9 found
Order:
  1.  23
    Kripke completeness of strictly positive modal logics over meet-semilattices with operators.Stanislav Kikot, Agi Kurucz, Yoshihito Tanaka, Frank Wolter & Michael Zakharyaschev - 2019 - Journal of Symbolic Logic 84 (2):533-588.
    Our concern is the completeness problem for spi-logics, that is, sets of implications between strictly positive formulas built from propositional variables, conjunction and modal diamond operators. Originated in logic, algebra and computer science, spi-logics have two natural semantics: meet-semilattices with monotone operators providing Birkhoff-style calculi and first-order relational structures (aka Kripke frames) often used as the intended structures in applications. Here we lay foundations for a completeness theory that aims to answer the question whether the two semantics define the same (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  2.  9
    The price of query rewriting in ontology-based data access.Georg Gottlob, Stanislav Kikot, Roman Kontchakov, Vladimir Podolskii, Thomas Schwentick & Michael Zakharyaschev - 2014 - Artificial Intelligence 213 (C):42-59.
  3.  18
    Non-finitely axiomatisable modal product logics with infinite canonical axiomatisations.Christopher Hampson, Stanislav Kikot, Agi Kurucz & Sérgio Marcelino - 2020 - Annals of Pure and Applied Logic 171 (5):102786.
    Our concern is the axiomatisation problem for modal and algebraic logics that correspond to various fragments of two-variable first-order logic with counting quantifiers. In particular, we consider modal products with Diff, the propositional unimodal logic of the difference operator. We show that the two-dimensional product logic $Diff \times Diff$ is non-finitely axiomatisable, but can be axiomatised by infinitely many Sahlqvist axioms. We also show that its ‘square’ version (the modal counterpart of the substitution and equality free fragment of two-variable first-order (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  4.  53
    An extension of Kracht's theorem to generalized Sahlqvist formulas.Stanislav Kikot - 2009 - Journal of Applied Non-Classical Logics 19 (2):227-251.
    Sahlqvist formulas are a syntactically specified class of modal formulas proposed by Hendrik Sahlqvist in 1975. They are important because of their first-order definability and canonicity, and hence axiomatize complete modal logics. The first-order properties definable by Sahlqvist formulas were syntactically characterized by Marcus Kracht in 1993. The present paper extends Kracht's theorem to the class of ‘generalized Sahlqvist formulas' introduced by Goranko and Vakarelov and describes an appropriate generalization of Kracht formulas.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  5.  18
    Modal definability of first-order formulas with free variables and query answering.Stanislav Kikot & Evgeny Zolin - 2013 - Journal of Applied Logic 11 (2):190-216.
  6.  15
    A Dichotomy for Some Elementarily Generated Modal Logics.Stanislav Kikot - 2015 - Studia Logica 103 (5):1063-1093.
    In this paper we consider the normal modal logics of elementary classes defined by first-order formulas of the form \. We prove that many properties of these logics, such as finite axiomatisability, elementarity, axiomatisability by a set of canonical formulas or by a single generalised Sahlqvist formula, together with modal definability of the initial formula, either simultaneously hold or simultaneously do not hold.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  7.  8
    Sahlqvist Theorems for Precontact Logics.Philippe Balbiani & Stanislav Kikot - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 55-70.
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark  
  8.  8
    A tetrachotomy of ontology-mediated queries with a covering axiom.Olga Gerasimova, Stanislav Kikot, Agi Kurucz, Vladimir Podolskii & Michael Zakharyaschev - 2022 - Artificial Intelligence 309 (C):103738.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  9.  11
    Semantic Characterization of Krancht Formulas.Stanislav Kikot - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 218-234.
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark