Modalities and Multimodalities

Modal logic and standard logic. Modal notions and quantifiers ; A non-modal basis for modal logics ; The semantical analysis of PC ; Constructive completeness of PC ; Decidability of PC ; Post-completeness and other properties of PC ; Exercises ; Further reading -- The syntax of normal modal systems. The relationship among modal operators ; Minimal properties of modal systems ; Systems between K and S5 ; Modalities in S5 ; Exercises ; Further reading -- The semantics of normal and modal systems. Matrices and Dugundji's theorem ; Carnapian models and relational models ; Correspondence theory and bisimulations ; The method of relational tableaux ; Exercises ; Further reading -- Completeness and canonicity. The constructive completeness of K and KT ; Completeness by Henkin's method ; Completeness : models versus frames ; The logic of arithmetical provability ; Exercises ; Further reading -- Incompleteness and finite models. An incompleteness result ; Finite model property and filtrations ; Exercises ; Further reading -- Temporal logics. Logics with two primitive modal operators ; Completeness and incompleteness of PF-logics ; Monomodal fragments of PF-logics ; Other temporal systems ; US-logics, metric tense logics and hybrid logics ; Exercises ; Further reading -- Epistemic logic : knowledge and belief. To know, to believe and their difficulties ; Knowledge, belief and agents ; The minimal logic of knowledge ; The systems Km, KTm, S4m, and S5m ; Common knowledge and implicit knowledge ; The logic of belief ; Exercises ; Further reading -- Multimodal logics. What are multimodalities? ; Multimodal languages ; The elementary multimodal systems ; Axioms for multimodal logics ; Multimodal systems and strict implication ; Multimodal models and completeness ; Exercises ; Further reading -- Towards quantified modal logic. Propositional quantifiers ; necessary and contingent identities ; The problem of completeness in first-order modal logic ; Inclusive domains and arbitrary domains ; Quantification and multimodalities ; Exercises ; Further reading.