Switch to: References

Citations of:

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

Mikhail Rybakov & Dmitry Shkatov

Studia Logica 107 (4):695-717 (2018)

Add citations

You must login to add citations.

Strictly Positive Fragments of the Provability Logic of Heyting Arithmetic.Ana de Almeida Borges & Joost J. Joosten - forthcoming - Studia Logica:1-33.details We determine the strictly positive fragment \(\textsf{QPL}^+(\textsf{HA})\) of the quantified provability logic \(\textsf{QPL}(\textsf{HA})\) of Heyting Arithmetic. We show that \(\textsf{QPL}^+(\textsf{HA})\) is decidable and that it coincides with \(\textsf{QPL}^+(\textsf{PA})\), which is the strictly positive fragment of the quantified provability logic of of Peano Arithmetic. This positively resolves a previous conjecture of the authors described in [ 14 ]. On our way to proving these results, we carve out the strictly positive fragment \(\textsf{PL}^+(\textsf{HA})\) of the provability logic \(\textsf{PL}(\textsf{HA})\) of Heyting Arithmetic, provide (...) Download Export citation Bookmark
Variations on the Kripke Trick.Mikhail Rybakov & Dmitry Shkatov - forthcoming - Studia Logica:1-48.details In the early 1960s, to prove undecidability of monadic fragments of sublogics of the predicate modal logic $$\textbf{QS5}$$ QS 5 that include the classical predicate logic $$\textbf{QCl}$$ QCl, Saul Kripke showed how a classical atomic formula with a binary predicate letter can be simulated by a monadic modal formula. We consider adaptations of Kripke’s simulation, which we call the Kripke trick, to various modal and superintuitionistic predicate logics not considered by Kripke. We also discuss settings where the Kripke trick does (...) Download Export citation Bookmark
Undecidability of the Logic of Partial Quasiary Predicates.Mikhail Rybakov & Dmitry Shkatov - 2022 - Logic Journal of the IGPL 30 (3):519-533.details We obtain an effective embedding of the classical predicate logic into the logic of partial quasiary predicates. The embedding has the property that an image of a non-theorem of the classical logic is refutable in a model of the logic of partial quasiary predicates that has the same cardinality as the classical countermodel of the non-theorem. Therefore, we also obtain an embedding of the classical predicate logic of finite models into the logic of partial quasiary predicates over finite structures. As (...) Download Export citation Bookmark
Predicate counterparts of modal logics of provability: High undecidability and Kripke incompleteness.Mikhail Rybakov - forthcoming - Logic Journal of the IGPL.details In this paper, the predicate counterparts, defined both axiomatically and semantically by means of Kripke frames, of the modal propositional logics $\textbf {GL}$, $\textbf {Grz}$, $\textbf {wGrz}$ and their extensions are considered. It is proved that the set of semantical consequences on Kripke frames of every logic between $\textbf {QwGrz}$ and $\textbf {QGL.3}$ or between $\textbf {QwGrz}$ and $\textbf {QGrz.3}$ is $\Pi ^1_1$-hard even in languages with three (sometimes, two) individual variables, two (sometimes, one) unary predicate letters, and a single (...) Download Export citation Bookmark 2 citations

1