Interpretations of open default theories in non-monotonic logics

It is shown that the translation of an open default into a modal formula x(L(x)LM ₁ (x)...LM _m (x)w(x)) gives rise to an embedding of open default systems into non-monotonic logics.     

A Delay-Averaged Logistic Model

For the equation x(t) = x(t) (1-(1/) _t-- ^t- x(u)du), > 0, > 0, > 0, conditions for the stability of a nonzero stationary solution under small perturbations are determined.     

Utilizing deontic operators in information systems specification

One major task in requirements specification is to capture the rules relevant to the problem at hand. Declarative, rule-based approaches have been suggested by many researchers in the field. However, when it comes to modeling large systems of rules, not only for the behavior of the computer system but also for the organizational environment surrounding it, current approaches have problems with limited expressiveness, flexibility, and poor comprehensibility. Hence, rule-based approaches may benefit from improvements in two directions: (1) improvement of the rule languages themselves and (2) better integration with other, complementary modeling approaches.In this article, both issues are addressed in an integrated manner. The proposal is presented in the context of the Tempora project on rule-based information systems development, but has also been integrated with PPP. Tempora has provided a rule language based on an executable temporal logic working on top of a temporal database. The rule language is integrated with static (ER-like) and dynamic (SA/RT-like) modeling approaches. In the current proposal, the integration with complementary modeling approaches is extended by including organization modeling (actors, roles), and the expressiveness of the rule language is increased by introducing deontic operators and rule hierarchies. The main contribution of the article is not seen as any one of the above-mentioned extensions, but as the resulting comprehensive modeling support. The approach is illustrated by examples taken from an industrial case study done in connection with Tempora.C. List of Symbols Subset of set - Not subset of set - Element of set - Not element of set - Equivalent to - Not equivalent to - ¬ Negation - Logical and - Logical or - Implication - Sometime in past - Sometime in future - Always in past - Always in future - Just before - Just after - u Until - s Since - Trigger - Condition - _s State condition - Consequence - _a Action - _s State - Role - Actor - ¬ - General deontic operator - O Obligatory - R Recommended - P Permitted - D Discouraged - F Forbidden - (/–) General rule - t _R Real time - t _M Model time     

Extremal Relations between Additive Loss Functions and the Kolmogorov Complexity

Conditions are presented under which the maximum of the Kolmogorov complexity (algorithmic entropy) K(₁... _N ) is attained, given the cost f( _i ) of a message ₁... _N . Various extremal relations between the message cost and the Kolmogorov complexity are also considered; in particular, the minimization problem for the function f( _i ) – K(₁... _N ) is studied. Here, is a parameter, called the temperature by analogy with thermodynamics. We also study domains of small variation of this function.     

States and the free orthogonality monoid

Let (X, #) be an orthogonality space such that the lattice C(X, #) of closed subsets of (X, #) is orthomodular and let (, ) denote the free orthogonality monoid over (X, #). Let C₀(, ) be the subset of C(, ), consisting of all closures of bounded orthogonal sets. We show that C₀(, ) is a suborthomodular lattice of C(, ) and we provide a necessary and sufficient condition for C₀(, ) to carry a full set of dispersion free states.The work of the second author on this paper was supported by National Science Foundation Grant GP-9005.     

Context-free text grammars

A text is a triple=(, ₁, ₂) such that is a labeling function, and ₁ and ₂ are linear orders on the domain of ; hence may be seen as a word (, ₁) together with an additional linear order ₂ on the domain of . The order ₂ is used to give to the word (, ₁) itsindividual hierarchical representation (syntactic structure) which may be a tree but it may be also more general than a tree. In this paper we introducecontext-free grammars for texts and investigate their basic properties. Since each text has its own individual structure, the role of such a grammar should be that of a definition of a pattern common to all individual texts. This leads to the notion of ashapely context-free text grammar also investigated in this paper.     

Schedulers for larger classes of pinwheel instances

The pinwheel is a hard-real-time scheduling problem for scheduling satellite ground stations to service a number of satellites without data loss. Given a multiset of positive integers (instance)A={a₁,..., a_n}, the problem is to find an infinite sequence (schedule) of symbols from {1,2,...,n} such that there is at least one symboli within any interval of a_i symbols (slots). Not all instancesA can be scheduled; for example, no successful schedule exists for instances whose density,(A)= _i ⁱ (l/a_i), is larger than 1. It has been shown that all instances whose densities are less than a 0.5 density threshold can always be scheduled. If a schedule exists, another concern is the design of a fast on-line scheduler (FOLS) which can generate each symbol of the schedule in constant time. Based on the idea of integer reduction, two new FOLSs which can schedule different classes of pinwheel instances, are proposed in this paper. One uses single-integer reduction and the other uses double-integer reduction. They both improve the previous 0.5 result and have density thresholds of 13/20 and2/3, respectively. In particular, if the elements inA are large, the density thresholds will asymptotically approach In 2 and 1/R2, respectively.This research was supported in part by ONR Grant N00014-87-K-0833, and was done while Francis Chin was visiting the Computer Science Program, The University of Texas at Dallas, Richardson, TX 75083, USA.     

Mesh Selection for a Nearly Singular Boundary Value Problem

In this paper, we investigate the numerical solution of a model equation u _xx = exp(– ) (and several slightly more general problems) when 1 using the standard central difference scheme on nonuniform grids. In particular, we are interested in the error behaviour in two limiting cases: (i) the total mesh point number N is fixed when the regularization parameter 0, and (ii) is fixed when N. Using a formal analysis, we show that a generalized version of a special piecewise uniform mesh 12 and an adaptive grid based on the equidistribution principle share some common features. And the optimal meshes give rates of convergence bounded by |log()| as 0 and N is given, which are shown to be sharp by numerical tests.     

A Modular Algorithm for Computing Cohomologies of Lie Algebras and Superalgebras

The paper describes an improved algorithm for computing cohomologies of Lie (super)algebras. The original algorithm developed earlier by the author of this paper is based on the decomposition of the entire cochain complex into minimal subcomplexes. The suggested improvement consists in the replacement of the arithmetic of rational or integer numbers by a more efficient arithmetic of modular fields and the use of the relationship dim H ^k( _p) dimH ^k() between the dimensions of cohomologies over an arbitrary modular field _p = /p and the filed of rational numbers . This inequality allows us to rapidly find subcomplexes for which dimH ^k( _p) > 0 (the number of such subcomplexes is usually not great) using computations over an arbitrary _p and, then, carry out all required computations over in these subcomplexes.     

Unextendible Product Bases and Locally Unconvertible Bound Entangled States

Mutual convertibility of bound entangled states under local quantum operations and classical communication (LOCC) is studied. We focus on states associated with unextendible product bases (UPB) in a system of three qubits. A complete classification of such UPBs is suggested. We prove that for any pair of UPBs S and T the associated bound entangled states _S and _T cannot be converted to each other by LOCC, unless S and T coincide up to local unitaries. More specifically, there exists a finite precision (S,T) > 0 such that for any LOCC protocol mapping _S into a probabilistic ensemble (p, ), the fidelity between _T and any possible final state satisfies F(_T, ) = 1 - (S,T).PACS: 03.65.Bz; 03.67.-a; 89.70+c.     

Separating complexity classes related to bounded alternating ω-branching programs

We develop a theory of communication within branching programs that provides exponential lower bounds on the size of branching programs that are bounded alternating. Our theory is based on the algebraic concept of -branching programs, : , a semiring homomorphism, that generalizes ordinary branching programs, -branching programs [M2] andMOD _p-branching programs [DKMW].Due to certain exponential lower and polynomial upper bounds on the size of bounded alternating -branching programs we are able to separate the corresponding complexity classesN _ba ,co-N _{ba ba} , andMOD _p - _ba ,p prime, from each other, and from that classes corresponding to oblivious linear length-bounded branching programs investigated in the past.     

Linear Interval Tolerance Problem and Linear Programming Techniques

In this paper, we consider the linear interval tolerance problem, which consists of finding the largest interval vector included in ([A], [b]) = {x R ⁿ | A [A], b [b], Ax = b}. We describe two different polyhedrons that represent subsets of all possible interval vectors in ([A], [b]), and we provide a new definition of the optimality of an interval vector included in ([A], [b]). Finally, we show how the Simplex algorithm can be applied to find an optimal interval vector in ([A], [b]).     

On a random Volterra integral equation

Summary Tsokos [12] showed the existence of a unique random solution of the random Volterra integral equation (*)x(t; ) = h(t; ) + _o ^t k(t, ; )f(, x(; )) d, where , the supporting set of a probability measure space (,A, P). It was required thatf must satisfy a Lipschitz condition in a certain subset of a Banach space. By using an extension of Banach's contraction-mapping principle, it is shown here that a unique random solution of (*) exists whenf is (, )-uniformly locally Lipschitz in the same subset of the Banach space considered in [12].     

Two and three-quarter dimensional meshing facilitators

This paper presents generated enhancements for robust two and three-quarter dimensional meshing, including: (1) automated interval assignment by integer programming for submapped surfaces and volumes, (2) surface submapping, and (3) volume submapping. An introduction to the simplex method, an optimization technique of integer programming, is presented. Simplification of complex geometry is required for the formulation of the integer programming problem. A method of i-j unfolding is defined which explains how irregular geometry can be realigned into a simplified form that is suitable for submap interval assignment solutions. Also presented is the processes by which submapping eliminates the decomposition of surface geometry, through a pseudodecomposition process, producing suitable mapped meshes. The process of submapping involves the creation of interpolated virtual edges, user defined vertex types and i-j-k space traversals. The creation of interpolated virtual edges is the method by which submapping automatically subdivides surface geometry. The interpolated virtual edge is formulated according to an interpolation scheme using the node discretization of curves on the surface. User defined vertex types allow direct user control of surface decomposition and interval assignment by modifying i-j-k space traversals. Volume submapping takes the geometry decomposition to a higher level by using mapped virtual surfaces to eliminate decomposition of complex volumes.     

A short note on simultaneous splitting

We show that for any alphabet there is a setL ^* such that ifC is any infinite co-infinite context-free language over , thenL splitsC (i.e., each ofL C,L , C, and is infinite).Preparation of this paper was supported in part by the National Science Foundation under Grant No. MCS77-11360.     

Types with intersection: An introduction

This paper is an informal introduction to the theory of types which use a connective for the intersection of two types and a constant for a universal type, besides the usual connective for function-types. This theory was first devised in about 1977 by Coppo, Dezani and Sallé in the context of-calculus and its main development has been by Coppo and Dezani and their collaborators in Turin. With suitable axioms and rules to assign types to-calculus terms, they obtained a system in which (i) the set of types given to a term does not change under-conversion, (ii) some interesting sets of terms, for example the solvable terms and the terms with normal form, can be characterised exactly by the types of their members, and (iii) the type-apparatus is not so complex as polymorphic systems with quantifier-containing types and therefore probably not so expensive to implement mechanically as these systems.There are in fact several variant systems with different detailed properties. This paper defines and motivates the simplest one from which the others are derived, and describes its most basic properties. No proofs are given but the motivation is shown by examples. A comprehensive bibliography is included.     

On the number of active *-operations needed to compute the discrete Fourier transform

Summary Let M(N) denote the number of active multiplications/divisions needed to compute the discrete Fourier transform of N variables. Winograd showed M(N) O(N). For N a power of two we analyse his method and find M(N)8 N–o(N). Using additional symmetries we improve this to M(N)2N–o(N). We also give a very short proof for M(N)4N-o(N). Finally we show M(N)N – 2 log N.     

Variable Precision Algorithm for the Numerical Computation of the Fermi–Dirac Function ℱj(x) of Order j=−3/2

The purpose of this technical note is to present a piecewise Chebyshev expansion for the numerical computation of the Fermi–Dirac function _–3/2(x), –<x<. The variable precision algorithm we given automatically adjusts the degrees of the Chebyshev expansions so that _–3/2(x) can be efficiently computed to d significant decimal digits of accuracy, for a user specified value of d in the range 1d15.     

Sound and Complete Qualitative Simulation Needs “Quantitative” Filtering

The AI methodology of qualitative reasoning furnishes useful tools to scientists and engineers who need to deal with incomplete system knowledge during design, analysis, or diagnosis tasks. Qualitative simulators have a theoretical soundness guarantee; they cannot overlook any concrete equation implied by their input. On the other hand, the basic qualitative simulation algorithms have been shown to suffer from the incompleteness problem; they may allow non-solutions of the input equation to appear in their output. The question of whether a simulator with purely qualitative input which never predicts spurious behaviors can ever be achieved by adding new filters to the existing algorithm has remained unanswered. In this paper, we show that, if such a sound and complete simulator exists, it will have to be able to handle numerical distinctions with such a high precision that it must contain a component that would better be called a quantitative, rather than qualitative reasoner. This is due to the ability of the pure qualitative format to allow the exact representation of the members of a rich set of numbers.     

Shape optimization of elasto-plastic bodies under plane strains: Sensitivity analysis and numerical implementation

Optimal shape design problems for an elastic body made from physically nonlinear material are presented. Sensitivity analysis is done by differentiating the discrete equations of equilibrium. Numerical examples are included.Notation U ^ad set of admissible continuous design parameters - U _h ^ad set of admissible discrete design parameters - function fromU _h ^ad defining shape of body - _h function fromU _h ^ad defining approximated shape of body - vector of nodal values of _h - { _n} sequence of functions tending to - () domain defined by - K bulk modulus - shear modulus - penalty parameter for contact condition - V() space of virtual displacements in() - V _h(_h) finite element approximation ofV() - J cost functional - J _h discretized cost functional - J algebraic form ofJ _h - (u) stress tensor - e(u) strain tensor - K stiffness matrix - f force vector - b(q) term arising from nonlinear boundary conditions - q vector of nodal degrees of freedom - p vector of adjoint state variables - J Jacobian of isoparametric mapping - |J| determinant ofJ - N vector of shape function values on parent element - L matrix of shape function derivatives on parent element - G matrix of Cartesian derivatives of shape functions - X matrix of nodal coordinates of element - D matrix of elastic coefficients - B strain-displacement matrix - _P part of boundary where tractions are prescribed - _u part of boundary where displacements are prescribed - variable part of boundary - strain invariant