Switch to: References

Citations of:

Hypersequents and the proof theory of intuitionistic fuzzy logic

In Peter G. Clote & Helmut Schwichtenberg (eds.), Computer Science Logic. 14th International Workshop, CSL 2000. Berlin: Springer. pp. 187– 201 (2000)

Add citations

You must login to add citations.
  1. A Proof-Theoretical Investigation of Global Intuitionistic (Fuzzy) Logic.Agata Ciabattoni - 2005 - Archive for Mathematical Logic 44 (4):435-457.
    We perform a proof-theoretical investigation of two modal predicate logics: global intuitionistic logic GI and global intuitionistic fuzzy logic GIF. These logics were introduced by Takeuti and Titani to formulate an intuitionistic set theory and an intuitionistic fuzzy set theory together with their metatheories. Here we define analytic Gentzen style calculi for GI and GIF. Among other things, these calculi allows one to prove Herbrand’s theorem for suitable fragments of GI and GIF.
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • First-Order Gödel Logics.Richard Zach, Matthias Baaz & Norbert Preining - 2007 - Annals of Pure and Applied Logic 147 (1):23-47.
    First-order Gödel logics are a family of finite- or infinite-valued logics where the sets of truth values V are closed subsets of [0,1] containing both 0 and 1. Different such sets V in general determine different Gödel logics GV (sets of those formulas which evaluate to 1 in every interpretation into V). It is shown that GV is axiomatizable iff V is finite, V is uncountable with 0 isolated in V, or every neighborhood of 0 in V is uncountable. Complete (...)
    Download  
     
    Export citation  
     
    Bookmark   16 citations  
  • Completeness of a Hypersequent Calculus for Some First-Order Gödel Logics with Delta.Matthias Baaz, Norbert Preining & Richard Zach - 2006 - In 36th International Symposium on Multiple-valued Logic. May 2006, Singapore. Proceedings. Los Alamitos: IEEE Press.
    All first-order Gödel logics G_V with globalization operator based on truth value sets V C [0,1] where 0 and 1 lie in the perfect kernel of V are axiomatized by Ciabattoni’s hypersequent calculus HGIF.
    Download  
     
    Export citation  
     
    Bookmark  
  • The Eskolemization of Universal Quantifiers.Rosalie Iemhoff - 2010 - Annals of Pure and Applied Logic 162 (3):201-212.
    This paper is a sequel to the papers Baaz and Iemhoff [4] and [6] in which an alternative skolemization method called eskolemization was introduced that, when restricted to strong existential quantifiers, is sound and complete for constructive theories. In this paper we extend the method to universal quantifiers and show that for theories satisfying the witness property it is sound and complete for all formulas. We obtain a Herbrand theorem from this, and apply the method to the intuitionistic theory of (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation