Ideas from 'Modal Logic' by Max J. Cresswell [2001], by Theme Structure

[found in 'Blackwell Guide to Philosophical Logic' (ed/tr Goble,Lou) [Blackwell 2001,0-631-20693-0]].

Click on the Idea Number for the full details    |     back to texts     |     expand these ideas


4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / b. System K
Normal system K has five axioms and rules
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / c. System D
D is valid on every serial frame, but not where there are dead ends
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4
S4 has 14 modalities, and always reduces to a maximum of three modal operators
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
In S5 all the long complex modalities reduce to just three, and their negations
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
Reject the Barcan if quantifiers are confined to worlds, and different things exist in other worlds
8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
A relation is 'Euclidean' if aRb and aRc imply bRc
10. Modality / A. Necessity / 4. De re / De dicto modality
A de dicto necessity is true in all worlds, but not necessarily of the same thing in each world