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Axiomatization of query equivalence and containment for several fragments of Core XPath 1.0 of Gottlob, Koch and Pichler: a somewhat unexpected use of modal and algebraic techniques. Full version of LiD paper, available only online. A journal version has been submitted and will appear on the website in due course

An outdated conference version of the paper. Journal version under preparation

If you are familiar with modal logic, you may expect that this is yet another paper on GL. Check if you're right!

An exercise in substructural logic, motivated partially by my earlier results in modal logic. We show that many varieties related to many-valued logics are not closed under any kind of completions - not just a specific one, like canonical completions. A significant part of the paper has been incorporated into this book. The original publication is available at Springer's website

The last and most advanced one in the series of papers based on or related to my PhD Thesis. It is also the one which attempts to put the whole research in a broader mathematical context. The theorem generalized here - Wim Blok's classfication of degrees of incompleteness of modal logics - is one of the most beautiful and surpring ones proved in the 1970's. If you have never heard about The Blok Theorem, or heard about it but want to learn more, enjoy! The original publication is available at Springer's website

An extension of a famous theorem by McKinsey and Tarski: topological completeness for hybrid logics. Should be developed into a larger work in future. Meanwhile, an important result for hybrid logic of the real line has been obtained by Andrey Kudinov. To the best of my knowledge, still unpublished

Tarski-style algebraization of a modal formalism equivalent to the bounded fragment of predicate logic. Cleaned some bugs and added a few comments. Page layout differs from the printed version

Previous title: "On the Gargov-Goranko Translation". The paper shows how to transfer a result on equivalent expressive power into a result on isomorphism between lattices of logics. If the AiML link for some reason does not work, try a local copy

The title adequately describes its content. The nice thing about this result is that usually low complexity results for a wide class of logics are shown with the help of polynomial finite model property. Our result covers numerous logics which do not have any Kripke frames or even any lattice-complete algebras; see the Blok theorem paper, the AiML 5 paper or the PhD Thesis for an explanation

The paper which laid the foundations for my PhD Thesis. Investigation of algebraically motivated notions generalizing standard Kripke completeness. The most interesting construction generalizes Yde Venema's result on varieties with no atomic algebras

The paper studies superintuitionistic version of the logic of chequered subsets introduced by Johan van Benthem, Guram Bezhanishvili and Mai Gehrke. In particular, the logic is compared with the famous system of Medvedev. The web version is slightly extended; in particular, the proof of main theorem is hopefully more readable. Very interesting follow-up results have been obtained by Gaelle Fontaine and Timofei Shatrov. The later is still unpublished, but claims to have settled negatively the issue of finite axiomatizably of Cheq!

This paper discusses the question to what extent incompleteness results over modal logic K4 can be generalized, in particular from algebraic point of view

The title adequately describes its content. Additional bonus is that the Shehtman's construction of the first incomplete superintuitionistic logic is described here in a perhaps less involved way than in the original paper