Preface
1 Modal Operators
1.1 A new language
1.2 Flavours of modality
1.3 The turnstile
1.4 Duality
1.5 A system of modal logic
2 Possible Worlds
2.1 The possible-worlds analysis of possibility and necessity
2.2 Models
2.3 Basic entailment and validity
2.4 Explorations in S5
2.5 Trees
3 Accessibility
3.1 Variable modality
3.2 The systems K and S5
3.3 Some other normal systems
3.4 Frames
3.5 More trees
4 Models and Proofs
4.1 Soundness and completeness
4.2 Soundness for trees
4.3 Completeness for trees
4.4 Soundness and completeness for axiomatic calculi
4.5 Loose ends
5 Epistemic Logic
5.1 Epistemic accessibility
5.2 The logic of knowledge
5.3 Multiple Agents
5.4 Knowledge, belief, and other modalities
6 Deontic Logic
6.1 Permission and obligation
6.2 Standard deontic logic
6.3 Norms and circumstances
6.4 Further challenges
6.5 Neighbourhood semantics
7 Temporal Logic
7.1 Reasoning about time
7.2 Temporal models
7.3 Logics of time
7.4 Branching time
7.5 Extending the language
8 Conditionals
8.1 Material conditionals
8.2 Strict conditionals
8.3 Variably strict conditionals
8.4 Restrictors
9 Towards Modal Predicate Logic
9.1 Predicate logic recap
9.2 Modal fragments of predicate logic
9.3 Predicate logic proofs
9.4 Modality de dicto and de re
9.5 Identity and descriptions
10 Semantics for Modal Predicate Logic
10.1 Constant domain semantics
10.2 Quantification and existence
10.3 Variable-domain semantics
10.4 Trans-world identity
11 Answers to the Exercises
1 Modal Operators
1.1 A new language
1.2 Flavours of modality
1.3 The turnstile
1.4 Duality
1.5 A system of modal logic
2 Possible Worlds
2.1 The possible-worlds analysis of possibility and necessity
2.2 Models
2.3 Basic entailment and validity
2.4 Explorations in S5
2.5 Trees
3 Accessibility
3.1 Variable modality
3.2 The systems K and S5
3.3 Some other normal systems
3.4 Frames
3.5 More trees
4 Models and Proofs
4.1 Soundness and completeness
4.2 Soundness for trees
4.3 Completeness for trees
4.4 Soundness and completeness for axiomatic calculi
4.5 Loose ends
5 Epistemic Logic
5.1 Epistemic accessibility
5.2 The logic of knowledge
5.3 Multiple Agents
5.4 Knowledge, belief, and other modalities
6 Deontic Logic
6.1 Permission and obligation
6.2 Standard deontic logic
6.3 Norms and circumstances
6.4 Further challenges
6.5 Neighbourhood semantics
7 Temporal Logic
7.1 Reasoning about time
7.2 Temporal models
7.3 Logics of time
7.4 Branching time
7.5 Extending the language
8 Conditionals
8.1 Material conditionals
8.2 Strict conditionals
8.3 Variably strict conditionals
8.4 Restrictors
9 Towards Modal Predicate Logic
9.1 Predicate logic recap
9.2 Modal fragments of predicate logic
9.3 Predicate logic proofs
9.4 Modality de dicto and de re
9.5 Identity and descriptions
10 Semantics for Modal Predicate Logic
10.1 Constant domain semantics
10.2 Quantification and existence
10.3 Variable-domain semantics
10.4 Trans-world identity
11 Answers to the Exercises