General Theories of Logical Systems - ALGV19015

• Title: General Theories of Logical Systems
• Guaranteed by: Department of Logic (21-KLOG)
• Faculty: Faculty of Arts
• Actual: from 2023
• Semester: both
• Points: 4
• E-Credits: 4
• Examination process: oral
• Hours per week, examination: 2/0, Ex [HT]
• Capacity: winter:unknown / unknown (unknown); summer:unknown / unknown (unknown)
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: no
• State of the course: taught
• Language: English
• Teaching methods: full-time
• Teaching methods: full-time
• Note: course can be enrolled in outside the study plan; enabled for web enrollment; you can enroll for the course in winter and in summer semester
• Guarantor: Mgr. Marta Bílková, Ph.D.; Chun-Yu Lin
• Teacher(s): Chun-Yu Lin

Annotation

Last update: Chun-Yu Lin (07.02.2024)

Algebraic logic is a subfield of mathematical logic that explores logical systems through the lens of algebraic semantics. It primarily capitalize on the Linbenbaum-Tarski completeness theorem for classical logic, which demonstrates completeness with respect to the two-element Boolean algebra. This approach can be similarly applied to various logical systems, achieving completeness by correlating them with different types of algebraic structures. In this course, we will introduce basic algebraid logic and touch upon abstract algebraic logic (AAL) and Universal algebraic logic (UAL) in the end of the semester. We will demonstrate how algebraization serves as a general theory for logical systems.

Literature

Last update: Chun-Yu Lin (07.02.2024)

There are several references for this course :

• Tommaso Moraschini, ”The Algebra of Logic”, Lecture Note : https://moraschini.github.io/files/teaching/AL.pdf

• Hajnal Andr ́eka et al., Universal Algebraic Logic, Birkh ̈auser, 2022.

• Petr Cintula and Carles Noguera, Logic and Implication, Springer, 2021.

• Josep Maria Font, Ramon Jansana, and Don Pigozzi : A survey of Abstract Algebraic Logic, Studia Logica, 74(1-2):13-97, 2003.

Syllabus

Last update: Chun-Yu Lin (07.02.2024)

This course will cover the following topics :

• Basic notions of algebraic logic• Lindenbaum-Tarski Process 

• Abstract Algebraic Logic : Leibniz operator on arbitrary logics

• Leibniz hierarchy : Algebraizable/Equivalential/Protoalgebraic logic

• Bridge Theorem and Transfer Theorem

• Universal Algebraic Logic