Dependency Concepts up to Equivalence
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.
Logics of dependence and independence
Team semantics
Existential second-order logic
Observational equivalence
Expressive power
Theory of computation~Logic
25:1-25:21
Regular Paper
Erich
Grädel
Erich Grädel
Mathematical Foundations of Computer Science, RWTH Aachen University, Aachen, Germany
This work has been initiated in a discussion between the first author and Jouko Väänänen during the Logical Structures in Computation Programme at the Simons Institute for Computing at UC Berkeley.
Matthias
Hoelzel
Matthias Hoelzel
Mathematical Foundations of Computer Science, RWTH Aachen University, Aachen, Germany
Supported by DFG.
10.4230/LIPIcs.CSL.2018.25
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Erich Grädel and Matthias Hoelzel
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