multiwavelets for second kind integral equations we consider a galerkin method for an elliptic pseudodifferential operator of order zero on a two dimensional manifold we use piecewise linear discontinuous trial functions on a triangular mesh and describe an orthonormal wavelet basis using this basis we can compress the stiffness matrix from n2 to o n log n nonzero entries and still obtain up to log n terms the same convergence rates as for the exact galerkin method

a wavelet algorithm for the boundary element solution of a geodetic boundary value problem abstract in this paper we consider a piecewise bilinear collocation method for the solution of a singular integral equation over a part of the surface of the earth this singular equation is the boundary integral equation corresponding to the oblique derivative boundary problem for laplace s equation we introduce special wavelet bases for the spaces of test and trial functions analogously to well known results on wavelet algorithms the stiffness matrices with respect to these bases can be reduced to sparse matrices such that the assembling of the matrices and the iterative solution of the matrix equations quicken though the theoretical results apply only to integral equations with smooth solutions over smooth manifolds we present numerical tests for a geometry as difficult as the surface of the earth

adaptive hybrid grid methods an adaptive refinement and redistribution method is presented for use on hybrid grids composed of prismatic pyramidal and tetrahedral elements the combined refinement and redistribution scheme minimizes the computational time and memory required for the solver and maximizes the numerical accuracy grid refinement is achieved via a priori source placement and also solution based splitting of the edges of the grid elements the prismatic and pyramidal elements are divided directionally and the tetrahedral elements may be refined isotropically or directionally the prismatic grid redistribution scheme attracts or repels points that are close to the wall surface so as to better capture boundary layers a method is developed to place newly created boundary nodes on the actual splined surface instead of the previous discretized surface this ensures that the grid refinement always represents the geometric model accurately several examples are presented to demonstrate the a priori source placement the solution based grid refinement and the prismatic grid redistribution

efficient solution methods for strand grid applications the strand cartesian grid approach offers many advantages in terms of automation efficiency and accuracy for complex moving body problems such as rotorcraft in this study the solution procedures for strand grids are investigated by testing a variety of explicit implicit and hybrid methods on canonical aerodynamics test cases involving inviscid and viscous flows in three dimensions a novel multigrid algorithm is formulated that acts at both the nonlinear pseudotime level and the linear level using line gauss seidel sweeps various approximations are tested for the jacobian and the impacts on memory and convergence are quantified the major result is that implicit schemes with first order approximate jacobians employing few gauss seidel sweeps are most efficient for strand grids the improvement by using the multigrid algorithm is significant for all cases tested and indicates o n convergence

is intractability of nonmonotonic reasoning a real drawback abstract several studies about computational complexity of nonmonotonic reasoning nmr showed that nonmonotonic inference is significantly harder than classical monotonic inference this contrasts with the general idea that nmr can be used to make knowledge representation and reasoning simpler not harder in this paper we show that to some extent nmr fulfills the representation goal in particular we prove that nonmonotonic formalisms such as circumscription and default logic allow for a much more compact and natural representation of propositional knowledge than propositional calculus proofs are based on a suitable definition of a compilable inference problem and on non uniform complexity classes some results about intractability of circumscription and default logic can therefore be interpreted as the price one has to pay for having such an extra compact representation on the other hand intractability of inference and compactness of representation are not equivalent notions we exhibit intractable nonmonotonic formalisms whose nonmonotonic assumptions are representable by few propositional formulae finally sometimes nmr really makes reasoning simpler we present prototypical scenarios where closed world reasoning and well founded semantics account for a faster complete and unsound approximation of classical reasoning

