Categorical Abstract Algebraic Logic Metalogical Properties

Metalogical properties that have traditionally been studied in the deductive system context (see, e.g., [21]) and transferred later to the institution context [33], are here formulated in the -institution context. Preservation under deductive equivalence of -institutions is investigated. If a property is known to hold in all algebraic -institutions and is preserved under deductive equivalence, then it follows that it holds in all algebraizable -institutions in the sense of [36].     

Found in Translation: Late Bilinguals Do Automatically Activate Their Native Language When They Are Not Using It

In their paper “Do Bilinguals Automatically Activate Their Native Language When They Are Not Using it?”, Costa, Pannunzi, Deco, and Pickering (Cognitive Science, 2017) proposed a reinterpretation of Thierry and Wu's (2004, 2007) finding of native language‐based (Chinese, L1) ERP effects when they tested Chinese–English late bilinguals exclusively in their second language (English, L2). Using simulations in a six‐node Hebbian learning model (three L1 nodes, three L2 nodes), Costa et al. suggested that form overlaps in L1 between otherwise unrelated words create a persistent relationship between their L2 translations. In this scenario, words in the nascent L2 lexicon overlapping in their L1 translations would become linked during learning because of the form overlap in L1; once the L2 words are learned, the direct link between them would be sufficient to generate robust, apparently “L1‐mediated” priming without requiring any activation of L1 translations. Costa et al. contend that links between L2 words remain beyond the learning phase, even after links to L1 representations have been severed, and thus that their model affords an alternative account to (but not a rebuttal of) Thierry and Wu's claim of language non‐selective activation—or automatic activation of translation equivalents—in late bilinguals. In this response, we build on Costa et al.'s original simulation code, showing that it can only reproduce L1‐independent priming when implementing the L1 disconnection in their particular way. By contrast, when severing inter‐language connections bidirectionally, their model fails to retain any sizeable influence of L1 form overlap on L2 activations. The model is not the theory, however, and we discuss several issues that would need to be addressed in further attempts to model language non‐selective activation in late bilinguals.     

Eye gaze patterns reveal how we reason about fractions

ABSTRACT

Fractions are defined by numerical relationships, and comparing two fractions’ magnitudes requires within-fraction (holistic) and/or between-fraction (componential) relational comparisons. To better understand how individuals spontaneously reason about fractions, we collected eye-tracking data while they performed a fraction comparison task with conditions that promoted or obstructed different types of comparisons. We found evidence for both componential and holistic processing in this mixed-pairs task, consistent with the hybrid theory of fraction representation. Additionally, making within-fraction eye movements on trials that promoted a between-fraction comparison strategy was associated with slower responses. Finally, participants who performed better on a non-numerical test of reasoning took longer to respond to the most difficult fraction trials, which suggests that those who had greater facility with non-numerical reasoning attended more to numerical relationships. These findings extend prior research and support the continued investigation into the mechanistic links between numerical and non-numerical reasoning.     

The role of numerosity in processing nonsymbolic proportions

The difficulty in processing fractions seems to be related to the interference between the whole-number value of the numerator and the denominator and the real value of the fraction. Here we assess whether the reported problems with symbolic fractions extend to the nonsymbolic domain, by presenting fractions as arrays of black and white dots representing the two operands. Participants were asked to compare a target array with a reference array in two separate tasks using the same stimuli: a numerosity task comparing just the number of white dots in the two arrays; and a proportion task comparing the proportion of black and white dots. The proportion task yielded lower accuracy and slower response, confirming that even with nonsymbolic stimuli accessing proportional information is relatively difficult. However, using a congruity manipulation in which the greater numerosity of white dots could co-occur with a lower proportion of them, and vice versa, it was found that both task-irrelevant dimensions would interfere with the task-relevant dimension suggesting that both numerosity and proportion information was automatically accessed. The results indicate that the magnitude of fractions can be automatically and holistically processed in the nonsymbolic domain.     

时间贴现的分段性

以延迟和相对延迟时间贴现的实验范式, 用选择法、匹配法确定价值主观相等点, 探讨时间贴现的分段性。三个实验和一个问卷调查发现, 时间贴现具有分段性。被试的时间贴现有三次显著变化, 表现为三个时段时间贴现心理状态的不同: 从现在到未来2周内规避损失、偏好风险、愿意短期等待, 从未来2周起直到未来10年采取非补偿性策略、需求与风险并重、愿意长期等待, 和从未来10年起直到未来50年规避风险、聊胜于无、不愿意等待。     

Categorical Abstract Algebraic Logic: Prealgebraicity and Protoalgebraicity

Two classes of π are studied whose properties are similar to those of the protoalgebraic deductive systems of Blok and Pigozzi. The first is the class of N-protoalgebraic π-institutions and the second is the wider class of N-prealgebraic π-institutions. Several characterizations are provided. For instance, N-prealgebraic π-institutions are exactly those π-institutions that satisfy monotonicity of the N-Leibniz operator on theory systems and N-protoalgebraic π-institutions those that satisfy monotonicity of the N-Leibniz operator on theory families. Analogs of the correspondence property of Blok and Pigozzi for π-institutions are also introduced and their connections with preand protoalgebraicity are explored. Finally, relations of these two classes with the (, N)-algebraic systems, introduced previously by the author as an analog of the -algebras of Font and Jansana, and with an analog of the Suszko operator of Czelakowski for π-institutions are also investigated. Presented by Josep Maria Font