The computer itself was born from logic, and logic plays indispensable roles in diverse fields of science today, including computer science, mathematics, linguistics, philosophy and beyond. This course covers advanced issues in classical logic and elements of non-classical logic with emphasis on completeness proof methodologies for various logical systems; (in)completeness is the most fundamental issue in logic, elucidating the relationships between the syntax (proof theory) and semantics (model theory) of logical systems, or the correspondence between symbolic language and reality/worlds. Familiarity with elementary logic is assumed as well as general mathematical knowledge (such as sets, relations, quotients under equivalence relations).

Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

1. Understand classical and non-classical logical systems and their significance
2. Evaluate differences (advantages/disadvantages) of logical systems
3. Analyse the syntax and semantics of logics and their meta-theoretical properties
4. Apply translation principles for comparing different logical systems
5. Create mathematical proofs in the area of formal logic
6. Reflect on common logical systems and evaluate their limitations

Research-Led Teaching

Uniform techniques to prove properties of logical systems have been established through the development of mathematical logic and this course utilises them to study various properties of diverse logical systems.

Required Resources

The Open Logic Text by the Open Logic Project: https://builds.openlogicproject.org/open-logic-complete.pdf

Staff Feedback

Students will be given feedback in the following forms in this course:

• Written comments
• Verbal comments
• Feedback to the whole class, to groups, to individuals, focus groups

Student Feedback

ANU is committed to the demonstration of educational excellence and regularly seeks feedback from students. Students are encouraged to offer feedback directly to their Course Convener or through their College and Course representatives (if applicable). The feedback given in these surveys is anonymous and provides the Colleges, University Education Committee and Academic Board with opportunities to recognise excellent teaching, and opportunities for improvement. The Surveys and Evaluation website provides more information on student surveys at ANU and reports on the feedback provided on ANU courses.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	introduction, fundamental notions in logic, propositional logic, sequent calculus
2	maximally consistent set, propositional completeness proof, first-order logic
3	Henkin constants, first-order completeness proof, limitations
4	modal logic, maximal canonical model, completeness proof
5	filtration, finite model property, decidability
6	the relationships between first-order logic and modal logic, simple correspondence theory
7	intuitionistic logic, prime canonical model, completeness proof
8	disjunction property, the relationships between classical and intuitionistic logics
9	finite model property, the relationships between modal and intuitionistic logics
10	logic as computation, lambda calculus, product type, function type
11	Curry-Howard-Lambek correspondence between logic and computation, advanced proof theory
12	conclusion, reflection, and outlook

Assessment Summary

Assessment task	Value	Learning Outcomes
Assignment	50 %	LO 1,2,3,4,5,6
Final Exam	50 %	LO 1,2,3,4,5,6

* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details

Policies

ANU has educational policies, procedures and guidelines, which are designed to ensure that staff and students are aware of the University’s academic standards, and implement them. Students are expected to have read the Academic Misconduct Rule before the commencement of their course. Other key policies and guidelines include:

• Student Assessment (Coursework) Policy and Procedure
• Special Assessment Consideration Policy and General Information
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure

Assessment Requirements

The ANU is using Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. For additional information regarding Turnitin please visit the ANU Online website Students may choose not to submit assessment items through Turnitin. In this instance you will be required to submit, alongside the assessment item itself, hard copies of all references included in the assessment item.

Moderation of Assessment

Marks that are allocated during Semester are to be considered provisional until formalised by the College examiners meeting at the end of each Semester. If appropriate, some moderation of marks might be applied prior to final results being released.

Assessment Task 1

Assignment

Cover basic issues for each topic of the course. Amount to 50% of the entire evaluation. There will usually be two assignments, the first one covering the first half of the course, which is due at the end of the teaching break, and the second one covering the second half, which is due at the end of the last teaching week.

Assessment Task 2

Final Exam

Exam will be either oral or report exam (depending on the actual enrolled students). Amount to 50% of the entire evaluation. Assessment will be made with respect to technical and conceptual understanding of fundamental properties of logical systems and deeper understanding beyond them.