a new mesh generation scheme for arbitrary planar domains this paper describes a new algorithm to generate interior nodes within any arbitrary multi connected regions the boundary nodes and the interior nodes are then linked up to form the best possible triangular elements by a completely revised technique in an efficient and stable manner owing to the generality of the central generation program the global domain is allowed to be divided into as many irregular subdomains as desired in order to model closely the actual physical situation moreover the boundaries of the sub domains are updated from time to time when necessary to include the possibilities of progressive refinement around a sharp corner generating radiating mesh from a prescribed node generating mesh between two circular arcs etc despite its flexibility and capabilities data for triangulation have been kept to a minimum by a logical input module no connectivity information between subregions is needed and common boundaries are defined once only all these features have contributed to a powerful method to generate 3 node or 6 node triangular element meshes of great variety within the most irregular heterogeneous regions

prismatic grid generation for three dimensional complex geometries the paper describes generation of semiunstructu red prismatic grids for three dimensional complex geometries a new method of generation is presented which couples both algebraic and elliptic steps this combination yields low computation cost as well as smoothness of the grid main advantages of the developed grid generator are its direct control of grid orthogonality and spacing as well as its generality for treatment of three dimensional geometries the method marches a surface consisting of triangular faces away from the body surface employment of prismatic elements is a relatively new approach toward three dimensional complex geometry numerical simulations of viscous flows a body surface is covered with triangles which gives the geometric flexibility whereas the structure of the mesh in the direction normal to the surface provides better resolution of the viscous regions an f 16a aircraft geometry was included in the applications to investigate efficiency and to demonstrate robustness of the method in handling relatively complex topologies grid generation time for the entire aircraft domain was of the order of minutes on a workstation

a practical determination strategy of optimal threshold parameter for matrix compression in wavelet bem a practical strategy is developed to determine the optimal threshold parameter for wavelet based boundary element be analysis the optimal parameter is determined so that the amount of storage and computational work is minimized without reducing the accuracy of the be solution in the present study the beylkin type truncation scheme is used in the matrix assembly to avoid unnecessary integration concerning the truncated entries of a coefficient matrix a priori estimation of the matrix entries is introduced and thus the truncated entries are determined twice before and after matrix assembly the optimal threshold parameter is set based on the equilibrium of the truncation and discretization errors these errors are estimated in the residual sense for laplace problems the discretization error is in particular indicated with the potential s contribution c to the residual norm r used in error estimation for mesh adaptation since the normalized residual norm c u u the potential components of be solution cannot be computed without main be analysis the discretization error is estimated by the approximate expression constructed through subsidiary be calculation with smaller degree of freedom dof the matrix compression using the proposed optimal threshold parameter enables us to generate a sparse matrix with o n 1 7 0 1 non zero entries although the quasi optimal memory requirements and complexity are not attained the compression rate of a few per cent can be achieved for n 1000

multigrid solution of the two dimensional euler equations on unstructured triangular meshes a multigrid algorithm has been developed to accelerate the convergence of the euler equations to a steady state on unstructured triangular meshes the method operates on a sequence of coarse and fine unstructured meshes and assumes no relation exists between the various meshes a tree search algorithm is used to efficiently identify regions of overlap between coarse and fine grid cells the multigrid method is applied to two different discretizations of the euler equations and results about multi element airfoils are presented for both discretization schemes convergence is accelerated by an order of magnitude resulting in convergence rates comparable to those obtained with structured multigrid algorithms

reasoning under minimal upper bounds in propositional logic reasoning from the minimal models of a theory as fostered by circumscription is in the area of artificial intelligence an important method to formalize common sense reasoning however as it appears minimal models may not always be suitable to capture the intuitive semantics of a knowledge base aiming intuitively at an exclusive interpretation of disjunctions of atoms i e if possible then assign at most one of the disjuncts the value true in a model in this paper we consider an approach which is more lenient and also admits non minimal models such that inclusive interpretation of disjunction also may be possible in cases where minimal model reasoning adopts an exclusive interpretation nonetheless in the spirit of minimization the approach aims at including only positive information that is necessary this is achieved by closing the set of admissible models of a theory under minimal upper bounds in the set of models of the theory which we refer to as curbing we demonstrate this method on some examples and investigate its semantical and computational properties we establish that curbing is an expressive reasoning method since the main reasoning tasks are shown to be pspace complete on the other hand we also present cases of lower complexity and in particular cases in which the complexity is located just as for ordinary minimal model reasoning at the second level of the polynomial hierarchy or even below

algebraic multigrid for stabilized finite element discretizations of the navier stokes equations abstract an algebraic multigrid method for the solution of stabilized finite element discretizations of the euler and navier stokes equations on generalized unstructured grids is described the method is based on an elemental agglomeration multigrid strategy employing a semi coarsening scheme designed to reduce grid anisotropy the viscous terms are discretized in a consistent manner on coarse grids using an algebraic galerkin coarse grid approximation in which higher order grid transfer operators are constructed from the underlying triangulation however the combination of higher order transfer operators and galerkin rediscretization diminishes the stability of stabilized inviscid operators on coarse grids and a modification is proposed to alleviate this problem a generalized line implicit relaxation scheme is also described where the lines are constructed to follow the direction of strongest coupling applications are demonstrated for convection diffusion euler and laminar navier stokes the results show that the convergence rate is largely unaffected by mesh size over a wide range of reynolds peclet numbers

high order flux correction finite difference schemes for strand grids a novel high order method combining unstructured flux correction along body surfaces and high order finite differences normal to surfaces is formulated for unsteady viscous flows on strand grids the flux correction algorithm is applied in each unstructured layer of the strand grid and the layers are then coupled together via a source term containing derivatives in the strand direction strand direction derivatives are approximated to high order via summation by parts operators for first derivatives and second derivatives with variable coefficients we show how this procedure allows for the proper truncation error canceling properties required for the flux correction scheme the resulting scheme possesses third order design accuracy but often exhibits fourth order accuracy when higher order derivatives are employed in the strand direction especially for highly viscous flows we prove discrete conservation for the new scheme and time stability in the absence of the flux correction terms results in two dimensions are presented that demonstrate improvements in accuracy with minimal computational and algorithmic overhead over traditional second order algorithms

multiresolution representation in unstructured meshes in this paper we describe techniques to represent data which originate from discretization of functions in unstructured meshes in terms of their local scale components to do so we consider a nested sequence of discretization which corresponds to increasing levels of resolution and we define the scales as the difference in information between any two successive levels we obtain data compression by eliminating scale coefficients which are sufficiently small this capability for data compression can be used to reduce the cost of numerical schemes by solving for the more compact representation of the numerical solution in terms of its significant scale coefficients

reducing belief revision to circumscription and vice versa nonmonotonic formalisms and belief revision operators have been introduced as useful tools to describe and reason about evolving scenarios both approaches have been proven effective in a number of different situations however little is known about their relationship previous work by winslett has shown some correlations between a specific operator and circumscription in this paper we greatly extend winslett s work by establishing new relations between circumscription and a large number of belief revision operators this highlights similarities and differences between these formalisms furthermore these connections provide us with the possibility of importing results in one field into the other one

computing minimal models by partial instantiation abstract unlike sets of definite horn clauses logic programs with disjunctions of atoms in clause heads are often interpreted in terms of minimal models it is also well known that the minimal models of logic programs are closely related to the so called stable models of logic programs with nonmonotonic negation in clause bodies as well as to circumscription methods to compute minimal models of logic programs are becoming increasingly important as an intermediate step in the computation of structures associated with nonmonotonic logic programs however to date all these techniques have been restricted to the case of propositional logic programs which means that an ordinary disjunctive logic program must be grounded out prior to computation grounding out in this manner leads to a combinatorial explosion in the number of clauses and hence is unacceptable in this paper we show how given any method m which correctly computes the set of minimal models of a propositional logic program we can develop a strategy to compute truth in a minimal model of a disjunctive logic program p the novel feature of our method is that it works on an instantiate by need basis and thus avoids unnecessary grounding

