We generalise the result of Ganzinger, Meyer and Veanes [14] 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 [14], 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 re...

We contribute to the question about decidability of firstorder logic on configuration graphs of collapsible pushdown automata. Our first result is decidability of existential FO sentences on configuration graphs (and their ε-closures) of collapsible pushdown automata of order 3, restricted to reachable configurations. Our second result is undecidability of whole first-order logic on configurati...

We study intransitive temporal logic implementing multiagent’s approach and formalizing knowledge and uncertainty. An innovative point here is usage of non-transitive linear time and multi-valued models the ones using separate valuations Vj for agent’s knowledge of facts and summarized (agreed) valuation together with rules for computation truth values for compound formulas. The basic mathemati...

We prove that the first-order theory of the one-step rewriting relation associated with a trace rewriting system is decidable and give a nonelementary lower bound for the complexity. The decidability extends known results on semi-Thue systems but our proofs use new methods; these new methods yield the decidability of local properties expressed in first-order logic augmented by modulo-counting q...

Justification logics are propositional modal-like logics that instead of statements A is known include statements of the form A is known for reason t where the term t can represent an informal justification for A or a formal proof of A. In our present work, we introduce model-theoretic tools, namely: filtrations and a certain form of generated submodels, in the context of justification logic in...