysis of implicature, understood as arising out of cooperative conversation. You will learn how to identify different maxims used in the generation of implicatures.

§6: Propositional Logic Programming (Computer Science)

This section covers the representation of propositional information in databases, Horn clauses and the logic programming language, Prolog. You will learn how Prolog applies the proof technique of resolution in the querying of digital databases.

Course assessments

The 100% of your final score will be made up from

• Two Graded Core Quizzes (20% each), for Week 1 and Week 2. These are due on Midnight 30th March PDT.
• You can complete work from any of the topic areas—Electronic Engineering; Philosophy; Linguistics and Computer Science. Each has assessment to the value of 20%, and you can choose as few or as many as you would like to complete. We suggest trying at least two.
  • In Computer Science, and in Engineering, the assessment is a Graded Quiz (20%).
  • In Philosophy, and in Linguistics, the assessment is a Graded Quiz (10%) and a Peer Assessment Task (10%).
• You are awarded the grades from your best two Application areas, plus a half of any extra Application areas you complete, to make up 40% of your final score. (For example, if you complete three application areas, with a score of 18, 12 and 10 each, your total score will be 35.)
• All Application Area Assessments (Quizzes or Peer Assessment writing tasks) are to be submitted by Midnight 6th April PDT.
• A Final Exam Peer Assessment Task (20%), due on Midnight 8th April PDT.
• All Peer grading must be completed by Midnight 13th April PDT.

To receive a certificate in the course, you need achieve a score of at least 50% in your total assessment. To receive a certificate with distinction, you need to achieve a score of at least 70%.