
39Evidence and plausibility in neighborhood structuresAnnals of Pure and Applied Logic 165 (1): 106133. 2014.The intuitive notion of evidence has both semantic and syntactic features. In this paper, we develop an evidence logic for epistemic agents faced with possibly contradictory evidence from different sources. The logic is based on a neighborhood semantics, where a neighborhood N indicates that the agent has reason to believe that the true state of the world lies in N. Further notions of relative plausibility between worlds and beliefs based on the latter ordering are then defined in terms of this …Read more

11Complete Intuitionistic Temporal Logics for Topological DynamicsJournal of Symbolic Logic 87 (3): 9951022. 2022.The language of linear temporal logic can be interpreted on the class of dynamic topological systems, giving rise to the intuitionistic temporal logic ${\sf ITL}^{\sf c}_{\Diamond \forall }$, recently shown to be decidable by FernándezDuque. In this article we axiomatize this logic, some fragments, and prove completeness for several familiar spaces.

7Finiteness classes arising from Ramseytheoretic statements in set theory without choiceAnnals of Pure and Applied Logic 172 (6): 102961. 2021.

5Framevalidity Games and Lower Bounds on the Complexity of Modal AxiomsLogic Journal of the IGPL 30 (1): 155185. 2022.We introduce frameequivalence games tailored for reasoning about the size, modal depth, number of occurrences of symbols and number of different propositional variables of modal formulae defining a given frame property. Using these games, we prove lower bounds on the above measures for a number of wellknown modal axioms; what is more, for some of the axioms, we show that they are optimal among the formulae defining the respective class of frames.

5Nondeterministic semantics for dynamic topological logicAnnals of Pure and Applied Logic 157 (23): 110121. 2009.Dynamic Topological Logic () is a combination of , under its topological interpretation, and the temporal logic interpreted over the natural numbers. is used to reason about properties of dynamical systems based on topological spaces. Semantics are given by dynamic topological models, which are tuples , where is a topological space, f a function on X and V a truth valuation assigning subsets of X to propositional variables. Our main result is that the set of valid formulas of over spaces with co…Read more

1Taming the ‘Elsewhere’: On Expressivity of Topological LanguagesReview of Symbolic Logic 110. forthcoming.In topological modal logic, it is well known that the Cantor derivative is more expressive than the topological closure, and the ‘elsewhere’, or ‘difference’, operator is more expressive than the ‘somewhere’ operator. In 2014, Kudinov and Shehtman asked whether the combination of closure and elsewhere becomes strictly more expressive when adding the Cantor derivative. In this paper we give an affirmative answer: in fact, the Cantor derivative alone can define properties of topological spaces not…Read more

Hindman’s theorem in the hierarchy of choice principlesJournal of Mathematical Logic. forthcoming.In the context of [Formula: see text], we analyze a version of Hindman’s finite unions theorem on infinite sets, which normally requires the Axiom of Choice to be proved. We establish the implication relations between this statement and various classical weak choice principles, thus precisely locating the strength of the statement as a weak form of the [Formula: see text].