This course provides an introduction into modal logic, in particular epistemic logic (logics of knowledge), intuitionistic logics, many valued logics, including fuzzy logics. My part of the lecture focuses on First-order modal logic.
This course introduces three frameworks representative of these two research traditions: monadic deontic logic (MDL), dyadic deontic logic (DDL), and input/output (I/O) logic. We describe their language, semantics, and axiom systems and give soundness and completeness theorems. We also introduce students to some of the main topics discussed in deontic logic, including reasoning about norm violation and conflicts.
The course covers a wide array of topics regarding proof systems for classical first-order logic, including soundness and completeness proofs; elements of model theory Löwenheim-Skolem, compactness, expressibility); computational aspects of logic; undecidability of first-order logic and its consequences; etc.