6 papers · 1 filter
Elementary modal logics and circuit complexity
Tenyo Takahashi
A modal logic is elementary if it is sound and complete with respect to an elementary class of Kripke frames. We prove that if a finitely axiomatizable modal logic is elementar…
Most properties are undecidable even in
Qian Chen, Tenyo Takahashi
We investigate decidability of properties in the lattice of extensions of the Grzegorczyk tense logic and the lattice $\mat…
The Cardinalities of Intervals of Equational Theories and Logics
Juan P. Aguilera, Nick Bezhanishvili, Tenyo Takahashi
We study the cardinality of classes of equational theories (varieties) and logics by applying descriptive set theory. We affirmatively solve open problems raised by Jackson and Lee…
Chopping More Finely: Finite Countermodels in Modal Logic via the Subdivision Construction
Tenyo Takahashi
We present a new method, the Subdivision Construction, for proving the finite model property (the fmp) for broad classes of modal logics and modal rule systems. The construction bu…
Decidability of Being a Union-splitting
Tenyo Takahashi
Many logical properties are known to be undecidable for normal modal logics, with few exceptions such as consistency and coincidence with . This paper shows that the pr…
Stable Canonical Rules and Formulas for Pre-transitive Logics via Definable Filtration
Tenyo Takahashi
We generalize the theory of stable canonical rules by adopting definable filtration, a generalization of the method of filtration. We show that for a modal rule system or a modal l…