Boolean dependence logic and partially-ordered connectives

Abstract

We introduce a new variant of dependence logic (D) called Boolean dependence logic (BD). In BD dependence atoms are of the type =(x 1 , . . . , x n , α), where α is a Boolean variable. Intuitively, with Boolean dependence atoms one can express quantification of relations, while standard dependence atoms express quantification over functions.We compare the expressive power of BD to D and first-order logic enriched by partially-ordered connectives, F O(POC). We show that the expressive power of BD and D coincide. We define natural syntactic fragments of BD and show that they coincide with the corresponding fragments of F O(POC) with respect to expressive power. We then show that the fragments form a strict hierarchy.

Inteligência artificial aplicada às ciências florestais e agricultura

“…A maioria das pessoas, na época, julgou que isso não tinha utilidade, motivo pelo qual a lógica booleana permaneceu na obscuridade por algum tempo. Tal lógica foi "redescoberta" e, juntamente com os circuitos integrados, trouxe à luz os microprocessadores e os computadores (BALBIANI;TINCHEV, 2010;EBBING et al, 2017;SCELLS et al, 2020).…”