Locality : A useful notion for proving inexpressibility in Finite Model Theory

This thesis discusses the notion of locality used in finite model theory to obtain results about the expressive power of first order logic. It turns out that the most commonly used Ehrenfeucht-Fraïssé games are also applicable over finite structures. However, we analyze with an example the need for simpler tools for finite structures due to the complex combinatorial arguments required while using EF-games. We argue that locality is such a tool, although the gap between games and locality is quite narrow as the latter is in fact based on the former. Intuitively speaking: locality of FO implies that in order to check the satisfiability of a FO formula over a finite structure, it is enough to look at a small portion of the universe (which will be called the neighborhood of a point). We discuss two commonly known notions of locality given by William Hanf and Haim Gaifman. We provide the original results of the authors and then their modified versions suitable for finite structures. We then show that first order logic over any relational vocabulary has both of these locality properties. In order to grasp the idea of locality we also include examples wherever required. Towards the end of the thesis we also discuss deficiencies and limitations of the two types of locality and possible solutions to overcome them. In the last section we also discuss locality of order-invariant first order formulas

A Van Benthem Theorem for Modal Team Semantics

The famous van Benthem theorem states that modal logic corresponds exactly to the fragment of first-order logic that is invariant under bisimulation. In this article we prove an exact analogue of this theorem in the framework of modal dependence logic MDL and team semantics. We show that modal team logic MTL, extending MDL by classical negation, captures exactly the FO-definable bisimulation invariant properties of Kripke structures and teams. We also compare the expressive power of MTL to most of the variants and extensions of MDL recently studied in the area

Quillen model categories-based notions of locality of logics over finite structures

Orientador: Marcelo Esteban ConiglioTese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciências HumanasResumo: No decorrer desta tese, eu desenvolvo um framework baseado em categorias modelo de Quillen para lidar com noções de localidade, em particular, Hanf/Gaifman localidadesAbstract: In the course of this thesis, I develop a framework based on Quillen model categories to deal with notions of locality, in particular, Hanf-locality and Gaifman-localityDoutoradoDoutor em Filosofia140719/2015-6CNP

Tilings and model theory

ISBN 978-5-94057-377-7International audienceIn this paper we emphasize the links between model theory and tilings. More precisely, after giving the definitions of what tilings are, we give a natural way to have an interpretation of the tiling rules in first order logics. This opens the way to map some model theoretical properties onto some properties of sets of tilings, or tilings themselves

Locality of Queries and Transformations

Locality is a standard notion of finite model theory. There are two well known flavors of it, based on Hanf’s and Gaifman’s theorems. Essentially they say that structures that locally look alike cannot be distinguished by first-order sentences. Very recently these standard notions have been generalized in two ways. The first extension makes the notion of “looking alike ” depend on logical indistinguishability, rather than isomorphism, of local neighborhoods. The second extension considers transformations defined by FO formulae, and requires that small neighborhoods be preserved by those transformations. In this survey we explain these new notions – as well as the standard ones – and show how they behave with respect to Hanf’s and Gaifman’s conditions