The complexity of the temporal logic with “until” over general linear time

It is shown that the decision problem for the temporal logic with the strict until operator over general linear time is PSPACE-complete. This shows that it is no harder to reason with arbitrary linear orderings than with discrete linear time temporal logics. New techniques are used to give a PSPACE procedure for the logic.     

Queries on ontologies with temporal dependences on Allen’s extended interval logic

This paper introduces Allen’s extended interval logic whose sentences are Boolean combinations of sentences of Allen’s interval logic with metric constraints on time points. For this extended logic, a deduction method based on analytic tableaux is defined. This method is used for answering queries on ontologies specified in Allen’s extended interval logic. An example illustrating the applicability of this extended logic to the problem of workflow specification is presented.     

A modal contrastive logic: The logic of ‘but’

In this paper we present a modal approach to contrastive logic, the logic of contrasts as these appear in natural language conjunctions such as but. We use a simple modal logic, which is an extension of the well-knownS5 logic, and base the contrastive operators proposed by Francez in [2] on the basic modalities that appear in this logic. We thus obtain a logic for contrastive operators that is more in accord with the tradition of intensional logic, and that, moreover — we argue — has some more natural properties. Particularly, attention is paid to nesting contrastive operators. We show that nestings of but give quite natural results, and indicate how nestings of other contrastive operators can be done adequately. Finally, we discuss the example of the Hangman's Paradox and some similarities (and differences) with default reasoning. But but us no buts, as they say.Also partially supported by Nijmegen University, Toernooiveld, 6525 ED Nijmegen, The Netherlands.     

The B-rich side of the B–C phase diagram

The melting behavior of ß-boron at the boron-rich side of the B–C binary phase diagram is a long standing question whether eutectic or peritectic. Floating zone experiments have been employed to determine the melting type on a series of C-containing feed-rods prepared by powder metallurgy and sinter techniques. Melting point data as a function of carbon-content clearly yielded a peritectic reaction isotherm: L+B_4+δC=(ßB). The partition coefficient of carbon is ~2.6. The experimental melting point data were used to improve the existing thermodynamic modeling of the system B–C. Relative to the thermodynamically accepted melting point of pure ßB (T_M=2075 °C), the calculated reaction isotherm is determined at 2100.6 °C, a peritectic point at 0.75 at% C and a maximum solid solubility of 1.43 at% C in (ßB) at reaction temperature. With the new melting data the refractory system Hf–B–C has been recalculated and the liquidus surface is presented. The influence of the melting behavior of (ßB) on the phase reactions in the B-rich corner of M–B–C diagrams will be discussed and demonstrated in case of the Ti–B–C system.     

Is the success of fuzzy logic really paradoxical?: Toward the actual logic behind expert systems

The formal concept of logical equivalence in fuzzy logic, while theoretically sound, seems impractical. The misinterpretation of this concept has led to some pessimistic conclusions. Motivated by practical interpretation of truth values for fuzzy propositions, we take the class (lattice) of all subintervals of the unit interval [0, 1] as the truth value space for fuzzy logic, subsuming the traditional class of numerical truth values from [0, 1]. The associated concept of logical equivalence is stronger than the traditional one. Technically, we are dealing with much smaller set of pairs of equivalent formulas, so that we are able to check equivalence algorithmically. The checking is done by showing that our strong equivalence notion coincides with the equivalence in logic programming. © 1996 John Wiley & Sons, Inc.     

The temporal aspects of the evidence-based influence maximization on social networks†

The influence maximization problem selects a set of seeds to initiate an optimal cascade of decisions. This paper uses parallel cascade evidence-based diffusion modelling, which views influence as a consequence of the evidence exchange between the connected actors, to investigate the temporal aspects of the social cascade propagation and effective time horizon for long-term campaign planning. Mixed-integer programming is used to explore the optimal timing of evidence injection and the ensuing network behaviour. The paper defines the notion of mid-term and long-term cascade stability and analyses the dynamics of social cascades for varied evidence discount factor values. This exploration reveals that the time horizon setting affects the optimal placement of seeds in a given problem and, hence, has to be set in a way to reflect the decision-maker's short-term or long-term goals. A Cplex-based heuristic algorithm is developed to iteratively find such a preferable cascade stability time horizon. Moreover, a conducted fractional factorial experiment reveals that the forgetfulness effect and the presence of competition significantly affect the cascade persistence. Somewhat counter-intuitively, it is discovered that a strong positive evidence can become more persistent (long-lasting) in the presence of weak opposing evidence.     

