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Mathematics, Applied
On semantically labelled syntax trees and the non-existence of certain Sahlqvist formulae
Petar Iliev
Summary: We discuss semantically labelled syntax trees as a means of proving the absence of modal formulas that satisfy specific syntactic properties and define a given class of frames. Using these trees, we demonstrate the existence of classes of Kripke frames that can be defined by both non-Sahlqvist and Sahlqvist formulas, with the latter requiring more propositional variables.
LOGIC JOURNAL OF THE IGPL (2023)
Article
Mathematics, Applied
Frame-validity games and lower bounds on the complexity of modal axioms
Philippe Balbiani et al.
Summary: We introduce frame-equivalence games that are designed 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. By using these games, we establish lower bounds on the aforementioned measures for several well-known modal axioms; moreover, for some of the axioms, we demonstrate their optimality among the formulae defining the respective class of frames.
LOGIC JOURNAL OF THE IGPL (2022)
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