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CATEGORIES:Logic &\; Semantics for Dummies
SUMMARY:Monadic modalities - Dima Szamozvancev
DTSTART;TZID=Europe/London:20190220T110000
DTEND;TZID=Europe/London:20190220T120000
UID:TALK120679AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/120679
DESCRIPTION:Modal logic is an extension of classical propositi
onal logic with operators that can let us express
modes of truth: instead of only differentiating be
tween true and false propositions\, we can talk ab
out truth depending on some notion such as time\,
knowledge\, possibility\, etc. Until relatively re
cently\, modal logic was the domain of logicians a
nd philosophers (with a subfield\, temporal logic\
, seeing wide use in formal verification since the
late 1970s)\, but a series of developments starti
ng with Moggi’s monadic metalanguage established i
ts relevance in type theory\, category theory\, an
d other areas of theoretical and applied computer
science.\nThis talk introduces the axiomatic found
ations of modal logic and how the axioms give rise
to different philosophical interpretations of mod
al operators. We then develop the categorical sema
ntics of S4 temporal modal logic\, rediscovering m
any concepts that have been discussed in previous
talks\, and introducing new ideas specific to temp
oral modalities. Finally\, we establish a nice con
nection between linear temporal logic and function
al reactive programming\, a declarative paradigm f
or programming interactive user interfaces.
LOCATION:Rainbow Room (FS07)\, Computer Laboratory
CONTACT:Nathanael Arkor
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