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SUMMARY:Semiring Semantics: Algebraic Properties vs. Logical Results - Sop
 hie Brinke (RWTH Aachen)
DTSTART:20251010T130000Z
DTEND:20251010T140000Z
UID:TALK237619@talks.cam.ac.uk
CONTACT:Ioannis Markakis
DESCRIPTION:Semiring provenance was originally introduced in database theo
 ry with the aim of explaining why certain tuples are (not) contained in th
 e answer of a query — to explain their provenance. To this end\, logical
  statements are not just evaluated to true or false but by values from a c
 ommutative semiring. This allows us to track which combinations of atomic 
 facts are responsible for the truth of a statement and to derive practical
  information about costs\, access levels\, or confidence scores. Recently\
 , this approach has been expanded to a systematic study of semiring semant
 ics for first-order logic and other logical systems. This talk gives an ov
 erview of the recent results on the generalisation of model-theoretic prop
 erties and methods such as compactness\, Ehrenfeucht-Fraïssé games\, or 
 locality beyond the Boolean semiring. Many model-theoretic notions admit n
 atural generalisations to the semiring framework (e.g. entailments can be 
 understood as inequalities of semiring valuations) while even simple prope
 rties lead to surprisingly difficult questions that require new proof tech
 niques. It turns out that most of the classical logical results and method
 s can be generalised to some semirings but fail for others. We shall discu
 ss how this is related to algebraic properties of the underlying semirings
  such as idempotence and absorption.
LOCATION:SS03\, Computer Laboratory
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