a new method for coarsening tetrahedral meshes summary to coarsen a mesh we usually remove a set of selected nodes one by one currently the basic operation used to remove a node is edge collapsing which does not perform well when applied to handling narrow regions in a tetrahedron mesh and could produce low quality elements or even fail to give valid results to overcome the drawbacks of edge collapsing we present a new node removal operator created by revising a topological transformation called small polyhedron reconnection spr this new operator can guarantee success if the cavity that forms after a node is removed is meshable and it produces higher quality results and keeps the nodes unmoved which is preferred for applications such as multigrid hierarchies in addition two other aspects of mesh coarsening that determine whether a node should be removed and the sequence in which to remove the selected nodes are also studied our strategy consists of constructing a coarse node set using the sphere packing method and removing the nodes in a reversed kd tree sequence the excellent performance of the new method is demonstrated by applying it to examples of adaptive meshing and multigrid hierarchy creation and comparing the results to those of the edge collapsing method

rapid solution of integral equations of classical potential theory an algorithm is described for rapid solution of classical boundary value problems dirichlet an neumann for the laplace equation based on iteratively solving integral equations of potential theory cpu time requirements for previously published algorithms of this type are proportional to n2 where n is the number of nodes in the discretization of the boundary of the region the cpu time requirements for the algorithm of the present paper are proportional to n making it considerably more practical for large scale problems

on solving first kind integral equations using wavelets on a bounded interval the conventional method of moments mom when applied directly to integral equations leads to a dense matrix which often becomes computationally intractable to overcome the difficulties wavelet bases have been used previously which lead to a sparse matrix the authors refer to mom with wavelet bases as wavelet mom there have been three different ways of applying the wavelet techniques to boundary integral equations 1 wavelets on the entire real line which requires the boundary conditions to be enforced explicitly 2 wavelet bases for the bounded interval obtained by periodizing the wavelets on the real line and 3 wavelet like basis functions furthermore only orthonormal on bases have been considered the present authors propose the use of compactly supported semi orthogonal so spline wavelets specially constructed for the bounded interval in solving first kind integral equations they apply this technique to analyze a problem involving 2d em scattering from metallic cylinders it is shown that the number of unknowns in the case of wavelet mom increases by m 1 as compared to conventional mom where m is the order of the spline function results for linear m 2 and cubic m 4 splines are presented along with their comparisons to conventional mom results it is observed that the use of cubic spline wavelets almost diagonalizes the matrix while maintaining less than 1 5 of relative normed error the authors also present the explicit closed form polynomial representation of the scaling functions and wavelets

on the use of wavelet expansions in the method of moments em scattering an approach which incorporates the theory of wavelet transforms in method of moments solutions for electromagnetic wave interaction problems is presented the unknown field or response is expressed as a twofold summation of shifted and dilated forms of a properly chosen basis function which is often referred to as the mother wavelet the wavelet expansion can adaptively fit itself to the various length scales associated with the scatterer by distributing the localized functions near the discontinuities and the more spatially diffused ones over the smooth expanses of the scatterer the approach is thus best suited for the analysis of scatterers which contain a broad spectrum of length scales ranging from a subwavelength to several wavelengths using a galerkin method and subsequently applying a threshold procedure the moment method matrix is rendered sparsely populated the structure of the matrix reveals the localized scale fitting distribution long before the matrix equation is solved the performance of the proposed discretization scheme is illustrated by a numerical study of electromagnetic coupling through a double slot aperture

wavelet galerkin algorithms for boundary integral equations the implementation of a fast wavelet based galerkin discretization of second kind integral equations on piecewise smooth surfaces gamma subset ir 3 is described it allows meshes consisting of triangles as well as quadrilaterals the algorithm generates a sparse approximate stiffness matrix with cn o n log n 2 nonvanishing entries in o n log n 4 operations where n is the number of degrees of freedom on the boundary while essentially retaining the asymptotic convergence rate of the full galerkin scheme a new proof of the matrix compression estimates is given based on derivative free kernel estimates the condition number of the sparse stiffness matrices is bounded independently of the meshwidth the data structure containing the compressed stiffness matrix is described in detail it requires o cn memory and can be set up in o cn operations numerical experiments show that the asymptotic performance estimates apply for moderate n problems with n 106 degrees of freedom were computed in core on a workstation the impact of various parameters in the compression scheme on the performance and the accuracy of the algorithm is studied

a hybrid wavelet expansion and boundary element analysis of electromagnetic scattering from conducting objects a new wavelet approach is presented for treating the two dimensional electromagnetic scattering problems over curved computation domains the wavelet expansion method in combination with the boundary element method bem is applied to solve the integral equation for the unknown surface current the unknown surface current is expanded in terms of a basis derived from a periodic orthogonal wavelet in interval 0 1 the geometrical representation of the bem is employed to establish the map between the curved computation domain and the interval 0 1 this technique exhibits the advantages of both the wavelet expansion method and the boundary element method sparse matrix system and accurately modeling of curved surfaces comparisons of the results from the new technique with the moment method solutions the analytical solutions or the data in previous publications are provided good agreements are observed

three dimensional unstructured adaptive multigrid scheme for the euler equations we present a solution adaptive multigrid scheme for the three dimensional euler equations the procedure begins with an initial coarse mesh and enriches this mesh by h refinement in regions of high solution gradient this adaptive procedure is used to generate the multigrid levels required by the solver new boundary nodes are added in a way to reflect the underlying surface representation of the geometry the h refinement procedure is extremely fast and results in a scheme where only a small percentage of the overall cpu time is spent in the meshing and refinement part of the algorithm the multigrid flow solver typically reduces the cpu time by an order of magnitude over the same case without multigrid

computing circumscriptive databases i theory and algorithms abstract though circumscription was introduced by mccarthy over a decade ago there has been relatively little work on algorithms for computing circumscriptive databases in this paper we develop algorithms to compute the preferred models of circumscriptive databases at compile time using mixed integer linear programming techniques two advantages of this bottom up approach are that it makes efficient re use of previous computations and it provides much faster run time performance some other advantages of using linear programming to automate deduction at compile time are that its re optimization facilities elegantly accommodate database updates and also that it leads to a completely declarative formulation in which ordering of rules and literals in rule bodies plays no real role finally we plan to use a standard relational database system as our run time environment this should yield relatively fast run time processing and provide a more expressive query language in which aggregates and the like can be expressed easily

fast wavelet transforms and numerical algorithms i a class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices in contrast the methods presented here are based on the recently developed theory of wavelets and are applicable to all calderon zygmund and pseudo differential operators the algorithms of this paper require order o n or o n log n operations to apply an n n matrix to a vector depending on the particular operator and the version of the algorithm being used and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here

eliminating the fixed predicates from a circumscription abstract parallel predicate circumscription is the primary circumscriptive technique used in formalizing commonsense reasoning in this paper we present a direct syntactic construction for transforming any parallel predicate circumscription using fixed predicates into an equivalent one which does not thus we show that predicate circumscription is no more expressive with fixed predicates than without we extend this result to prioritized circumscription these results are expected to be useful for comparing circumscription to other nonmonotonic formalisms such as autoepistemic logic and assumption based truth maintenance and for implementing fixed predicates

an efficient method for eliminating varying predicates from a circumscription abstract circumscription appears to be the most powerful and well studied technique used in formalizing common sense reasoning the general form of predicate circumscription allows for fixed and varying floating predicates we show that the inference problem under this form of circumscription is efficiently reducible to inferencing under circumscription without varying predicates in fact we transform this problem even into circumscription without fixed and varying predicates that is where all predicates are minimized thus any theorem prover or algorithm for inferencing under circumscription without fixed and varying predicates is able to handle inferencing under the general form of predicate circumscription as a consequence algorithms that compute circumscription for an inference task can be simplified

