We prove that the class of all languages that are definable in 11(FO2), that is, in (non-monadic) existential second-order logic with only two first-order variables, coincides with the regular languages. This provides an alternative logical description of regularity to both the traditional one in terms of monadic second-order logic, due to Büchi and Trakhtenbrot, and the more recent ones in ter...

We consider the problem of extending any two-variable mean M(·, ·) to a multi-variable mean, using no other tool than M(·, ·) itself. Pálfia proposed an iterative procedure that consists in evaluating successively two-variable means according to a cyclic pattern. We propose here a variant of his procedure to improve the convergence speed. Our approach consists in re-ordering the iterates after ...

In [14], we studied the computational behaviour of various first-order and modal languages interpreted in metric or weaker distance spaces. [13] gave an axiomatisation of an expressive and decidable metric logic. The main result of this paper is in showing that the technique of representing metric spaces by means of Kripke frames can be extended to cover the modal (hybrid) language that is expr...

We study the class of languages of finitely-labelled countable linear orderings definable in twovariable first-order logic. We give a number of characterisations, in particular an algebraic one in terms of circle monoids, using equations. This generalises the corresponding characterisation, namely variety DA, over finite words to the countable case. A corollary is that the membership in this cl...

We introduce a modal language L which is obtained from standard modal logic by adding the diierence operator and modal operators interpreted by boolean combinations and the converse of accessibility relations. It is proved that L has the same expressive power as the two-variable fragment F O 2 of rst-order logic but speaks less succinctly about relational structures: if the number of relations ...

This paper presents a tableau approach for deciding description logics outside the scope of OWL DL/1.1 and current state-of-the-art tableau-based description logic systems. In particular, we de ne a sound and complete tableau calculus for the description logic ALBO and show that it provides a basis for decision procedures for this logic and numerous other description logics with full role negat...