Academic Integrity

Academic integrity is a core part of our culture as a community of scholars. At its heart, academic integrity is about behaving ethically. This means that all members of the community commit to honest and responsible scholarly practice and to upholding these values with respect and fairness. The Australian National University commits to embedding the values of academic integrity in our teaching and learning. We ensure that all members of our community understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. The ANU expects staff and students to uphold high standards of academic integrity and act ethically and honestly, to ensure the quality and value of the qualification that you will graduate with. The University has policies and procedures in place to promote academic integrity and manage academic misconduct. Visit the following Academic honesty & plagiarism website for more information about academic integrity and what the ANU considers academic misconduct. The ANU offers a number of services to assist students with their assignments, examinations, and other learning activities. The Academic Skills and Learning Centre offers a number of workshops and seminars that you may find useful for your studies.

Online Submission

The ANU uses Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. While the use of Turnitin is not mandatory, the ANU highly recommends Turnitin is used by both teaching staff and students. For additional information regarding Turnitin please visit the ANU Online website.

Hardcopy Submission

For some forms of assessment (hand written assignments, art works, laboratory notes, etc.) hard copy submission is appropriate when approved by the Associate Dean (Education). Hard copy submissions must utilise the Assignment Cover Sheet. Please keep a copy of tasks completed for your records.

Late Submission

No submission of assessment tasks without an extension after the due date will be permitted. If an assessment task is not submitted by the due date, a mark of 0 will be awarded. OR Late submission of assessment tasks without an extension are penalised at the rate of 5% of the possible marks available per working day or part thereof. Late submission of assessment tasks is not accepted after 10 working days after the due date, or on or after the date specified in the course outline for the return of the assessment item. Late submission is not accepted for take-home examinations.

Referencing Requirements

Accepted academic practice for referencing sources that you use in presentations can be found via the links on the Wattle site, under the file named “ANU and College Policies, Program Information, Student Support Services and Assessment”. Alternatively, you can seek help through the Students Learning Development website.

Extensions and Penalties

Extensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure The Course Convener may grant extensions for assessment pieces that are not examinations or take-home examinations. If you need an extension, you must request an extension in writing on or before the due date. If you have documented and appropriate medical evidence that demonstrates you were not able to request an extension on or before the due date, you may be able to request it after the due date.

Privacy Notice

The ANU has made a number of third party, online, databases available for students to use. Use of each online database is conditional on student end users first agreeing to the database licensor’s terms of service and/or privacy policy. Students should read these carefully. In some cases student end users will be required to register an account with the database licensor and submit personal information, including their: first name; last name; ANU email address; and other information. In cases where student end users are asked to submit ‘content’ to a database, such as an assignment or short answers, the database licensor may only use the student’s ‘content’ in accordance with the terms of service — including any (copyright) licence the student grants to the database licensor. Any personal information or content a student submits may be stored by the licensor, potentially offshore, and will be used to process the database service in accordance with the licensors terms of service and/or privacy policy. If any student chooses not to agree to the database licensor’s terms of service or privacy policy, the student will not be able to access and use the database. In these circumstances students should contact their lecturer to enquire about alternative arrangements that are available.

Distribution of grades policy

Academic Quality Assurance Committee monitors the performance of students, including attrition, further study and employment rates and grade distribution, and College reports on quality assurance processes for assessment activities, including alignment with national and international disciplinary and interdisciplinary standards, as well as qualification type learning outcomes. Since first semester 1994, ANU uses a grading scale for all courses. This grading scale is used by all academic areas of the University.

Support for students

The University offers students support through several different services. You may contact the services listed below directly or seek advice from your Course Convener, Student Administrators, or your College and Course representatives (if applicable).

• ANU Health, safety & wellbeing for medical services, counselling, mental health and spiritual support
• ANU Diversity and inclusion for students with a disability or ongoing or chronic illness
• ANU Dean of Students for confidential, impartial advice and help to resolve problems between students and the academic or administrative areas of the University
• ANU Academic Skills and Learning Centre supports you make your own decisions about how you learn and manage your workload.
• ANU Counselling Centre promotes, supports and enhances mental health and wellbeing within the University student community.
• ANUSA supports and represents undergraduate and ANU College students
• PARSA supports and represents postgraduate and research students