Nature and mysterium towards culture : César Manrique on the idea of artistic creativity

The article refers to the issues surrounding ideas of art and the creativity in arts. I intend to illustrate such concerns by drawing on the example of the works of César Manrique. The following samples of his work show that the relationship between man and nature can reveal the problem of artistic creativity in a new cultural perspective. This article was written in scientific cooperation with the César Manrique. Foundation (Lanzarote, Canary Islands) and is part of a research project conducted by the author and Mr. Wojciech Rubiś

Finite Satisfiability of the Two-Variable Guarded Fragment with Transitive Guards and Related Variants

We consider extensions of the two-variable guarded fragment, GF2, where distinguished binary predicates that occur only in guards are required to be interpreted in a special way (as transitive relations, equivalence relations, pre-orders or partial orders). We prove that the only fragment that retains the finite (exponential) model property is GF2 with equivalence guards without equality. For remaining fragments we show that the size of a minimal finite model is at most doubly exponential. To obtain the result we invent a strategy of building finite models that are formed from a number of multidimensional grids placed over a cylindrical surface. The construction yields a 2NExpTime-upper bound on the complexity of the finite satisfiability problem for these fragments. We improve the bounds and obtain optimal ones for all the fragments considered, in particular NExpTime for GF2 with equivalence guards, and 2ExpTime for GF2 with transitive guards. To obtain our results we essentially use some results from integer programming.Comment: Accepted for ACM TOC