The dark side of the boon? Credibility,selective exposure and the proliferation of online sources of political information

While the media industry may consider credibility its most valuable asset, scholars suggest there is a potential “dark side” to credibility: Perceptions of credibility of a source lead to selective exposure and selective avoidance, and both lead to increased fragmentation and polarization of social and political views. The link between credibility and selective exposure and avoidance has not received much academic attention, therefore this study employed a survey of politically interested Internet users during the 2008 presidential campaign to test the influence of credibility and reliance on selective exposure and avoidance after controlling for demographic and political factors. This study found little evidence of a dark side to credibility. Respondents who judge blogs as credible search for information that supports their point of view, as well as challenges their opinions.     

Implementing the ‘Fool's model’ of combinatory logic

This paper studies Fool's models of combinatory logic, and relates them to Hindley's D-completeness problem. A fool's model is a family of sets of formulas, closed under condensed detachment. Alternatively, it is a model ofCL in naive set theory. We examine Resolution; and the P-W problem. A sequel shows T is D-complete; also, its extensions. We close with an implementation FMO of these ideas.     

The evolution of periodic waves of the coupled nonlinear Schrödinger equations

Systems of coupled nonlinear Schrödinger equations (CNLS) arise in several branches of physics, e.g., hydrodynamics and nonlinear optics. The Hopscotch method is applied to solve CNLS numerically. The algorithm is basically a finite difference method but with a special procedure for marching forward in time. The accuracy of the scheme is ensured as the system is proved to satisfy certain conserved quantities. Physically, the goal is to study the effects of an initial phase difference on the evolution of periodic, plane waves. The outcome will depend on the precise nature of the cubic nonlinearity, or in physical terms, the nature of polarization in optical applications.     

Approximate syllogisms – on the logic of everyday life

Since Aristotle it is recognised that a valid syllogism cannot have two particular premises. However, that is not how a lay person sees it; at least as long as the premises read many, most etc, instead of a plain some. The lay people are right if one considers that these syllogisms do not have strict but approximate (Zadeh) validity. Typically there are only particular premises available in everyday life and one is dependent on such syllogisms. – Some rules on the usage of particular premises are given below.     

The use of multi‐temporal Landsat images for the change detection of the coastal zone near Hurghada,Egypt

A Landsat 5 Thematic Mapper (TM) image of 1987 and a Landsat 7 Enhanced Thematic Mapper Plus (ETM+) image of 2000 were used to examine changes in land use/land cover (LULC) around Hurghada, Egypt, and changes in the composition of coral reefs offshore. Prior to coral reef bottom‐type classification, the radiance values were transformed to depth‐invariant bottom indices to reduce the effect of the water column. Subsequently, a multi‐component change detection procedure was applied to these indices to define changes. Preliminary results showed significant changes in LULC during the period 1987–2000 as well as changes in coral reef composition. Direct impacts along the coastline were clearly shown, but it was more difficult to link offshore changes in coral reef composition to indirect impacts of the changing LULC. Further research is needed to explore the effects of the different image‐processing steps, and to discover possible links between indirect impacts of LULC changes and changes in the coral reef composition.     

The Pötzl Effect: Corroboration of a Cybernetic Hypothesis

The deferred-updating cybernetic theory of the mind/brain information-processing system was devised to explain the purpose of sleep [2]. This theory predicts the existence of an intermediate memory, the circadian memory [14]. This is different from, and auxiliary to, both short-term and long-term mem⊙ry. One of the prime functions of circadian memory, according to the theory, is to store incoming information until it can be integrated into long-term memory. This takes place during sleep, the purpose of which, from an information-processing point of view, is to allow the system to go off-line to accomplish the integration.     

Stabilization of Rössler chaotic dynamical system using fuzzy logic control algorithm

This paper proposes a fuzzy logic control algorithm (FLCA) to stabilize the Rössler chaotic dynamical system. The fuzzy logic control system is based on a Takagi-Sugeno-Kang inference engine and the stability analysis in the sense of Lyapunov is carried out using Lyapunov’s direct method. The new FLCA is formulated to offer sufficient inequality stability conditions. The asymptotic complexity of our algorithm is analyzed and proved to be lower in comparison with that of linear matrix inequality-based FLCAs. A set of simulation results illustrates the effectiveness of the proposed FLCA.     

The focusing nonlinear Schrödinger equation: Effect of the coupling to a low frequency field

The main properties of the focusing nonlinear Schrödinger equation for a multidimensional wavepacket envelop are reviewed. The coupling to a mean field or to low frequency acoustic waves stirred by the wavepacket is analyzed.     

The Efficient Computation of Certain Determinants Arising in the Treatment of Schrödinger's Equations

The solution of Schrödinger's equation leads to a high number N of independent variables. Furthermore, the restriction to (anti)symmetric functions implies some complications. We propose a sparse-grid approximation which leads to a set of non-orthogonal basis. Due to the antisymmetry, scalar products are expressed by sums of N×N-determinants. Because of the sparsity of the sparse-grid approximation, these determinants can be reduced from N×N to a much smaller size K×K. The sums over all permutations reduce to the quantities det _K (α₁,…,α _K ):=∑≤i ₁,i ₂,…,i _K ≤Ndet(a _iα ,i _β ^(αβ))_{α,β=1,…, K} to be determined, where a _i , _j ^(αβ) are certain one-dimensional scalar products involving (sparse-grid) basis functions ?α_β. We propose a method to evaluate this expression such that the asymptotics of the computational cost with respect to N is O(N ³) for fixed K, while the storage requirements increase only with the factor N ². Furthermore, we describe a parallel version (N processors) with full speed up.     

The Hidden Face of the Vault: Unveiling The Expression of the Avant-Garde Through the Use of the Sphere in Teposcolula’s Open Chapel

Benjamin Ibarra-Sevilla examines the role of the sphere in the Open Chapel built in San Pedro y San Pablo Teposcolula during sixteenth century. This unique Mexican building contains a complex ribbed vault designed on a hexagonal plan forming a semi-spherical dome. The investigation examines the use of the sphere in this structure in light of the design precepts practiced during the Renaissance in Europe. Furthermore, the study finds the connections of these precepts with a mathematical solution to the sphere based on convex shapes theories. By revealing the intricacies of the underlying geometry applied to design this building, this text aims to demonstrate the scholastic and architectural relevance of this refined Mexican piece of architecture.     

Möbius–deBruijn: The product of Möbius cube and deBruijn digraph

Möbius cube and deBruijn digraph have been proved to be two of the most popular interconnection architectures, due to their desirable properties. Some of the attractive properties of one, however, are not found in the other. The Möbius–deBruijn architecture, proposed in this paper, is the product of Möbius cube and deBruijn digraph, which is a combination of the two architectures. It employs the Möbius cube as a unit cluster and connects many such clusters by means of given number of parallel deBruijn digraphs. Consequently, the Möbius–deBruijn provides some of the desirable properties of both the architectures, such as the flexibility in terms of embedding of parallel algorithms, the high level of fault-tolerant, and the efficient inter-cluster communication. The proposed architecture also possesses the logarithmic diameter, the optimal connectivity, and the simple routing mechanism amenable to network faults. The methodology to construct the Möbius–deBruijn can apply to the product of deBruijn digraph and other hypercube-like networks, and also applies to the product of Kautz digraph and hypercube-like networks.     

The root and Bell’s disk iteration methods are of the same error propagation characteristics in the simultaneous determination of the zeros of a polynomial,Part II: Round-off error analysis by use of interval arithmetic

In Part I (Ikhile, 2008) [4], it was established that the root and Bell’s disk/point iteration methods with or without correction term are of the same asymptotic error propagation characteristics in the simultaneous determination of the zeros of a polynomial. This concluding part of the investigation is a study in round-offs, its propagation and its effects on convergence employing interval arithmetic means. The purpose is to consequently draw attention on the effects of round-off errors introduced from the point arithmetic part, on the rate of convergence of the generalized root and Bell’s simultaneous interval iteration algorithms and its enhanced modifications introduced in Part I for the numerical inclusion of all the zeros of a polynomial simultaneously. The motivation for studying the effects of round-off error propagation comes from the fact that the readily available computing devices at the moment are limited in precision, more so that accuracy expected from some programming or computing environments or from these numerical methods are or can be machine dependent. In fact, a part of the finding is that round-off propagation effects beyond a certain controllable order induces overwhelmingly delayed or even a severely retarded convergence speed which manifest glaringly as poor accuracy of these interval iteration methods in the computation of the zeros of a polynomial simultaneously. However, in this present consideration and even in the presence of overwhelming influence of round-offs, we give conditions under which convergence is still possible and derive the error/round-off relations along with the order/$R$-order of convergence of these methods with the results extended to similar interval iteration methods for computing the zeros of a polynomial simultaneously, especially to Bell’s interval methods for refinement of zeros that form a cluster. Our findings are instructive and quite revealing and supported by evidence from numerical experiments. The analysis is preferred in circular interval arithmetic.