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Rules, Regularities, Randomness. Festschrift for Michiel van Lambalgen

Amsterdam, The Netherlands: Institute for Logic, Language and Computation (2022)

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  1. On a decidable generalized quantifier logic corresponding to a decidable fragment of first-order logic.Natasha Alechina - 1995 - Journal of Logic, Language and Information 4 (3):177-189.
    Van Lambalgen (1990) proposed a translation from a language containing a generalized quantifierQ into a first-order language enriched with a family of predicatesR i, for every arityi (or an infinitary predicateR) which takesQxg(x, y1,..., yn) to x(R(x, y1,..., y1) (x,y1,...,yn)) (y 1,...,yn are precisely the free variables ofQx). The logic ofQ (without ordinary quantifiers) corresponds therefore to the fragment of first-order logic which contains only specially restricted quantification. We prove that it is decidable using the method of analytic tableaux. Related (...)
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  • The axiomatization of randomness.Michiel van Lambalgen - 1990 - Journal of Symbolic Logic 55 (3):1143-1167.
    We present a faithful axiomatization of von Mises' notion of a random sequence, using an abstract independence relation. A byproduct is a quantifier elimination theorem for Friedman's "almost all" quantifier in terms of this independence relation.
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