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PHL431Arts3 Unitsintermediate

Further Logic

This course, Further Logic, deepens learners' skills in formal proof of validity and sharpens their understanding of mathematical logic. It covers the logic of quantification, analyzing the internal structures of simple propositions, and symbolizing propositions with quantifiers. Students will learn quantification rules, predicate calculus, conditional and indirect proofs, proofs of invalidity, and truth tree analysis. The course also explores rule of inference in truth trees and the application of truth tree to first order logic.

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120h
Study Time
13
Weeks
9h
Per Week
intermediate
Math Level
Course Keywords
Quantificational LogicPredicate CalculusTruth Tree AnalysisFormal ProofSymbolization

Course Overview

Everything you need to know about this course

Course Difficulty

Intermediate Level
Builds on foundational knowledge
65%
intermediate
📊
Math Level
Moderate Math
📖
Learning Type
Theoretical Focus

Course Topics

Key areas covered in this course

1

Quantificational Logic

2

Symbolization

3

Relational Propositions

4

Properties of Relations

5

Formal Proof of Validity

6

Conditional Proof

7

Indirect Proof

8

Truth Tree Tests

9

Predicate Logic

Total Topics9 topics

Requirements

Knowledge and skills recommended for success

PHL301: Introduction to Logic

💡 Don't have all requirements? Don't worry! Many students successfully complete this course with basic preparation and dedication.

Assessment Methods

How your progress will be evaluated (3 methods)

Assignments

Comprehensive evaluation of course material understanding

Written Assessment

Tutor-Marked Assessments

Comprehensive evaluation of course material understanding

Written Assessment

Final Examination

Comprehensive evaluation of course material understanding

Written Assessment

Career Opportunities

Explore the career paths this course opens up for you

Logician

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Analyst

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Researcher

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Educator

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Critical Thinking Consultant

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Industry Applications

Real-world sectors where you can apply your knowledge

AcademiaResearch InstitutionsGovernmentConsultingArtificial Intelligence

Study Schedule Beta

A structured 13-week journey through the course content

Week
1

Module 1: Quantificational Logic

3h

Unit 1: Quantificational Logic

3 study hours
  • •Read the introduction to Quantificational Logic.
  • •Analyze simple propositions into subject and predicate terms.
  • •Practice obtaining propositions from propositional functions.
  • •Symbolize universal and particular propositions.
Week
2

Module 1: Quantificational Logic

3h

Unit 2: Symbolization in Quantificational Logic

3 study hours
  • •Study the techniques for symbolization in quantificational logic.
  • •Translate expressions into logical notation.
  • •Identify the scope of quantifiers.
  • •Differentiate between free and bound occurrences of variables.
Week
3

Module 1: Quantificational Logic

3h

Unit 3: Symbolizing Relational Propositions

3 study hours
  • •Learn to symbolize relational propositions.
  • •Analyze the internal structure of relational propositions.
  • •Understand the types of relationships between propositions.
  • •Practice using quantifiers in symbolizing relational propositions.
Week
4

Module 1: Quantificational Logic

3h

Unit 4: Properties of Relations

3 study hours
  • •Study the properties of relations: symmetrical, transitive, and reflexive.
  • •Symbolize various categories of relational properties.
  • •Distinguish between different types of relations.
  • •Practice symbolizing relational propositions with appropriate predicates and variables.
Week
5

Module 2: Formal Proof of Validity

3h

Unit 1: Formal Proof of Validity in Quantificational Logic

3 study hours
  • •Understand the rules of quantification.
  • •Recapitulate the rules of inference.
  • •Apply rules of quantification and inference.
  • •Construct formal proofs of validity for arguments in quantificational logic.
Week
6

Module 2: Formal Proof of Validity

3h

Unit 2: Conditional Proof

3 study hours
  • •Learn the method of conditional proof.
  • •Construct formal proofs of validity using conditional proof.
  • •Apply conditional proof in formal proof of validity.
  • •Understand the strengthened rule of conditional proof.
Week
7

Module 2: Formal Proof of Validity

3h

Unit 3: Indirect Proof

3 study hours
  • •Study the method of indirect proof.
  • •Construct formal proofs of validity using indirect proof.
  • •Apply indirect proof in formal proof of validity.
  • •Understand the rule of quantifier negation.
Week
8

Module 3: Truth-Tree Tests

3h

Unit 1: Truth-Tree Tests of Propositions

3 study hours
  • •Understand the general procedure for constructing truth trees.
  • •Learn about decomposition of propositions.
  • •Construct truth trees involving reduction of compound statements.
  • •Apply truth tree tests to determine consistency and contradiction.
Week
9

Module 3: Truth-Tree Tests

3h

Unit 2: Truth Tree Test of Validity in Propositional Logic

3 study hours
  • •Apply truth tree tests to determine consistency and contradiction.
  • •Practice testing groups of statements for consistency.
  • •Construct truth trees for various propositional logic arguments.
Week
10

Module 3: Truth-Tree Tests

3h

Unit 3: Proving Invalidity in Predicate Logic

3 study hours
  • •Learn to prove invalidity in predicate logic.
  • •Understand the rules governing proof of invalidity.
  • •Construct truth tree tests of invalidity in predicate logic.
  • •Practice applying truth tree method to test validity in Predicate Logic
Week
11

Module 2: Formal Proof of Validity

3h

Unit 1: Formal Proof of Validity in Quantificational Logic

3 study hours
  • •Review Formal Proof of Validity in Quantificational Logic
  • •Practice constructing formal proofs of validity for arguments in quantificational logic.
Week
12

Module 2: Formal Proof of Validity

3h

Unit 2: Conditional Proof

3 study hours
  • •Review Conditional Proof
  • •Practice constructing formal proofs of validity using conditional proof.
Week
13

Module 2: Formal Proof of Validity

3h

Unit 3: Indirect Proof

3 study hours
  • •Review Indirect Proof
  • •Practice constructing formal proofs of validity using indirect proof.

This study schedule is in beta and may not be accurate. Please use it as a guide and consult the course outline for the most accurate information.

Course PDF Material

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Study Tips & Exam Preparation

Expert tips to help you succeed in this course

1

Create detailed concept maps linking key concepts from each module.

2

Practice symbolization exercises from Units 1-4 weekly.

3

Work through all examples of formal proofs in Units 5-7, focusing on rule application.

4

Master truth tree construction techniques from Units 8-10, emphasizing strategic path selection.

5

Review all exercises from the course guide, focusing on areas of weakness.

6

Allocate specific time slots for focused study and practice each day.

7

Form study groups to discuss challenging concepts and practice problem-solving.

8

Prioritize understanding the underlying principles over memorization of rules.

9

Simulate exam conditions by completing practice questions within time limits.

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