Students will be able to construct proofs in a system of propositional logic not studied on previous modules.
Students will be able to explain the distinction between primitive and derived rules of inference and prove, of derived rules, that they are derived.
Students will be able to explain the relationships between necessity, possibility, impossibility and contingency.
Students will be distinguish between the systems K, M, B, S4 and S5 and to construct proofs in these systems.
Students will be able to explain the working of the system of deontic logic D, an applied modal logic dealing with moral/legal obligation and permissibility and to construct proofs in D.
Students will be able to explain and employ concepts from model-theoretical semantics for modal logics.
Students will be able to explain the the relationships between various systems in terms of the properties of the accessibility relation.
Students will be able to assess sequents for validity in modal systems using trees, to construct counter-models for invalid sequents and to verify counter-models by appeal to model-theoretical considerations.
Students will be able to explain the features of various systems of quantified modal logic and their semantics, including distinguishing between differing approaches to quantified modal logic (e.g., QML based on free logic, QML based on classical logic, constant and varying domain semantics, objectual and non-objectual interpretations of the quantifiers).
Students will be able to construct proofs in natural deduction in various QMLs and to employ trees for QMLs.