eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-08-29
25:1
25:21
10.4230/LIPIcs.CSL.2018.25
article
Dependency Concepts up to Equivalence
Grädel, Erich
1
Hoelzel, Matthias
1
Mathematical Foundations of Computer Science, RWTH Aachen University, Aachen, Germany
Modern logics of dependence and independence are based on different variants of atomic dependency statements (such as dependence, exclusion, inclusion, or independence) and on team semantics: A formula is evaluated not with a single assignment of values to the free variables, but with a set of such assignments, called a team.
In this paper we explore logics of dependence and independence where the atomic dependency statements cannot distinguish elements up to equality, but only up to a given equivalence relation (which may model observational indistinguishabilities, for instance between states of a computational process or between values obtained in an experiment).
Our main goal is to analyse the power of such logics, by identifying equally expressive fragments of existential second-order logic or greatest fixed-point logic, with relations that are closed under the given equivalence. Using an adaptation of the Ehrenfeucht-Fraïssé method we further study conditions on the given equivalences under which these logics collapse to first-order logic, are equivalent to full existential second-order logic, or are strictly between first-order and existential second-order logic.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol119-csl2018/LIPIcs.CSL.2018.25/LIPIcs.CSL.2018.25.pdf
Logics of dependence and independence
Team semantics
Existential second-order logic
Observational equivalence
Expressive power