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SUMMARY:Monadic modalities - Dima Szamozvancev
DTSTART:20190220T110000Z
DTEND:20190220T120000Z
UID:TALK120679@talks.cam.ac.uk
CONTACT:Nathanael Arkor
DESCRIPTION:Modal logic is an extension of classical propositional logic w
 ith operators that can let us express modes of truth: instead of only diff
 erentiating between true and false propositions\, we can talk about truth 
 depending on some notion such as time\, knowledge\, possibility\, etc. Unt
 il relatively recently\, modal logic was the domain of logicians and philo
 sophers (with a subfield\, temporal logic\, seeing wide use in formal veri
 fication since the late 1970s)\, but a series of developments starting wit
 h Moggi’s monadic metalanguage established its relevance in type theory\
 , category theory\, and other areas of theoretical and applied computer sc
 ience.\nThis talk introduces the axiomatic foundations of modal logic and 
 how the axioms give rise to different philosophical interpretations of mod
 al operators. We then develop the categorical semantics of S4 temporal mod
 al logic\, rediscovering many concepts that have been discussed in previou
 s talks\, and introducing new ideas specific to temporal modalities. Final
 ly\, we establish a nice connection between linear temporal logic and func
 tional reactive programming\, a declarative paradigm for programming inter
 active user interfaces.
LOCATION:Rainbow Room (FS07)\, Computer Laboratory
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