Advanced applications of first-order logic. The logical structure of theories, including formal number theory. Proof of the completeness of first-order logic (everything provable in it is valid and everything valid in it is provable).

This paper is an introduction to non-classical logic, covering the basics of systems that go beyond "black and white" reasoning (eg modal, intuitionistic, relevant and many-valued logics). Philosophical issues are discussed alongside formal techniques.

Paper title Advanced Formal Logic PHIL312 Philosophy 0.1500 18 points Not offered in 2017 \$851.85 \$3,585.00
Prerequisite
PHIL 212 or PHIL 222 or PHIL 322
Schedule C
Arts and Music
Contact
zach.weber@otago.ac.nz
Teaching staff
Dr Zach Weber
Paper Structure
Two 1-hour lectures per week and one tutorial

Weekly lectures expand on the basic material covered in readings. After a review of classical logic, we use the method of semantic tableaux ('trees') and Kripke frames to study a range of logics in a unified way. Each logic is motivated by philosophical problems (eg the 'paradoxes of implication'), which challenge our intuitive notions of logical correctness. At a rate of approximately one logic per week, we examine modal logics (with and without 'impossible worlds'), intuitionistic, paraconsistent, paracomplete, relevant and fuzzy logic. The relationship between model structures and proofs is emphasised throughout.

Assessment:
• Weekly homework assignments 10%
• Two in-class tests 15% each
• Final exam 60%
Teaching Arrangements
Learning logic is like learning a foreign language - you have to practice! Weekly homeworks are announced in class at the start of the week and collected and discussed in tutorials. These are exercises to help you keep up with the material, which is cumulative.
Textbooks
Introduction to Non-Classical Logic by Graham Priest
Lifelong learning, Scholarship, Critical thinking, Information literacy, Research, Self-motivation.
Learning Outcomes
Students who successfully complete the paper will acquire
• A working knowledge of several non-classical logics, including the philosophical motivations for these logics
• Competence with checking the validity of arguments in different logics and constructing counterexamples to invalid arguments
• Demonstrated ability to work with abstract models and understand their relationship to data

## Timetable

### Not offered in 2017

Location
Dunedin
Teaching method
This paper is taught On Campus
Learning management system
None

Advanced applications of first-order logic. The logical structure of theories, including formal number theory. Proof of the completeness of first-order logic (everything provable in it is valid and everything valid in it is provable).

This paper is an introduction to non-classical logic, covering the basics of systems that go beyond "black and white" reasoning (e.g. modal, intuitionistic, relevant and many-valued logics). Philosophical issues are discussed alongside formal techniques.

Paper title Advanced Formal Logic PHIL312 Philosophy 0.1500 18 points Second Semester Tuition Fees for 2018 have not yet been set Tuition Fees for international students are elsewhere on this website.
Prerequisite
PHIL 212 or PHIL 222 or PHIL 322
Schedule C
Arts and Music
Eligibility
Pre-requisites may be waived on a case-by-case basis.
Contact
zach.weber@otago.ac.nz
Teaching staff
Dr Zach Weber
Paper Structure
Two 1-hour lectures per week and one tutorial

Weekly lectures expand on the basic material covered in readings. At a rate of approximately one topic per week, we examine modal logics, intuitionistic, paraconsistent, paracomplete, relevant and fuzzy logic. Each logic is motivated by philosophical problems, which challenge our intuitive notions of logical correctness. The relationship between model structures and proofs is emphasised throughout.

Assessment:
• Weekly homework assignments collected and discussed in tutorials
• Two in-class tests
• Final exam
Teaching Arrangements
Learning logic is like learning a foreign language - you have to practice! Weekly homeworks are announced in class at the start of the week and collected and discussed in tutorials. These are exercises to help you keep up with the material, which is cumulative.
Textbooks
Introduction to Non-Classical Logic by Graham Priest
Lifelong learning, Scholarship, Critical thinking, Self-motivation.
Learning Outcomes
Students who successfully complete the paper will acquire
• A working knowledge of several non-classical logics, including the philosophical motivations for these logics
• Competence with checking the validity of arguments in different logics and constructing counterexamples to invalid arguments
• Demonstrated ability to work with abstract models and understand their relationship to data

## Timetable

### Second Semester

Location
Dunedin
Teaching method
This paper is taught On Campus
Learning management system
None

#### Lecture

Stream Days Times Weeks
Attend
L1 Monday 10:00-10:50 28-34, 36-41
Tuesday 11:00-11:50 28-34, 36-41
Wednesday 14:00-14:50 28-34, 36-41