2014/09/30 by Vilém Vychodil, Vilem Vychodil
Computer Science · Mathematics · #Algebra over a field #Artificial intelligence #Commutative property #Computer science #Data mining #Dependency theory (database theory) #Discrete mathematics #Functional dependency #Logic, Reasoning, and Knowledge #Mathematics #Programming language #Pure mathematics #Relational database #Residuated lattice #Rough Sets and Fuzzy Logic #Semantic Web and Ontologies #Semantics (computer science) #Theoretical computer science #acm:03B52 #acm:03G10 #acm:68P15 #cs.DB #msc:03B52 #msc:03G10 #msc:68P15
paper · pdf · doi:10.1016/j.jcss.2015.03.006
published as Journal of Computer and System Sciences 81(7) (2015) 1357-1372
openalex publication_date 2015/04/17 · arxiv created 2015/07/03 · arxiv updated 2015/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a complete logic for reasoning with functional dependencies (FDs) with semantics defined over classes of commutative integral partially ordered monoids and complete residuated lattices. The dependencies allow us to express stronger relationships between attribute values than the ordinary FDs. In our setting, the dependencies not only express that certain values are determined by others but also express that similar values of attributes imply similar values of other attributes. We show complete axiomatization using a system of Armstrong-like rules, comment on related computational issues, and the relational vs. propositional semantics of the dependencies.