Order:
  1.  9
    On Logics and Semantics for Interpretability.Luka Mikec - 2022 - Bulletin of Symbolic Logic 28 (2):265-265.
  2.  12
    Interpretability logics and generalised Veltman semantics.Luka Mikec & Mladen Vuković - 2020 - Journal of Symbolic Logic 85 (2):749-772.
    We obtain modal completeness of the interpretability logics IL $\!\!\textsf {P}_{\textsf {0}}$ and ILR w.r.t. generalised Veltman semantics. Our proofs are based on the notion of full labels [2]. We also give shorter proofs of completeness w.r.t. the generalised semantics for many classical interpretability logics. We obtain decidability and finite model property w.r.t. the generalised semantics for IL $\textsf {P}_{\textsf {0}}$ and ILR. Finally, we develop a construction that might be useful for proofs of completeness of extensions of ILW w.r.t. (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  3.  12
    Complexity of the interpretability logic IL.Luka Mikec, Fedor Pakhomov & Mladen Vuković - forthcoming - Logic Journal of the IGPL.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  4.  8
    Theory and application of labelling techniques for interpretability logics.Evan Goris, Marta Bílková, Joost J. Joosten & Luka Mikec - 2022 - Mathematical Logic Quarterly 68 (3):352-374.
    The notion of a critical successor [5] in relational semantics has been central to most classic modal completeness proofs in interpretability logics. In this paper we shall work with a more general notion, that of an assuring successor. This will enable more concisely formulated completeness proofs, both with respect to ordinary and generalised Veltman semantics. Due to their interesting theoretical properties, we will devote some space to the study of a particular kind of assuring labels, the so‐called full labels and (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  5.  8
    Complexity of the interpretability logics ILW and ILP.Luka Mikec - 2023 - Logic Journal of the IGPL 31 (1):194-213.
    The interpretability logic ILP is the interpretability logic of all sufficiently strong |$\varSigma _1$|-sound finitely axiomatised theories, such as the Gödel-Bernays set theory. The interpretability logic IL is a strict subset of the intersection of the interpretability logics of all so-called reasonable theories, IL(All). It is known that both ILP and ILW are decidable, however their complexity has not been resolved previously. In [10] it was shown that the basic interpretability logic IL is PSPACE-complete. Here we prove the same for (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  6.  6
    Existential definability of modal frame classes.Tin Perkov & Luka Mikec - 2020 - Mathematical Logic Quarterly 66 (3):316-325.
    We prove an existential analogue of the Goldblatt‐Thomason Theorem which characterizes modal definability of elementary classes of Kripke frames using closure under model theoretic constructions. The less known version of the Goldblatt‐Thomason Theorem gives general conditions, without the assumption of first‐order definability, but uses non‐standard constructions and algebraic semantics. We present a non‐algebraic proof of this result and we prove an analogous characterization for an alternative notion of modal definability, in which a class is defined by formulas which are satisfiable (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark