A. Dawar. Generalized Quantifiers and Logical Reducibilities. J. Logic and Computation, 5(2):213--226, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....closure. Another well known example of generalized quantifiers are Henkin (or branching) quantifiers [19] which have been studied extensively in logic. Generalized quantifiers have applications in various areas including linguistics, finite model theory, Artificial Intelligence and databases, cf. [3, 5, 2, 20]. For this reason, we believe that this extension of logic programming has high potential for applications beyond modular logic programming, which originally has driven this research on generalized quantifiers; in this paper, we introduce the technical framework of logic programming with ....

A. Dawar. Generalized Quantifiers and Logical Reducibilities. J. Logic and Computation, 5(2):213--226, 1995.

....classes associated with AC 0 . 3.2 Turing Reductions There is another way of looking at the difference between FOL[ATC] and IFPL, which was suggested to us by A. Dawar. On ordered finite structures FOL[ATC] captures P and also many one P reductions (Karp reductions) as shown independently in [Daw93, Daw94] and in [MP93, MP94] What our result here shows, is that FOL[ATC] does not capture Turing reductions (Cook reductions) The difference is, that in many one reductions the oracle is applied only once, whereas in Turing reductions it may be applied several times. What FOL[ATC] is missing is the ....

A. Dawar. Generalized quantifiers and logical reducibilities. Logic and Computation, to appear, 1995.

....Conjecture1 (Gurevich) For P there is no unordered Gurevich Logic capturing P, unless, say, P = NP Co Gamma NP. We dare the following generalization: Conjecture 2. For D P there are no unordered Gurevich Logics capturing D unless D = NP Co Gamma NP. Implicite Definable Orders Dawar [Daw94] has observed that for capturing P with an unordered Gurevich Logic, one has to understand better order invariant definable classes, i.e. classes of structures definable with, but invariantly under permutation of an order relation. In a last part we discuss the exact scope of closure under ....

A. Dawar. Generalized quantifiers and logical reducibilities. Logic and Computation, XX:xx--yy, 1994, to appear.

....as presented in [EFT80, CK90] or in [Ebb85] of [BF85] We start by introducing a notion of relational regular complexity classes, similar in spirit to both Lindstrom s abstract definition of logics and the computable queries of A. Chandra and D. Harel [CH80, CH82] Independently A. Dawar in [Daw94] introduced basically the same concept for unordered structures. We denote vocabularies (similarity types) by ; oe. Vocabularies are assumed to be relational and finite. If we speak of ordered structures, vocabularies contain a distinguished binary relation symbol for the order relation. ....

....as introduced by Immerman and Dahlhaus [Dah82, Dah83, Imm87] to any regular logic L. We first presented this concept in [MP93] Our definition is very close to Rabin s notion of interpretability as described in [Rab65] A similar notion is also used in [Cou92] and, for general logics, in [Daw94] Definition18 (L reducibility) Let K 1 ; K 2 be classes of 1 ; 2 structures closed under isomorphisms and L be a regular logic. i) Let 2 = fR 1 ; Rm g and let ae(R i ) be the arity of R i . Let Phi = hOE; 1 ; m i be 1 formulas of L. Phi is n feasible for 2 ....

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A. Dawar. Generalized quantifiers and logical reducibilities. Logic and Computation, XX:xx--yy, 1994, to appear.

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