# Justification Logic (JL)

- Tuesday from 09:15 to 12:00

### Description:

Justification logics are closely related to modal logics and can be viewed as a refinement of the later with machinery for justification manipulation. Justifications are represented directly in the language by terms that can be interpreted as formal proofs in a proof system, evidence for knowledge, winning strategy in a game, etc. This more expressive language proved beneficial in both proof theory and epistemology and helped investigate problems ranging from a provability semantics for intuitionistic logic to the logical omniscience problem. It has connections with intuitionistic logic, lambda calculus, epistemic logic, provability logic, and structural proof theory. Justification logic is a new and fast evolving field that offers unexpected results and insights into old problems. Its position at the junction of mathematics, philosophy, and computer science makes it of interest to a wide audience.

We plan to discuss the following topics:

- Relationship between modal and justification logic; justification extraction
- Formal semantics for representing justifications
- Quantitative approach to the logic omniscience problem
- Self referential proofs in modal logic
- Philosophical puzzles and paradoxes about knowledge (e.g. Gettier examples)
- Common knowledge and multi-agent systems

After this course, students will be able to:

- describe various model constructions for justification logics including modular models, fully explanatory models, and generated models
- establish decidability of justification logics
- describe complexity bounds for justification logic
- explain the connection between modal logic and justification logic
- apply justification logic to study philosophical puzzles and paradoxes about knowledge (e.g. Gettier examples)
- discuss the feasibility approach to the logical omniscience problem
- explain self-referentiality in the context of modal and justification logic