皆様、
FAU Erlangen-Nürnberg の Tadeusz Litak さんの講演のお知らせです。 ふるってご参加ください。
問い合わせ先： 佐野勝彦 北陸先端科学技術大学院大学 情報科学研究科 e-mail: v-sano@jaist.ac.jp
---------------------------------------------------------------------------------------------------- * JAIST Logic Seminar Series *
Date: Thursday, 18th September, 2014, 15:10-17:00
Place: JAIST Collaboration Room 6 (I57-g) (Access:http://www.jaist.ac.jp/english/location/access.html)
Speaker: Tadeusz Litak (Department Informatik, Technische Fakultät, FAU Erlangen-Nürnberg, Germany)
Title: Relational lattices
Abstract: We study an interpretation of lattice connectives as natural join and inner union between database relations with non-uniform headers. We show that this interpretation proposed by database experts (Vadim Tropashko from Oracle) yields a class of lattices which has not been considered in the existing lattice-theoretical literature. We discuss axiomatizability and decidability of their (quasi-)equational theory and propose an equational axiomatization for a corresponding abstract algebraic class. It turns out that addition of just the “header constant” to the lattice signature already allows mimicking the Maddux technique for cylindric algebras and encode the word problem for semigroups in the quasiequational theory. Relational lattices, however, are not as intangible as one may fear: for example, they do form a pseudoelementary class. We also apply the tools of Formal Concept Analysis and investigate standard contexts of relational lattices, obtaining, e.g., results on their subdirect irreducibility.
This is a joint work with Szabolcs Mikulas and Jan Hidders ----------------------------------------------------------------------------------------------------