algebraic turbulence modeling for adaptive unstructured grids algebraic turbulence models are quite common in flow numerical simulations their simplicity and low computation cost as well as their applicability to specific classes of flows have made them attractive compared to the more expensive multiple equation models adaptive unstructured grid algorithms have become quite popular over the last years due to their flexibility in treating complex geometries as well their high resolution capability for local flow phenomena however application of algebraic turbulence models with unstructured grids proves to be nontrivial the difficulties associated with implementation of those models with such grids have generally impeded use of unstructured grids for turbulent flow simulations this paper presents a novel method of implementing an algebraic turbulence model with embedded unstructured grids the baldwinlomax model was chosen in order to test the implementation modifications to the application of the original model on structured grids are suggested as well comparisons with both experiments and other numerical simulations are employed in order to evaluate accuracy of the implementation method onsiderable progress has been made in the development of numerical methods for the solution of the navier stokes equations however most of those methods are impractical for complicated flows in a design environment the primary reason is poor efficiency which makes it difficult to obtain accurate results very fine resolution is needed which results in long computation times even with the use of available supercomputers in general the selection of the equations to be solved the scheme and the grid all are determined a priori by the user before starting the solution procedure and quite often some and even all of these factors must be modified by the user in order to improve the results the robustness of current numerical schemes as well as present computer capabilities has recently allowed a dramatic change in this philosophy general algorithms have been developed that are flexible enough to adaptively adjust those parameters during the solution procedure without intervention by the user one of the most efficient adaptive methods consists of local refinement by dividing grid cells an initially coarse grid is embedded in regions with large flow gradients e g boundary layers shocks wakes etc the algorithm senses high gradient regions and automatically divides grid cells in such regions this approach has been used for the resolution of shocks in flowfields described by euler equations 1 2 the embedded scheme was used as part of an adaptive algorithm for turbulent flows 3 6 algebraic turbulence models are quite common in aerodynamics numerical simulations their simplicity and low computation cost as well as their accuracy for specific classes of flows have made them attractive compared to the more expensive multiple equation models however such models require nonlocal information that characterizes an entire shearlayer profile the adaptive algorithm results in an unstructured mesh which is a major issue in the implementation of an algebraic turbulence model grid interfaces frequently interrupt normal to wall meshlines and therefore models that employ information from an entire shear layer profile cannot be applied similarly in the case of triangular meshes such normal grid lines generally do not exist a new method of

finite element euler computations in three dimensions an explicit finite element solution procedure for the three dimensional euler equations is presented the solution domain is automatically meshed using a tetrahedral mesh generator which is an extension of our previous two dimensional work several examples are included to illustrate the performance of the generator and solver an adaptive mesh regeneration procedure is used for the first time in three dimensions

multicloud multigrid convergence with a meshless operator the primary objective of this work is to develop and test a new convergence acceleration technique we call multicloud multicloud is well founded in the mathematical basis of multigrid but relies on a meshless operator on coarse levels the meshless operator enables extremely simple and automatic coarsening procedures for arbitrary meshes using arbitrary fine level discretization schemes the performance of multicloud is compared with established multigrid techniques for structured and unstructured meshes for the euler equations on two dimensional test cases results indicate comparable convergence rates per unit work for multicloud and multigrid however because of its mesh and scheme transparency multicloud may be applied to a wide array of problems with no modification of fine level schemes as is often required with agglomeration techniques the implication is that multicloud can be implemented in a completely modular fashion allowing researchers to develop fine level algorithms independent of the convergence accelerator for complex three dimensional problems

robust multigrid methods for nonsmooth coefficient elliptic linear systems we survey the literature on robust multigrid methods which have been developed in recent years for solving second order elliptic pdes with nonsmooth coefficients we highlight the key ideas of designing robust multigrid methods which are able to recover the usual multigrid efficiency for nonsmooth coefficient pdes on structured or unstructured grids in particular we shall describe various approaches for constructing the interpolation and the smoothing operators and the coarse grid points selections

