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  1. Lauri Hella, Merlijn Sevenster & Tero Tulenheimo (2008). Partially Ordered Connectives and Monadic Monotone Strict Np. Journal of Logic, Language and Information 17 (3):323-344.
    Motivated by constraint satisfaction problems, Feder and Vardi (SIAM Journal of Computing, 28, 57–104, 1998) set out to search for fragments of satisfying the dichotomy property: every problem definable in is either in P or else NP-complete. Feder and Vardi considered in this connection two logics, strict NP (or SNP) and monadic, monotone, strict NP without inequalities (or MMSNP). The former consists of formulas of the form , where is a quantifier-free formula in a relational vocabulary; and the latter is (...)
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  2. Lauri Hella & Juha Nurmonen (2000). Vectorization Hierarchies of Some Graph Quantifiers. Archive for Mathematical Logic 39 (3):183-207.
    We give a sufficient condition for the inexpressibility of the k-th extended vectorization of a generalized quantifier $\sf Q$ in ${\rm FO}({\vec Q}_k)$ , the extension of first-order logic by all k-ary quantifiers. The condition is based on a model construction which, given two ${\rm FO}({\vec Q}_1)$ -equivalent models with certain additional structure, yields a pair of ${\rm FO}({\vec Q}_k)$ -equivalent models. We also consider some applications of this condition to quantifiers that correspond to graph properties, such as connectivity and (...)
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  3. Lauri Hella, Leonid Libkin & Juha Nurmonen (1999). Notions of Locality and Their Logical Characterizations Over Finite Models. Journal of Symbolic Logic 64 (4):1751-1773.
    Many known tools for proving expressibility bounds for first-order logic are based on one of several locality properties. In this paper we characterize the relationship between those notions of locality. We note that Gaifman's locality theorem gives rise to two notions: one deals with sentences and one with open formulae. We prove that the former implies Hanf's notion of locality, which in turn implies Gaifman's locality for open formulae. Each of these implies the bounded degree property, which is one of (...)
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  4. Anuj Dawar, Georg Gottlob & Lauri Hella (1998). Capturing Relativized Complexity Classes Without Order. Mathematical Logic Quarterly 44 (1):109-122.
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  5. Anita Feferman, Solomon Feferman, Robert Goldblatt, Yuri Gurevich, Klaus Grue, Sven Ove Hansson, Lauri Hella, Robert K. Meyer & Petri Mäenpää (1997). Stål Anderaa (Oslo), A Traktenbrot Inseparability Theorem for Groups. Peter Dybjer (G Öteborg), Normalization by Yoneda Embedding (Joint Work with D. Cubric and PJ Scott). Abbas Edalat (Imperial College), Dynamical Systems, Measures, Fractals, and Exact Real Number Arithmetic Via Domain Theory. [REVIEW] Bulletin of Symbolic Logic 3 (4).
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  6. Lauri Hella, Phokion G. Kolaitis & Kerkko Luosto (1997). How to Define a Linear Order on Finite Models. Annals of Pure and Applied Logic 87 (3):241-267.
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  7. Lauri Hella, Jouko Väänänen & Dag Westerståhl (1997). Definability of Polyadic Lifts of Generalized Quantifiers. Journal of Logic, Language and Information 6 (3):305-335.
    We study generalized quantifiers on finite structures.With every function : we associate a quantifier Q by letting Q x say there are at least (n) elementsx satisfying , where n is the sizeof the universe. This is the general form ofwhat is known as a monotone quantifier of type .We study so called polyadic liftsof such quantifiers. The particular lifts we considerare Ramseyfication, branching and resumption.In each case we get exact criteria fordefinability of the lift in terms of simpler quantifiers.
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  8. Martin Grohe & Lauri Hella (1996). A Double Arity Hierarchy Theorem for Transitive Closure Logic. Archive for Mathematical Logic 35 (3):157-171.
    In this paper we prove that thek-ary fragment of transitive closure logic is not contained in the extension of the (k−1)-ary fragment of partial fixed point logic by all (2k−1)-ary generalized quantifiers. As a consequence, the arity hierarchies of all the familiar forms of fixed point logic are strict simultaneously with respect to the arity of the induction predicates and the arity of generalized quantifiers.Although it is known that our theorem cannot be extended to the sublogic deterministic transitive closure logic, (...)
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  9. Lauri Hella, Phokion G. Kolaitis & Kerkko Luosto (1996). Almost Everywhere Equivalence of Logics in Finite Model Theory. 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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  10. Lauri Hella, Kerkko Luosto & Jouko Väänänen (1996). The Hierarchy Theorem for Generalized Quantifiers. 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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  11. Lauri Hella & Kerkko Luosto (1995). Finite Generation Problem and N-Ary Quantifiers. In M. Krynicki, M. Mostowski & L. Szczerba (eds.), Quantifiers: Logics, Models and Computation. Kluwer Academic Publishers. 63--104.
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  12. Lauri Hella & Gabriel Sandu (1995). Partially Ordered Connectives and Finite Graphs. In M. Krynicki, M. Mostowski & L. Szczerba (eds.), Quantifiers: Logics, Models and Computation. Kluwer Academic Publishers. 79--88.
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  13. Lauri Hella & Kerkko Luosto (1992). The Beth-Closure of L(Qα) is Not Finitely Generated. 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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  14. Lauri Hella & Kerkko Luosto (1992). The Beth-Closure of $Mathscr{L}(Q_alpha)$ is Not Finitely Generated. 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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  15. Lauri Hella & Michal Krynicki (1991). Remarks on The Cartesian Closure. Mathematical Logic Quarterly 37 (33‐35):539-545.
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  16. Lauri Hella (1989). Definability Hierarchies of Generalized Quantifiers. Annals of Pure and Applied Logic 43 (3):235-271.
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