Quantified Propositional Logic and the Number of Lines of Tree-Like Proofs

There is an exponential speed-up in the number of lines of the quantified propositional sequent calculus over Substitution Frege Systems, if one considers proofs as trees. Whether this is true also for the number of symbols, is still an open problem. This revised version was published online in June 2006 with corrections to the Cover Date.     

A Note on Graded Modal Logic

We introduce a notion of bisimulation for graded modal logic. Using this notion, the model theory of graded modal logic can be developed in a uniform manner. We illustrate this by establishing the finite model property and proving invariance and definability results.     

Skepticism and Epistemic Logic

This essay attempts to implement epistemic logic through a non-classical inference relation. Given that relation, an account of '(the individual) a knows that A' is constructed as an unfamiliar non-normal modal logic. One advantage to this approach is a new analysis of the skeptical argument.     

Intuitionistic Propositional Logic without 'Contraction' but with 'Reductio'

Routley-Meyer type relational complete semantics are constructed for intuitionistic contractionless logic with reductio. Different negation completions of positive intuitionistic logic without contraction are treated in a systematical, unified and semantically complete setting.     

基于阶层线性理论的多层级中介效应

本文介绍了三种常见的多层级中介效应模型, 并根据阶层线性理论和依次检验回归系数的方法, 详述了多层级中介效应的检验步骤以及中介效应量的估计方法, 在2-1-1和1-1-1中介效应模型中, 推荐采用对层1自变量按组均值中心化, 同时将组均值置于层2截距方程式的中心化方法, 以实现组间和组内中介效应的有效分离。本文还展望了多层级中介效应模型的拓展方向, 即多层级调节性中介模型和多层级结构方程模型; 以及检验方法的拓展, 即Sobel检验和置信区间检验。     

Fourier‐Motzkin elimination method in MOLP problems

This paper introduces a method for finding the non‐dominated set in criterion space of an MOLP problem based on Fourier–Motzkin Elimination. The method incorporates a procedure that eliminates decision variables from constraints and transforms a feasible region from decision space to criterion space. While avoiding characterization of the efficient set in decision space, it finds the non‐dominated set in criterion space. After the decision maker's most preferred criterion vector has been identified, the corresponding efficient solutions can be found by backward substitution. The method was implemented in MATLAB using a tabular form and computational experiments were conducted. The results indicate that although the method performs well for relatively small problems, it can be computationally intensive for larger problems. Nonetheless, the method is intuitively appealing and it provides useful insights into the geometry and theory of MOLP. As such it makes it a valuable educational tool for students of multi‐criteria decision analysis. Copyright © 2003 John Wiley & Sons, Ltd.     

An interactive fuzzy satisficing method for multiobjective stochastic linear programming problems using chance constrained conditions

Two major approaches to deal with randomness or ambiguity involved in mathematical programming problems have been developed. They are stochastic programming approaches and fuzzy programming approaches. In this paper, we focus on multiobjective linear programming problems with random variable coefficients in objective functions and/or constraints. Using chance constrained programming techniques, the stochastic programming problems are transformed into deterministic ones. As a fusion of stochastic approaches and fuzzy ones, after determining the fuzzy goals of the decision maker, interactive fuzzy satisficing methods to derive a satisficing solution for the decision maker by updating the reference membership levels is presented. Copyright © 2003 John Wiley & Sons, Ltd.     

On Stage with Gunk

A structure is temporally gunky just in case all of its temporal parts have proper temporal parts. Joshua Stuchlik [2003] objects to the stage theory of persistence from temporal gunk by arguing that the former requires instantaneous entities while the latter precludes them. It is argued here that stage theory can accommodate temporal gunk by invoking short-lived persisting stages. However, a new and more serious problem for stage theory is not far to seek. The short-lived stages that are needed to accommodate gunk accord with stage theory only if they are appropriately qualitatively static. The problem is that, unless stage theory abandons much of its dialectical force, some of the required stages fail this condition. Thus, Stuchlik is right that gunk shows a large class of worlds not to be stages, but wrong about which worlds these are.     

A caveat on the Savage–Dickey density ratio: The case of computing Bayes factors for regression parameters

The Savage–Dickey density ratio is a simple method for computing the Bayes factor for an equality constraint on one or more parameters of a statistical model. In regression analysis, this includes the important scenario of testing whether one or more of the covariates have an effect on the dependent variable. However, the Savage–Dickey ratio only provides the correct Bayes factor if the prior distribution of the nuisance parameters under the nested model is identical to the conditional prior under the full model given the equality constraint. This condition is violated for multiple regression models with a Jeffreys–Zellner–Siow prior, which is often used as a default prior in psychology. Besides linear regression models, the limitation of the Savage–Dickey ratio is especially relevant when analytical solutions for the Bayes factor are not available. This is the case for generalized linear models, non-linear models, or cognitive process models with regression extensions. As a remedy, the correct Bayes factor can be computed using a generalized version of the Savage–Dickey density ratio.