Switch to: References

Add citations

You must login to add citations.
  1. Generalized Quantifiers.Dag Westerståhl - 2008 - Stanford Encyclopedia of Philosophy.
  • Convergence Laws for Very Sparse Random Structures with Generalized Quantifiers.Risto Kaila - 2002 - Mathematical Logic Quarterly 48 (2):301-320.
    We prove convergence laws for logics of the form equation image, where equation image is a properly chosen collection of generalized quantifiers, on very sparse finite random structures. We also study probabilistic collapsing of the logics equation image, where equation image is a collection of generalized quantifiers and k ∈ ℕ+, under arbitrary probability measures of finite structures.
    Direct download  
     
    Export citation  
     
    Bookmark  
  • Finite Variable Logics in Descriptive Complexity Theory.Martin Grohe - 1998 - Bulletin of Symbolic Logic 4 (4):345-398.
  • The Metamathematics of Random Graphs.John T. Baldwin - 2006 - Annals of Pure and Applied Logic 143 (1-3):20-28.
    We explain and summarize the use of logic to provide a uniform perspective for studying limit laws on finite probability spaces. This work connects developments in stability theory, finite model theory, abstract model theory, and probability. We conclude by linking this context with work on the Urysohn space.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • Strong Convergence in Finite Model Theory.Wafik Boulos Lotfallah - 2002 - Journal of Symbolic Logic 67 (3):1083-1092.
    In [9] we introduced a new framework for asymptotic probabilities, in which a $\sigma-additive$ measure is defined on the sample space of all sequences $A = $ of finite models, where the universe of An is {1, 2, .., n}. In this framework we investigated the strong 0-1 law for sentences, which states that each sentence either holds in An eventually almost surely or fails in An eventually almost surely. In this paper we define the strong convergence law for formulas, (...)
    Direct download (10 more)  
     
    Export citation  
     
    Bookmark  
  • Almost Everywhere Elimination of Probability Quantifiers.H. Jerome Keisler & Wafik Boulos Lotfallah - 2009 - Journal of Symbolic Logic 74 (4):1121 - 1142.
    We obtain an almost everywhere quantifier elimination for (the noncritical fragment of) the logic with probability quantifiers, introduced by the first author in [10]. This logic has quantifiers like $\exists ^{ \ge 3/4} y$ which says that "for at least 3/4 of all y". These results improve upon the 0-1 law for a fragment of this logic obtained by Knyazev [11]. Our improvements are: 1. We deal with the quantifier $\exists ^{ \ge r} y$ , where y is a tuple (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • How to Define a Linear Order on Finite Models.Lauri Hella, Phokion G. Kolaitis & Kerkko Luosto - 1997 - Annals of Pure and Applied Logic 87 (3):241-267.
    We carry out a systematic investigation of the definability of linear order on classes of finite rigid structures. We obtain upper and lower bounds for the expressibility of linear order in various logics that have been studied extensively in finite model theory, such as least fixpoint logic LFP, partial fixpoint logic PFP, infinitary logic Lω∞ω with a finite number of variables, as well as the closures of these logics under implicit definitions. Moreover, we show that the upper and lower bounds (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  • Strong 0-1 Laws in Finite Model Theory.Wafik Boulos Lotfallah - 2000 - Journal of Symbolic Logic 65 (4):1686-1704.
    We introduce a new framework for asymptotic probabilities of sentences, in which we have a σ-additive measure on the sample space of all sequences A = {A n } of finite models, where the universe of A n is {1,2... n}, and use this framework to strengthen 0-1 laws for logics.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark  
  • Zero-One Law and Definability of Linear Order.Hannu Niemistö - 2009 - Journal of Symbolic Logic 74 (1):105-123.