Ph. G. Kolaitis and Jouko A. Vaananen. Generalized quanti ers and pebble games on nite structures. Annals of Pure and Applied Logic, 74(1):23-75, 1995. Home/Search Document Not in Database Summary Related Articles Check |
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Ordering Finite Variable Types with Generalized Quantifiers - Dawar, Hella (Correct)
....1 A ; U j V j A n j then (A; V 1 ; V j ) 2 C. For each n, the basis Bn (Q) of Q is de ned to be the set of minimal elements (with respect to component wise inclusion ordering) of the set f(A; U 1 ; U j ) 2 C j jAj = ng. The following de nition is motivated by [19] and generalizes the concept of simple bounded montone quanti er in [19] De nition 32 A monotone quanti er Q of type (n 1 ; n j ) is t bounded if there is an integer t such that for all n, A; U 1 ; U j ) 2 Bn (Q) and each i, 1 i j, either jU i j t or jU i j jAj t. ....
....For each n, the basis Bn (Q) of Q is de ned to be the set of minimal elements (with respect to component wise inclusion ordering) of the set f(A; U 1 ; U j ) 2 C j jAj = ng. The following de nition is motivated by [19] and generalizes the concept of simple bounded montone quanti er in [19]. De nition 32 A monotone quanti er Q of type (n 1 ; n j ) is t bounded if there is an integer t such that for all n, A; U 1 ; U j ) 2 Bn (Q) and each i, 1 i j, either jU i j t or jU i j jAj t. Q is bounded if it is t bounded for some t. Note that there are ....
P. G. Kolaitis and J. A. Vaananen. Generalized quanti ers and pebble games on nite structures. Annals of Pure and Applied Logic, 74(1):23-75.
On the Expressive Power of Monotone Natural Language.. - Väänänen.. (Correct)
....of the added expressive power of CE quanti ers was proved already in Barwise and Cooper [1] namely, that most is not de nable in FO(Q R ) FO logic with Q R as an added generalized quanti er. 6 This is an instance of the result, proved in Westerst ahl [12] and Kolaitis and V a an anen [8], that for Q simple unary and monotone, Q rel is FO de nable in FO(Q) if and only if Q is already FO de nable. The result about most was generalized further in Kolaitis and V a an anen [8] by showing that most is not de nable in terms of any nite number of simple unary quanti ers. Now, an ....
....quanti er. 6 This is an instance of the result, proved in Westerst ahl [12] and Kolaitis and V a an anen [8] that for Q simple unary and monotone, Q rel is FO de nable in FO(Q) if and only if Q is already FO de nable. The result about most was generalized further in Kolaitis and V a an anen [8] by showing that most is not de nable in terms of any nite number of simple unary quanti ers. Now, an even number of is the relativization of the simple unary Q e , where (Q e ) M (A) jAj is even. These two quanti ers are equally expressive, since (Q e ) M (A) an even number of M (M;A) ....
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Kolaitis, Ph. and Vaananen, J., 1995. Generalized quantiers and pebble games on nite structures, Annals of Pure and Applied Logic 74, 23-75. 32
Logics Capturing Local Properties - Libkin (2001) (Correct)
.... graphs of xed maximum degree) The characterization for Hanf locality uses a logic L 1 (C) introduced in [Libkin 2000] This logic subsumes a number of counting extensions of FO (such as FO with counting quanti ers [Immerman and Lander 1990] FO with unary generalized quanti ers [Hella 1996; Kolaitis and V a an anen 1995], FO with unary counters [Benedikt and Keisler. 1997] and is quite easy to deal with. A result in [Hella et al. 1999a] states that Hanf local properties on structures of bounded valence are precisely those de nable in L 1 (C) The question naturally arises whether this continues to hold for ....
Kolaitis, Ph. and V a an anen, J. 1995. Generalized quantiers and pebble games on nite structures. Annals of Pure and Applied Logic 74, 23-75.
Vectorization Hierarchies of Some Graph Quantifiers - Hella, Nurmonen (Correct)
....C is the set of all counting quanti ers there are at least m elements for each natural number m. It can be seen that the game of Immerman and Lander is equivalent to the bijective game BP k 1 . Hence for every k, L k 1 (Q 1 ) has the same expressive power as the logic L k 1 (C) see also [KV95]) 5 2.2 Hanf s technique and unary quanti ers Hanf [Han65] introduced a technique based on the number of local isomorphism types to guarantee elementary equivalence of two structures ( nite or in nite) with respect to rst order logic. Fagin, Stockmeyer and Vardi [FSV95] formulated this ....
Ph. G. Kolaitis and J. A. Vaananen. Generalized quantiers and pebble games on nite structures. Annals of Pure and Applied Logic, 74(1):23-75, June 1995.
Adding for-Loops to First-Order Logic - Neven, Otto, Tyszkiewicz, Van den .. (2000) (1 citation) (Correct)
.... jY j (mod m) The Spoiler now puts pebble i on an element b 2 B, whereafter the Duplicator puts pebble i on an element a 2 A such that a 2 X if and only if b 2 Y . The winning conditions are de ned just as for the ordinary pebble game. 26 It follows from the work of Kolaitis and V a an anen [KV95] that if the Duplicator wins the (k; D n ) pebble game on A and B with the pebbles initially placed on a and b, then for any FO(IFP) formula with at most k di erent variables and that uses only quanti ers Dm with m n: A j= a) B j= b) Suppose towards a contradiction that Q ....
Ph. G. Kolaitis and Jouko A. Vaananen. Generalized quantiers and pebble games on nite structures. Annals of Pure and Applied Logic, 74(1):23-75, 1995.
Adding for-Loops to First-Order Logic - Neven, Otto, Tyszkiewicz, Van den .. (1999) (1 citation) (Correct)
....jXj jY j (mod m) The Spoiler now puts pebble i on an element b 2 B, whereafter the Duplicator puts pebble i on an element a 2 A such that a 2 X if and only if b 2 Y . The winning conditions are de ned just as for the ordinary pebble game. It follows from the work of Kolaitis and V a an anen [KV95] that if the Duplicator wins the (k; D n ) pebble game on A and B with the pebbles initially 26 placed on a and b, then for any FO(IFP) formula with at most k di erent variables and that uses only quanti ers Dm with m n: A j= a) B j= b) Suppose towards a contradiction ....
Ph. G. Kolaitis and Jouko A. Vaananen. Generalized quantiers and pebble games on nite structures. Annals of Pure and Applied Logic, 74(1):23-75, 1995.
Adding for-Loops to First-Order Logic - Neven, Otto, Tyszkiewicz, Van den .. (2000) (1 citation) (Correct)
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Ph. G. Kolaitis and Jouko A. Vaananen. Generalized quanti ers and pebble games on nite structures. Annals of Pure and Applied Logic, 74(1):23-75, 1995.
Game-based Notions of Locality over Finite Models - Arenas, Barcelo, Libkin (Correct)
No context found.
Ph. Kolaitis and J. Vaananen. Generalized quanti ers and pebble games on nite structures. Annals of Pure and Applied Logic 74: 23-75 (1995).
Logics with Aggregate Operators - Hella, Libkin, Nurmonen, Wong (5 citations) (Correct)
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Ph. Kolaitis and J. Vaananen. Generalized quantiers and pebble games on nite structures. Annals of Pure and Applied Logic, 74 (1995), 23-75.
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