Sylabus
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
Anotace
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.