THE NATURE OF PHYSICAL REALITY

Abstract. This account of the dynamical theory of chaos leads to a metaphysical picture of a world with an open future, in which the laws of physics are emergent-downward approximations to a more subtle and supple reality and in which there is downward causation through information input as well as upward causation through energy input. Such a metaphysical picture can accommodate both human and divine agency.     

A Common Abstraction of MV-Algebras and Abelian l-groups

We investigate the class of strongly distributive pregroups, a common abstraction of MV-algebras and Abelian l-groups which was introduced by E.Casari. The main result of the paper is a representation theorem which yields both Chang's representation of MV-algebras and Clifford's representation of Abelian l-groups as immediate corollaries.     

A Set Theory with Support for Partial Functions

Partial functions can be easily represented in set theory as certain sets of ordered pairs. However, classical set theory provides no special machinery for reasoning about partial functions. For instance, there is no direct way of handling the application of a function to an argument outside its domain as in partial logic. There is also no utilization of lambda-notation and sorts or types as in type theory. This paper introduces a version of von-Neumann-Bernays-Gödel set theory for reasoning about sets, proper classes, and partial functions represented as classes of ordered pairs. The underlying logic of the system is a partial first-order logic, so class-valued terms may be nondenoting. Functions can be specified using lambda-notation, and reasoning about the application of functions to arguments is facilitated using sorts similar to those employed in the logic of the IMPS Interactive Mathematical Proof System. The set theory is intended to serve as a foundation for mechanized mathematics systems.     

A comparison of stimulus set size on tact training for children with autism spectrum disorder

Previous studies on skill acquisition have taught targets in stimulus sets composed of different numbers of stimuli. Although the rationale for selection of a stimulus set size is not clear, the number of target stimuli trained within a set is a treatment decision for which there is limited empirical support. The current investigation compared the efficiency of tact training in 4 stimulus set sizes, each of which included 12 stimuli grouped into (a) 4 sets of 3 stimuli, (b) 3 sets of 4 stimuli, (c) 2 sets of 6 stimuli, and (d) 1 set of 12 stimuli. Results of all 4 participants with autism spectrum disorder show tact training with larger (i.e., 6 and 12) stimulus set sizes was more efficient than training with smaller (i.e., 3 and 4) stimulus set sizes.     

Fuzzy partition models for fitting a set of partitions

Methodology is described for fitting a fuzzy consensus partition to a set of partitions of the same set of objects. Three models defining median partitions are described: two of them are obtained from a least-squares fit of a set of membership functions, and the third (proposed by Pittau and Vichi) is acquired from a least-squares fit of a set of joint membership functions. The models are illustrated by application to both a set of hard partitions and a set of fuzzy partitions and comparisons are made between them and an alternative approach to obtaining a consensus fuzzy partition proposed by Sato and Sato; a discussion is given of some interesting differences in the results.We are grateful to Dr. M.G. Pittau for carrying out the analyses of the macroeconomic data using the method of Sato and Sato (1994).     

应用层次析分法和模糊综合评判研究保健品消费心理

将层次分析方法与模糊综合评判理论相结合,以营养成分、包装情况、价格因素、广告宣传、售后服务为一级评判指标,以保健品专卖店、大型超市、小型超市、杂货店、厂家邮购五种销售渠道为二级评价指标,给出一种模糊判断的权重计算方法,建立了保健品消费心理的层次模糊决策模型。应用该模型对长春地区消费者的保健品消费心理进行了测试,结果表明：测试结果与实际销售情况相符。说明应用该方法建立起来的模型在了解消费者对保健品的消费心理方面是可行的,同时也为新型保健品的开发和市场推广提供了一定的依据。     

Ambiguous comparative judgment: Fuzzy set model and data analysis

Abstract:  This paper proposed two types of fuzzy set models for ambiguous comparative judgments, which did not always hold transitivity and comparability properties. The first type of model was a fuzzy theoretical extension of the additive difference model for preference that was used to explain ambiguous preference strength. The second was a fuzzy logic model for explaining ambiguous preference in which preference strength was bounded, such as a probability measure. In both models, multi-attribute weighting parameters and all attribute values were assumed to be asymmetric fuzzy L-R numbers. For each model, a method of parameter estimation using fuzzy regression analysis was proposed. Numerical examples were also provided for comparison. Finally, the theoretical and practical implications of the proposed models were discussed.     

Continuous representability of interval orders and biorders

We furnish a characterization of the representability of an interval order through a pair of continuous real-valued functions which in addition represent two total preorders associated to the given interval order. Our techniques lean on the key concept of a biorder. We introduce the concept of a natural topology for an interval order, and through such concept we extend the classical biorder approach to the continuous case.     

Badiou,Priest, and the Hegelian Infinite

Abstract

Hegel’s distinction between the bad and true infinites has provoked contrasting reactions in the works of Alain Badiou and Graham Priest. Badiou claims that Hegel illegitimately attempts to impose a distinction that is only relevant to the qualitative realm onto the quantitative realm. He suggests that Cantor’s mathematical account of infinite multiplicities that are determinate and actual remains an endlessly proliferating bad infinite when placed within Hegel’s faulty schema. In contrast, Priest affirms the Hegelian true infinite, claiming that Cantor’s formal mechanisms of boundary transcendence, such as ‘diagonalization’, are implicit in Hegel’s dialectic. While arguing that a clear dividing line can be drawn here between these two interpretations of the relationship between Hegel and Cantor, this paper also mounts a defence of the Hegelian true infinite by developing Priest’s suggestion that Cantorian diagonalizing functions are prefigured by Hegel’s dialectical overcoming of limits.