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Kerkko Luosto [11]K. Luosto [2]
  1. Almost Everywhere Equivalence of Logics in Finite Model Theory.Lauri Hella, Phokion G. Kolaitis & Kerkko Luosto - 1996 - Bulletin of Symbolic Logic 2 (4):422-443.
    We introduce a new framework for classifying logics on finite structures and studying their expressive power. This framework is based on the concept of almost everywhere equivalence of logics, that is to say, two logics having the same expressive power on a class of asymptotic measure 1. More precisely, if L, L ′ are two logics and μ is an asymptotic measure on finite structures, then $\scr{L}\equiv _{\text{a.e.}}\scr{L}^{\prime}(\mu)$ means that there is a class C of finite structures with μ (C)=1 (...)
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  2. The Hierarchy Theorem for Generalized Quantifiers.Lauri Hella, Kerkko Luosto & Jouko Väänänen - 1996 - Journal of Symbolic Logic 61 (3):802-817.
    The concept of a generalized quantifier of a given similarity type was defined in [12]. Our main result says that on finite structures different similarity types give rise to different classes of generalized quantifiers. More exactly, for every similarity type t there is a generalized quantifier of type t which is not definable in the extension of first order logic by all generalized quantifiers of type smaller than t. This was proved for unary similarity types by Per Lindström [17] with (...)
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  3.  3
    The Expressive Power of Modal Dependence Logic.Lauri Hella, Kerkko Luosto, Katsuhiko Sano & Jonni Virtema - 2014 - In Rajeev Goré, Barteld Kooi & Agi Kurucz (eds.), Advances in Modal Logic, Volume 10. CSLI Publications. pp. 294-312.
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  4.  7
    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 (...)
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  5.  90
    Hierarchies of Monadic Generalized Quantifiers.Kerkko Luosto - 2000 - Journal of Symbolic Logic 65 (3):1241-1263.
    A combinatorial criterium is given when a monadic quantifier is expressible by means of universe-independent monadic quantifiers of width n. It is proved that the corresponding hierarchy does not collapse. As an application, it is shown that the second resumption (or vectorization) of the Hartig quantifier is not definable by monadic quantifiers. The techniques rely on Ramsey theory.
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  6.  40
    On Vectorizations of Unary Generalized Quantifiers.Kerkko Luosto - 2012 - Archive for Mathematical Logic 51 (3-4):241-255.
    Vectorization of a class of structures is a natural notion in finite model theory. Roughly speaking, vectorizations allow tuples to be treated similarly to elements of structures. The importance of vectorizations is highlighted by the fact that if the complexity class PTIME corresponds to a logic with reasonable syntax, then it corresponds to a logic generated via vectorizations by a single generalized quantifier (Dawar in J Log Comput 5(2):213–226, 1995). It is somewhat surprising, then, that there have been few systematic (...)
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    The Hierarchy Theorem for Generalized Quantifiers.Lauri Hella, Kerkko Luosto & Jouko Vaananen - 1996 - Journal of Symbolic Logic 61 (2):802-817.
    The concept of a generalized quantifier of a given similarity type was defined in [12]. Our main result says that on finite structures different similarity types give rise to different classes of generalized quantifiers. More exactly, for every similarity type $t$ there is a generalized quantifier of type $t$ which is not definable in the extension of first order logic by all generalized quantifiers of type smaller than $t$. This was proved for unary similarity types by Per Lindstrom [17] with (...)
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  8.  13
    The Beth-Closure of $Mathscr{L}(Q_alpha)$ is Not Finitely Generated.Lauri Hella & Kerkko Luosto - 1992 - Journal of Symbolic Logic 57 (2):442-448.
    We prove that if $\aleph_\alpha$ is uncountable and regular, then the Beth-closure of $\mathscr{L}_{\omega\omega}(Q_\alpha)$ is not a sublogic of $\mathscr{L}_{\infty\omega}(\mathbf{Q}_n)$, where $\mathbf{Q}_n$ is the class of all $n$-ary generalized quantifiers. In particular, $B(\mathscr{L}_{\omega\omega}(Q_\alpha))$ is not a sublogic of any finitely generated logic; i.e., there does not exist a finite set $\mathbf{Q}$ of Lindstrom quantifiers such that $B(\mathscr{L}_{\omega\omega}(Q_\alpha)) \leq \mathscr{L}_{\omega\omega}(\mathbf{Q})$.
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    The Beth-Closure of L(Qα) is Not Finitely Generated.Lauri Hella & Kerkko Luosto - 1992 - Journal of Symbolic Logic 57 (2):442 - 448.
    We prove that if ℵα is uncountable and regular, then the Beth-closure of Lωω(Qα) is not a sublogic of L∞ω(Qn), where Qn is the class of all n-ary generalized quantifiers. In particular, B(Lωω(Qα)) is not a sublogic of any finitely generated logic; i.e., there does not exist a finite set Q of Lindstrom quantifiers such that B(Lωω(Qα)) ≤ Lωω(Q).
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  10.  4
    REVIEWS-How to Define a Linear Order on Finite Models.L. Hella, Ph Kolaitis, K. Luosto & M. Otto - 2000 - Bulletin of Symbolic Logic 6 (3):355-355.
  11.  3
    Finite Generation Problem and N-Ary Quantifiers.Lauri Hella & Kerkko Luosto - 1995 - In M. Krynicki, M. Mostowski & L. Szczerba (eds.), Quantifiers: Logics, Models and Computation. Kluwer Academic Publishers. pp. 63--104.
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