Switch to: References

Add citations

You must login to add citations.
  1. Proof Theory for Positive Logic with Weak Negation.Marta Bílková & Almudena Colacito - 2020 - Studia Logica 108 (4):649-686.
    Proof-theoretic methods are developed for subsystems of Johansson’s logic obtained by extending the positive fragment of intuitionistic logic with weak negations. These methods are exploited to establish properties of the logical systems. In particular, cut-free complete sequent calculi are introduced and used to provide a proof of the fact that the systems satisfy the Craig interpolation property. Alternative versions of the calculi are later obtained by means of an appropriate loop-checking history mechanism. Termination of the new calculi is proved, and (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Variations on the Kripke Trick.Mikhail Rybakov & Dmitry Shkatov - forthcoming - Studia Logica:1-48.
    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  
  • Predicate counterparts of modal logics of provability: High undecidability and Kripke incompleteness.Mikhail Rybakov - forthcoming - Logic Journal of the IGPL.
    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  
  • Undecidability of the Logic of Partial Quasiary Predicates.Mikhail Rybakov & Dmitry Shkatov - 2022 - Logic Journal of the IGPL 30 (3):519-533.
    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  
  • Undecidability of First-Order Modal and Intuitionistic Logics with Two Variables and One Monadic Predicate Letter.Mikhail Rybakov & Dmitry Shkatov - 2018 - Studia Logica 107 (4):695-717.
    We prove that the positive fragment of first-order intuitionistic logic in the language with two individual variables and a single monadic predicate letter, without functional symbols, constants, and equality, is undecidable. This holds true regardless of whether we consider semantics with expanding or constant domains. We then generalise this result to intervals \ and \, where QKC is the logic of the weak law of the excluded middle and QBL and QFL are first-order counterparts of Visser’s basic and formal logics, (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Transitive primal infon logic.Carlos Cotrini & Yuri Gurevich - 2013 - Review of Symbolic Logic 6 (2):281-304.
    Primal infon logic was introduced in 2009 in connection with access control. In addition to traditional logic constructs, it contains unary connectives p said indispensable in the intended access control applications. Propositional primal infon logic is decidable in linear time, yet suffices for many common access control scenarios. The most obvious limitation on its expressivity is the failure of the transitivity law for implication: \$$ \to \$$ and \$$ \to \$$ do not necessarily yield \$$ \to \$$. Here we introduce (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation