5 found
Order:
  1.  10
    Tomasz Połacik (1998). Propositional Quantification in the Monadic Fragment of Intuitionistic Logic. Journal of Symbolic Logic 63 (1):269-300.
    We study the monadic fragment of second order intuitionistic propositional logic in the language containing the standard propositional connectives and propositional quantifiers. It is proved that under the topological interpretation over any dense-in-itself metric space, the considered fragment collapses to Heyting calculus. Moreover, we prove that the topological interpretation over any dense-in-itself metric space of fragment in question coincides with the so-called Pitts' interpretation. We also prove that all the nonstandard propositional operators of the form q $\mapsto \exists$ p (q (...)
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  2.  5
    Tomasz Połacik (1994). Second Order Propositional Operators Over Cantor Space. Studia Logica 53 (1):93 - 105.
  3.  2
    Tomasz Połacik (1998). Pitts' Quantifiers Are Not Topological Quantification. Notre Dame Journal of Formal Logic 39 (4):531-544.
    We show that Pitts' modeling of propositional quantification in intuitionistic logic (as the appropriate interpolants) does not coincide with the topological interpretation. This contrasts with the case of the monadic language and the interpretation over sufficiently regular topological spaces. We also point to the difference between the topological interpretation over sufficiently regular spaces and the interpretation of propositional quantifiers in Kripke models.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  4. Tomasz Połacik (forthcoming). A Semantic Approach to Conservativity. Studia Logica:1-14.
    The aim of this paper is to describe from a semantic perspective the problem of conservativity of classical first-order theories over their intuitionistic counterparts. In particular, we describe a class of formulae for which such conservativity results can be proven in case of any intuitionistic theory T which is complete with respect to a class of T-normal Kripke models. We also prove conservativity results for intuitionistic theories which are closed under the Friedman translation and complete with respect to a class (...)
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  5. Tomasz Połacik (2008). Back and Forth Between First-Order Kripke Models. Logic Journal of the Igpl 16 (4):335-355.
    We introduce the notion of bisimulation for first-order Kripke models. It is defined as a relation that satisfies certain zig-zag conditions involving back-and-forth moves between nodes of Kripke models and, simultaneously, between the domains of their underlying structures. As one of our main results, we prove that if two Kripke models bisimulate to a certain degree, then they are logically equivalent with respect to the class of formulae of the appropriate complexity. Two applications of the notion introduced in the paper (...)
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography