Complexity of the Universal Theory of Modal Algebras

Studia Logica - We apply the theory of partial algebras, following the approach developed by Van Alten (Theor Comput Sci 501:82–92, 2013), to the study of the computational...     

On Independent Axiomatizability of Quasi-Normal Modal Logics

Studia Logica - We give a negative solution to the problem, posed by A. Chagrov and M. Zakharyaschev, of whether every quasi-normal propositional modal logic can be axiomatized by an independent...     

A general method for proving decidability of intuitionistic modal logics

We generalise the result of [H. Ganzinger, C. Meyer, M. Veanes, The two-variable guarded fragment with transitive relations, in: Proc. 14th IEEE Symposium on Logic in Computer Science, IEEE Computer Society Press, 1999, pp. 24–34] on decidability of the two variable monadic guarded fragment of first order logic with constraints on the guard relations expressible in monadic second order logic. In [H. Ganzinger, C. Meyer, M. Veanes, The two-variable guarded fragment with transitive relations, in: Proc. 14th IEEE Symposium on Logic in Computer Science, IEEE Computer Society Press, 1999, pp. 24–34], such constraints apply to one relation at a time. We modify their proof to obtain decidability for constraints involving several relations. Now we can use this result to prove decidability of multi-modal modal logics where conditions on accessibility relations involve more than one relation. Our main application is intuitionistic modal logic, where the intuitionistic and modal accessibility relations usually interact in a non-trivial way.     

Correction to: Complexity of the Universal Theory of Modal Algebras

Studia Logica - In the original publication of the article, the authors name were abbreviated as “D. Shkatov” and “C. J. Van Alten”. However it should be “Dmitry...     

Undecidability of First-Order Modal and Intuitionistic Logics with Two Variables and One Monadic Predicate Letter

Studia Logica - We prove that the positive fragment of first-order intuitionistic logic in the language with two individual variables and a single monadic predicate letter, without functional...