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CATEGORIES:Logic and Semantics Seminar (Computer Laboratory)
SUMMARY:Mixing finite and infinite structure - Michael Ben
edikt\, University of Oxford
DTSTART;TZID=Europe/London:20221010T160000
DTEND;TZID=Europe/London:20221010T170000
UID:TALK182999AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/182999
DESCRIPTION:A basic distinction between logic in databases and
“vanilla mathematical\nlogic” is that in the form
er quantifiers range over the objects that are\nst
ored in finite relations — stuff in the database\;
while in the latter\nwe quantify over the domain
of the model\, which can be infinite -- all\nstrin
gs\, all real numbers\, all integers\, etc. Once u
pon a time\,\nresearchers studied what happens whe
n you mix these two kinds of\nquantification withi
n the same logic. In the resulting formalism\,\n“e
mbedded finite model theory”\, you can\, for examp
le\, write a query\nasking whether there is a vec
tor of real numbers which satisfy certain\ninequal
ities with respect to all rows in a database table
.\n\nThe talk will revisit embedded finite model t
heory\, arguing that it’s\nrelevant to a number of
recent develpments in data management\, such as\n
performing linear algebra and ML tasks within a DB
MS. The talk focus\nwill be on new connections to
theoretical CS: spectrum problems\, bounds\nin dec
ision procedures\, and Ramsey theory.\n\nThere wil
l be some classical model theory in the lecture\,
but it should\nbe accessible to a theory-leaning C
S audience. The talk includes joint\nwork with Ehu
d Hrushovski and joint work with Anthony Lin.
LOCATION:SS03
CONTACT:Jamie Vicary
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