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Modal Logic Notes

https://www.youtube.com/watch?v=sW0SQA386p0 "A Quick Introduction to Modal Logic, part 1" by eric pacuit.

History at 1:17:

Mathematical Modal Logic: a View of its Evolution. Robert Goldblatt. Centre for Logic, Language and Computation. Victoria University, P. O. Box 600, Wellington, New Zealand.

http://homepages.mcs.vuw.ac.nz/~rob/papers/modalhist.pdf

p26: Prior conceived the idea of using a logical system with temporal operators analogous to those of modal logic

p39: the algebraic study by Robert Bull, a student of Arthur Prior,38 of logics characterised by linearly ordered structures. Prior had observed that the Diodorean temporal reading of ✷α as “α is and always will be true” leads, on intuitive grounds, to a logic that includes S4 but not S5. ... In effect he was dealing with the complex closure algebra Cm(ω, ≤), where ω = {0, 1, 2, . . .} is the set of natural numbers viewed as a sequence of moments of time ... Prior called this logic D.


✷(p → q) → (✷p → ✷q) ---- where ✷ is necessity (or box)

S5 false for my temporal logic: S5 is S1 plus ✸p => ✷✸p (diamond p implies box diamond p)


https://www.researchgate.net/publication/228965141_The_Search_for_the_Diodorean_Frame by Roberto Ciuni


U+25C7 WHITE DIAMOND (U+25C7) ( ◇ ) #9671

U+25A2 WHITE SQUARE WITH ROUNDED CORNERS (U+25A2) ( ▢ ) #9634

'WHITE MEDIUM SQUARE' (U+25FB) ( ◻ ) #9723

U+25EF LARGE CIRCLE (U+25EF) ( ◯ ) #9711

U+25CB WHITE CIRCLE (U+25CB) ( ○ ) #9675

U+26AA MEDIUM WHITE CIRLE ( ⚪ ) #9898

U+2192 RIGHTWARD ARROW ( → ) #8594

LOGICAL AND ( ∧ ) #8743

LOGICAL OR ( ∨ ) #8744

'NOT SIGN' (U+00AC) ( ¬ ) #172

▢(⚪R → ◇R)

◻(T = ¬F)

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