Automated model construction: A logic based approach

Attempts to integrate Artificial Intelligence (AI) techniques into Decision Support Systems (DSS) have received much attention in recent years. Significant among these has been the application of knowledge-based techniques to support various phases of the modeling process. This paper describes a logic based approach to mechanically construct Linear Programming (LP) models from qualitative problem specifications and illustrates it in the context of production, distribution and inventory planning problems. Specifically, we describe the features of a first-order logic based formal language called PM which is at the heart of an implemented knowledge-based tool for model construction. Problems specified in PM define a logic model which is then used to generate problem-specific inferences, and as input to a set of logic programming procedures that perform model construction.     

A new algorithm for summing divergent series Part 2: A two-component Borel summability model

If $\text{S}\text{(}\text{1}\text{n}\text{) ～ Σ}\text{e}{}_{\mathrm{S}}\text{/}\text{n}{}^{\mathrm{s}}$ is a descending series in n, and |e_S| ultimately increases approximately as (2s)!, then the new two-component Borel algorithm, with quadratic terms in the integrands involved, is suggested as a summing technique. The linear equations which arise have been triangulated, so that approximants to the original series are simple to set up and not as subject to round-off error as other approaches.     

A new model for Boolean algebra

This new model for set theory is a graph. It is similar in many ways to a Venn diagram or Karnaugh map, but it does not pose as a rival, merely as an alternative model which may be useful in some contexts. Defined with reference to the duality of lines and points, the graph is a fitting framework in which to display the rich duality of Boolean algebra.

In the first four sections the graph is developed as a natural embodiment of Boolean theory and it is hoped that it will be seen, not as a more computational device but as helpful for demonstrating Boolean theory. The second half of the article is devoted to practical applications. The graph can be applied (and has been applied in school teaching) extensively in set theory, in logic, in probability, in genetics and in switching circuits, but space does not allow the elaboration of all these in detail. So this article concentrates mainly on one of these applications, switching circuits. The graph is used to simplify and minimize logic circuits with techniques different from Karnaugh's and in some instances more comprehensive.     

A new model for record values

A new mathematical model of record values, named confirmed records, is constructed. It is based on the notion of kth record values, which, in turn, is a generalization of ordinary mathematical records and extremal order statistics. Confirmed records are considered for arbitrary k = 1, 2, ... under the assumption that the original random variables X ₁, X ₂, ... are independent and have the same continuous distribution function. For new record values, two representations are obtained in the most important special cases where the original variables have the exponential and the uniform distribution. For uniform and exponential confirmed records, means and variances are found.     

Swedish employment offices: A new model for evaluating effectiveness

We measure how well Swedish employment offices perform in delivering the services required of them by the Swedish government. In contrast to earlier studies we use a dynamic efficiency framework, which allows us to better model the intertemporal nature of these services, explicitly allowing for placements of intermediate nature across periods. Rather than using second stage analysis to assess the effects of varying local labor market conditions and differences in client characteristics on performance, we include a measure of the office’s expected work load directly in the model. This measure, derived from duration analysis, is designed to capture the variation across offices in resources needed before an average individual can obtain employment. It is estimated from the characteristics of all unemployed individual and local labor market conditions.     

A new end-of-auction model for curbing sniping

The online auction market has been growing at a spectacular rate. Most auctionsare open-bid auctions where all the participants know the current highest bid.This knowledge has led to a phenomenon known as sniping, whereby somebidders may wait until the last possible moment before bidding, therebydepriving other bidders of the opportunity to respond and also preventingsellers from obtaining the highest price for an item. This is especially true inthe case of the commonly used second-price, fixed-deadline auction. We considera procedure involving a randomly determined stopping time and show that thisapproach eliminates the potential benefits to a sniper. The scheme enables allbidders to compete more fairly and promotes an early bidding strategy, which islikely to increase the price received by the seller while providing adequatebidding opportunities for would-be buyers.     

A new coupled model for alloy solidification

A new coupled model in the binary alloy solidification has been developed. The model is based on the cellular automaton (CA) technique to calculate the evolution of the interface governed by temperature, solute diffusion and Gibbs-Thomson effect. The diffusion equation of temperature with the release of latent heat on the solid/liquid (S/L) interface is valid in the entire domain. The temperature diffusion without the release of latent heat and solute diffusion are solved in the entire domain. In the interface cells, the     

A new coupled model for alloy solidification

A new coupled model in the binary alloy solidification has been developed. The model is based on the cellular automaton (CA) technique to calculate the evolution of the interface governed by temperature, solute diffusion and Gibbs-Thomson effect. The diffusion equation of temperature with the release of latent heat on the solid/liquid (S/L) interface is valid in the entire domain. The temperature diffusion without the release of latent heat and solute diffusion are solved in the entire domain. In the interface cells, the energy and solute conservation, thermodynamic and chemical potential equilibrium are adopted to calculate the temperature, solid concentration, liquid concentration and the increment of solid fraction. Compared with other models where the release of latent heat is solved in implicit or explicit form according to the solid/liquid (S/L) interface velocity, the energy diffusion and the release of latent heat in this model are solved at different scales, i.e. the macro-scale and micro-scale. The variation of solid fraction in this model is solved using several algebraic relations coming from the chemical potential equilibrium and thermodynamic equilibrium which can be cheaply solved instead of the calculation of S/L interface velocity. With the assumption of the solute conservation and energy conservation, the solid fraction can be directly obtained according to the thermodynamic data. This model is natural to be applied to multiple (< 2) spatial dimension case and multiple (< 2) component alloy. The morphologies of equiaxed dendrite are obtained in numerical experiments.     

A new model for automated examination timetabling

Automated examination timetabling has been addressed by a wide variety of methodologies and techniques over the last ten years or so. Many of the methods in this broad range of approaches have been evaluated on a collection of benchmark instances provided at the University of Toronto in 1996. Whilst the existence of these datasets has provided an invaluable resource for research into examination timetabling, the instances have significant limitations in terms of their relevance to real-world examination timetabling in modern universities. This paper presents a detailed model which draws upon experiences of implementing examination timetabling systems in universities in Europe, Australasia and America.     

Piecewise lexicographic programming: A new model for practical decision problems

A new model for practical decision problems is presented. It allows one to consider lexicographic preference structures by introducing the new class of piecewise lexicographic functions which impose a total order in the objective-and-constraint space. In this way, the concepts of objective and constraints are merged into a new unified notion of co-objective. Moreover, the lexicographic preference structure may be applied not only among different coobjectives, but also among different ranges of the same decision variable. The main merits of this model appear to be its versatility (it is able to deal with different types of multiobjective optimization situations without requiring user interaction) and its compactness (it does not require one to increase the original number of decision variables and constraints). A linear version of the model is investigated in more detail.     

A new face of the branching recurrence of computability logic

This letter introduces a new, substantially simplified version of the branching recurrence operation of computability logic, and proves its equivalence to the old, “canonical” version.     

A new characterization of graphs based on interception relations

While graphs are normally defined in terms of the 2-place relation of adjacency, we take the 3-place relation of interception as the basic primitive of their definition. The paper views graphs as an economical scheme for encoding interception relations, and establishes an axiomatic characterization of relations that lend themselves to representation in terms of graph interception, thus providing a new characterization of graphs. © 1996 John Wiley & Sons, Inc.     

A characterization theorem for geometric logic

We establish a criterion for deciding whether a class of structures is the class of models of a geometric theory inside Grothendieck toposes; then we specialize this result to obtain a characterization of the infinitary first-order theories which are geometric in terms of their models in Grothendieck toposes, solving a problem posed by Ieke Moerdijk in 1989.     

A semantic hierarchy for intuitionistic logic

Brouwer’s views on the foundations of mathematics have inspired the study of intuitionistic logic, including the study of the intuitionistic propositional calculus and its extensions. The theory of these systems has become an independent branch of logic with connections to lattice theory, topology, modal logic, and other areas. This paper aims to present a modern account of semantics for intuitionistic propositional systems. The guiding idea is that of a hierarchy of semantics, organized by increasing generality: from the least general Kripke semantics on through Beth semantics, topological semantics, Dragalin semantics, and finally to the most general algebraic semantics. While the Kripke, topological, and algebraic semantics have been extensively studied, the Beth and Dragalin semantics have received less attention. We bring Beth and Dragalin semantics to the fore, relating them to the concept of a nucleus from pointfree topology, which provides a unifying perspective on the semantic hierarchy.     

A new goldfish model

A new integrable (indeed, solvable) model of goldfish type is identified, and some of its properties are discussed. A version of its Newtonian equations of motion reads as follows:

A new shimmy model

Shimmy is a phenomenon of intense angular self-excited vibrations of the wheels of a carriage. Such self-excited vibrations present a serious threat to traffic safety, which accounts for the great interest of researchers in this phenomenon. The problem is of highest importance for the front wheels of aircraft. Usually, the deformation of pneumatic tires is considered to be the main factor responsible for shimmy. Without challenging this thesis, we nevertheless note that this is not the only factor. The shimmy phenomenon can be observed in everyday life in the case of various carriages that often have nothing to do with pneumatics if the wheels are rigid. Below we will show that the theory of polycomponent dry friction fully explains the shimmy phenomenon for absolutely rigid wheels and, hence, is at least one of the factors responsible for shimmy in the general case. The reason why researchers have not taken dry friction into account when explaining shimmy is that the theory of this kind of friction has not been well developed; at the same time one has failed to explain shimmy in the framework of other existing theories.