preprocessing of intractable problems some computationally hard problems e g deduction in logical knowledge bases are such that part of an instance is known well before the rest of it and remains the same for several subsequent instances of the problem in these cases it is useful to preprocess off line this known part so as to simplify the remaining on line problem in this paper we investigate such a technique in the context of intractable i e np hard problems recent results in the literature show that not all np hard problems behave in the same way for some of them preprocessing yields polynomial time on line simplified problems we call them compilable while for other ones their compilability implies some consequences that are considered unlikely our primary goal is to provide a sound methodology that can be used to either prove or disprove that a problem is compilable to this end we define new models of computation complexity classes and reductions we find complete problems for such classes completeness meaning they are the less likely to be compilable we also investigate preprocessing that does not yield polynomial time on line algorithms but generically decreases complexity this leads us to define hierarchies of compilability that are the analog of the polynomial hierarchy a detailed comparison of our framework to the idea of parameterized tractability shows the differences between the two approaches

agglomeration multigrid for the three dimensional euler equations a multigrid procedure that makes use of coarse grids generated by the agglomeration of control volumes is advocated as a practical approach for solving the three dimensional euler equations on unstructured grids about complex configurations it is shown that the agglomeration procedure can be tailored to achieve certain coarse grid properties such as the sizes of the coarse grids and aspect ratios of the coarse grid cells the agglomeration is done as a preprocessing step and runs in linear time the implications for multigrid of using arbitrary polyhedral coarse grids are discussed the agglomeration multigrid technique compares very favorably with existing multigrid procedures both in terms of convergence rates and elapsed times the main advantage of the present approach is the ease with which coarse grids of any desired degree of coarseness may be generated in three dimensions without being constrained by considerations of geometry inviscid flows over a variety of complex configurations are computed using the agglomeration multigrid strategy

on compact representations of propositional circumscription we prove that unless the polynomial hierarchy collapses at the second level the size of a purely propositional representation of the circumscription circ t of a propositional formula t grows faster than any polynomial as the size of t increases we then analyze the significance of this result in the related field of closed world reasoning

applications of circumscription to formalizing common sense knowledge we present a new and more symmetric version of the circumscription method of nonmonotonic reasoning first described in mccarthy 1980 and some applications to formalizing common sense knowledge the applications in this paper are mostly based on minimizing the abnormality of different aspects of various entities included are nonmonotonic treatments of is a hierarchies the unique names hypothesis and the frame problem the new circumscription may be called formula circumscription to distinguish it from the previously defined domain circumscription and predicate circumscription a still more general formalism called prioritized circumscription is briefly explored

wavelet approximations for first kind boundary integral equations on polygons an elliptic boundary value problem in the interior or exterior of a polygon is transformed into an equivalent first kind boundary integral equation its galerkin discretization with n degrees of freedom on the boundary with spline wavelets as basis functions is analyzed a truncation strategy is presented which allows to reduce the number of nonzero elements in the stiffness matrix from o n 2 to o n log n entries the condition numbers are bounded independently of the meshwidth it is proved that the compressed scheme thus obtained yields in o n log n 2 operations approximate solutions with the same asymptotic convergence rates as the full galerkin scheme in the boundary energy norm as well as in interior points numerical examples show the asymptotic error analysis to be valid already for moderate values of n

an algorithm to compute circumscription abstract mccarthy s theory of circumscription appears to be the most powerful among various formalizations of nonmonotonic reasoning designed to handle incomplete and negative information in knowledge representation systems in this paper we describe a query answering algorithm for circumscriptive theories the closed world assumption cwa and its generalizations the generalized closed world assumption gcwa and the extended closed world assumption ecwa can be considered as special forms of circumscription consequently our algorithm also applies to answering queries in theories using the closed world assumption and its generalizations similarly since prioritized circumscription is equivalent to a conjunction of parallel circumscriptions our algorithm can be used to answer queries in theories circumscribed by prioritized circumscription