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METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20230421T134835Z
DTSTART:20230426T141500Z
DTEND:20230426T151500Z
SUMMARY:Luca Reggio (UCL)
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}h1ed-lgqlxe
u9-yddsbk
DESCRIPTION:Title: Logical resources and arboreal adjunctions\n\nAbstract
:\n\nI will give an overview of some recent work on applying categorical
methods in finite model theory and descriptive complexity.\n\nA key ide
a of a research program started by Abramsky\, Dawar et al. in 2017 is th
at various forms of model comparison game\, central to finite model theo
ry\, can be encoded as `game comonads'\, i.e. resource-indexed comonads
on the category of relational structures. For example\, the following in
gredients can be captured in a syntax-free way: Ehrenfeucht-Fraïssé game
s\, fragments of first-order logic with bounded quantifier rank\, and th
e combinatorial parameter of tree-depth. This approach covers also finit
e variable fragments\, modal and guarded fragments\, and more.\n\nThe pa
ttern of game comonads has been axiomatised at a general level in terms
of `arboreal adjunctions'\, i.e. adjunctions between an extensional cate
gory (typically\, in the examples\, a category of relational structures)
and a resource-indexed family of `arboreal categories'. If time allows\
, I will illustrate an application of this axiomatic framework to the st
udy of `equi-resource' homomorphism preservation theorems in model theor
y (exemplified by Rossman's equirank homomorphism preservation theorem)
and discuss recent work on identifying the expressive power of arboreal
adjunctions.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1 (and zoom\, link in email)\, Alan Turing Building\
, Manchester
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