Modal Logic
Rationale
Modal logic is a prominent and useful branch of logic which should be taught systematically.
Course Description
Modal logic originated in the domain of Philosophy, but during the past decades became a vibrant area with fundamental applications in computer science, AI, mathematics, epistemology, etc. This course offers a systematic exposition of fundamentals of modal logic together with an adjacent area of constructive reasoning.
Learning Goals/Outcomes
Students are expected to

understand the concepts of logical language, models, deduction and decidability.

apply these concepts to a variety of modal logics and related systems,

learn a wide variety of applications of modal logics in computer science, AI, mathematics and epistemology,

become prepared to conduct research in modal logics and their applications.
Mastering the following theoretical concepts:

Constructive reasoning and its proof semantics.

Intuitinistic logic, proof systems and Kripke semantics.

Semantics of realizability and computational content of constructive reasoning.

Classical modal logic, its alethic, epistemic, deontic and temporal motivations.

Possible world semantics, frame conditions.

Temporal logics and verification.

Proof systems for modal logics, canonical models.

Epistemic logic, common knowledge.

Goedel embeddings of intuitionistic logic into classical modal logic.

Modal logics of provability and explicit proofs, justification logics,

Knowability paradox and its resolution in bimodal classical logic.

Constructive epistemic logic.
Assessment
There will be manageable homework assignments expected to be prepared on weekly basis. The subjects will be clustered in three groups according to the learning goals 13, each accounts for 30% of the final grade. The attendance and participation will account for 10% of the final grade. Those who don't score the top grades for the homework clusters, will be offered a comprehensive test at the end of the course.