On Consistent Subsets of Large Sets of Satisfiable Sentences

We extend some results of Adam Kolany to show that large sets of satisfiable sentences generally contain equally large subsets of mutually consistent sentences. In particular, this is always true for sets of uncountable cofinality, and remains true for sets of denumerable cofinality if we put appropriate bounding conditions on the sentences. The results apply to both the propositional and the predicate calculus. To obtain these results, we use delta sets for regular cardinals, and, for singular cardinals, a generalization of delta sets. All of our results are theorems in ZFC.     

A modern elaboration of the ramified theory of types

The paper first formalizes the ramified type theory as (informally) described in the Principia Mathematica [32]. This formalization is close to the ideas of the Principia, but also meets contemporary requirements on formality and accuracy, and therefore is a new supply to the known literature on the Principia (like [25], [19], [6] and [7]).As an alternative, notions from the ramified type theory are expressed in a lambda calculus style. This situates the type system of Russell and Whitehead in a modern setting. Both formalizations are inspired by current developments in research on type theory and typed lambda calculus; see [3].Supported by the Co-operation Centre Tilburg and Eindhoven Universities. ¹[32], Introduction, Chapter II, Section I, p. 37.Presented by Wolfgang Rautenberg     

Representation and Reasoning about Evolutions of the World in the Context of Reasoning about Actions

The first step in reasoning about actions and change involves reasoning about how the world would evolve if a certain action is executed in a certain state. Most research on this assumes the evolution to be only a single step and focus on formulating the transition function that defines changes between states due to actions. In this paper we consider cases where the evolution is more than just a single change between one state and another. This is manifested when the execution of an action may trigger execution of other actions, or when multiple agents act on the environment following certain strategies.     

高低情感开放性者概率内隐序列学习进程差异

大五人格情感开放性子量表(openness/feeling)能否预测内隐序列学习的问题存在争议。本研究采用概率性内隐序列学习范式, 比较高低情感开放性者在各反应刺激间隔(response stimulus interval, 即RSI)的差异。发现：(1) RSI = 0 ms和250 ms, 高分组在转移组块后习得高概率序列, RSI = 500 ms及以上在其之前习得; 所有RSI点低分组都在其之前习得。每个RSI点只有高分组习得低概率序列。证明随RSI增加两者内隐进程有本质差异, openness/feeling子量表可预测内隐序列学习个体差异。(2)低概率序列可作为测量概率性内隐序列学习及个体差异的新指标, 经典转移组块、再认、生成任务的测量效果却十分有限。     

线索呈现位置对概率类别学习的影响

当前概率类别学习中主要存在多系统和单系统两种观点之争, 而持不同观点的研究者在其实验中分别采用了不同的线索位置呈现方式, 因此本研究采用经典的天气预测任务通过操纵线索位置的呈现方式来进一步探讨其对概率类别学习的影响。本研究包括2个实验：实验1考察所有线索位置固定和随机对概率类别学习系统的影响; 实验2通过单线索模式下线索位置固定考察概率类别学习的策略。结果发现, 当所有线索的呈现位置固定时, 概率类别学习是外显学习; 而当所有线索的呈现位置随机时, 概率类别学习是内隐学习; 而当只在线索单独出现时固定其位置, 概率类别学习仍是内隐学习。结果表明, 线索位置的不同呈现方式会影响概率类别学习中外显和内隐学习系统的竞争, 研究支持了多系统观点, 且概率类别学习的主要策略可能是多线索策略而不是单模式策略。     

Estimation of the hypothesis hierarchy in probabilistic inference tasks*

Is there a hierarchical order among the hypotheses about functional rules in probabilistic inference tasks, i.e. what is the construction and the procedure of the “hypothesis sampling mechanism” employed by the subjects in this kind of task? According to the hypothesis sampling model initially proposed by Brehmer (1974) there should be a hierarchical order among the hypotheses in the subject's hypothesis pools. The procedures of hypothesis sampling and testing ought to follow this strict data independent order (see e.g. Sniezek, 1986; Brehmer, 1987). Knez (1991a, b) showed, however, that this assumption may be incorrect. As a follow up to these results the question regarding the construction of the subject's hypothesis pools was reapproached in the present study. The results indicated a consistency with the hierarchical assumption (Brehmer, 1974) only regarding the relation between the linear and nonlinear rules but not within these types of rules.     

Marginalia on Sequent Calculi

The paper discusses the relationship between normal natural deductions and cutfree proofs in Gentzen (sequent) calculi in the absence of term labeling. For Gentzen calculi this is the usual version; for natural deduction this is the version under the complete discharge convention, where open assumptions are always discharged as soon as possible. The paper supplements work by Mints, Pinto, Dyckhoff, and Schwichtenberg on the labeled calculi.     

A probabilistic model of intensive designs

Without internal validity, experimental data are uninterpretable. With intensive designs, most methods presented to quantify a design's internal validity have been subject to criticism. A probabilistic model of intensive designs is presented that demonstrates the high degree of internal validity of these designs without relying on adaptations from traditional inferential statistics. Where the experimenter is able to conform to the restrictions of the model, the equations provide an estimation of internal validity for either reversal or multiple-baseline designs. More importantly, the model provides mathematical bases for some of the common recommendations and design considerations in intensive research (such as the desirability of within-subject replications and of four or more multiple baselines).