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zpravodaj ČSKI - duben 2018 [ pdf ]
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datum: 25.4.2018 v 10:00
název: Abstract consequence relations I: from multiset consequence to a general picture
přednášející: Petr Cintula (UI)
místo konání: UI, 2.patro, místnost č.318

souhrn: We present a generalization of Blok-Jónsson theory of equivalence between structural consequence relation in such a way as to naturally accommodate multiset-based consequence relations as well.
While Blok and Jónsson admit, in place of sheer formulas, a wider range of syntactic units to be manipulated in deductions (including sequents and equations), these objects are invariably aggregated via set theoretical union. Our approach is more general in that non-idempotent forms of premises and conclusion aggregation, including multiset sum and fuzzy set union, are considered.
In the first part we focus on multiset consequence relation, present a natural general framework for their study, introduce basic syntactical and semantical notions and prove completeness.
In the second part we present an abstract categorical framework generalizing Galatos-Tsinakis take on Blok-Jónsson theory.