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. Syntactic Cut-Elimination for Intuitionistic Fuzzy Logic Via Linear Nested Sequents.Tim Lyon - 2020 - In Sergei Artemov & Anil Nerode (eds.), Logical Foundations of Computer Science. Cham: pp. 156-176.
    This paper employs the linear nested sequent framework to design a new cut-free calculus (LNIF) for intuitionistic fuzzy logic---the first-order Goedel logic characterized by linear relational frames with constant domains. Linear nested sequents---which are nested sequents restricted to linear structures---prove to be a well-suited proof-theoretic formalism for intuitionistic fuzzy logic. We show that the calculus LNIF possesses highly desirable proof-theoretic properties such as invertibility of all rules, admissibility of structural rules, and syntactic cut-elimination.
    Download  
     
    Export citation  
     
    Bookmark  
  • 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