We study the expressibility problem: given a finite constraint language Γ on a finite domain and another relation R, can Γ express R? We prove, by an explicit family of examples, that the standard witnesses to expressibility and inexpressibility (gadgets/formulas/conjunctive queries and polymorphisms respectively) may be required to be exponentially larger than the instances. We also show that ...

In the present paper we consider a non-tabular extension L of the well-known propositional provability logic GL together with the notion of parametric expressibility of formulas in a logic proposed by A. V. Kuznetsov. We prove that there are infinitely many precomplete with respect to parametric expressibility classes of formulas in the above mentioned logic L.

This paper presents a syntax of approximate formulae suited for the logic with counting quantifiers SOLP. This logic was formalised by us in [1] where, among other properties, we showed the following facts: (i) In the presence of a built–in (linear) order, SOLP can describe NP–complete problems and some of its fragments capture the classes P and NL; (ii) weakening the ordering relation to an al...

In this paper we present a project on the expressibility of valued constraints. We recall the result of Cohen et al. [2] which characterises the expressibility of valued constraints in terms of algebraic properties of the constraints. We show why the current algebraic characterisation is rather unsatisfactory and what are the ways we try to explore in order to find a better one.

During the seventeenth century, several apparently very disparate reasons were advanced for a believing that there is an important distinction between primary and secondary qualities. The most prominent were (1) the overall explanatory success of a physical science which refers only to primary qualities (2) the mathematical expressibility of primary but not secondary qualities, and (3) the immu...

In the present paper we consider the simplest non-classical extension GL4 of the well-known propositional provability logic GL together with the notion of expressibility of formulas in a logic proposed by A. V. Kuznetsov. Conditions for expressibility of constants in GL4 are found out, which were first announced in a author’s paper in 1996.