Algebraization, Parametrized Local Deduction Theorem and Interpolation for Substructural Logics over FL

Substructural logics have received a lot of attention in recent years from the communities of both logic and algebra. We discuss the algebraization of substructural logics over the full Lambek calculus and their connections to residuated lattices, and establish a weak form of the deduction theorem that is known as parametrized local deduction theorem. Finally, we study certain interpolation properties and explain how they imply the amalgamation property for certain varieties of residuated lattices. Dedicated to the memory of Willem Johannes Blok     

A base logic for default reasoning

Based on a close study of benchmark examples in default reasoning, such as Nixon Diamond, Penguin Principle, etc., this paper provides an in depth analysis of the basic features of default reasoning. We formalize default inferences based on Modus Ponens for Default Implication, and mark the distinction between “local inferences” (to infer a conclusion from a subset of given premises) and “global inferences” (to infer a conclusion from the entire set of given premises). These conceptual analyses are captured by a formal semantics that is built upon the set-selection function technique. A minimal logic system M of default reasoning that accommodates Modus Ponens for Default Implication and suitable for local inferences is proposed, and its soundness is proved. __________ Translated from Zhexue Yanjiu 哲学研究 (Philosophical Studies), 2003 (special issue) by Ye Feng     

Hintikka’s Logical Revolution

Hintikka thinks that second-order logic is not pure logic, and because of Gödel’s incompleteness theorems, he suggests that we should liberate ourselves from the mistaken idea that first-order logic is the foundational logic of mathematics. With this background he introduces his independence friendly logic (IFL). In this paper, I argue that approaches taking Hintikka’s IFL as a foundational logic of mathematics face serious challenges. First, the quantifiers in Hintikka’s IFL are not distinguishable from Linström’s general quantifiers, which means that the quantifiers in IFL involve higher order entities. Second, if we take Wright’s interpretation of quantifiers or if we take Hale’s criterion for the identity of concepts, Quine’s thesis that second-order logic is set theory will be rejected. Third, Hintikka’s definition of truth itself cannot be expressed in the extension of language of IFL. Since second-order logic can do what IFL does, the significance of IFL for the foundations of mathematics is weakened.     

Trinitarian Mission and Practical Theology

The contextual dimension of mission remains both critical and relevant in understanding the nature and scope of the church with regard to its place and purpose. This is formed against the backdrop of the continual importance of the missio Dei in framing its engagement. Newbigin's conception of trinitarian mission is one approach that can give specific focus to this understanding. A trinitarian missional ecclesiology can find common ground with practical theology in service of mission. Practical theology should be understood contextually and can be conceived missiologically. By bringing Newbigin's trinitarian mission into conversation with practical theology, an important conversation is generated regarding the contextual nature of both the discipline of practical theology and the missio Dei.     

Factor copula models for mixed data

We develop factor copula models to analyse the dependence among mixed continuous and discrete responses. Factor copula models are canonical vine copulas that involve both observed and latent variables, hence they allow tail, asymmetric and nonlinear dependence. They can be explained as conditional independence models with latent variables that do not necessarily have an additive latent structure. We focus on important issues of interest to the social data analyst, such as model selection and goodness of fit. Our general methodology is demonstrated with an extensive simulation study and illustrated by reanalysing three mixed response data sets. Our studies suggest that there can be a substantial improvement over the standard factor model for mixed data and make the argument for moving to factor copula models.     

AN ABSOLUTE DISTINCTION BETWEEN FAITH AND SCIENCE: CONTRAST WITHOUT COMPARTMENTALIZATION

This article argues for acknowledging the existence of an absolute distinction between faith and science. It is often assumed in the science and religion debate that such a distinction would be ahistorical and uncontextual. After discussing this critique, the analogy with love and facts will be used to explain how an absolute distinction between faith and science may exist nonetheless. This contrast, however, does not imply compartmentalization. It is shown that the absolute distinction between faith and science is of crucial importance to understand the historical contexts that so many contributors to the science and religion debate refer to in their argument against the approaches of Independence or Contrast. The article concludes that within our messy and complex practices there is an absolute distinction between faith and science—our historical contexts cannot be understood without it.     

Cultural variation in implicit independence: An extension of Kitayama et al. ()

Previous research shows that European Americans are consistently more independent (or less interdependent) than Japanese when implicit indices are used to assess independence (vs. interdependence). The present work extended this evidence by including a novel implicit association test (IAT), as an index of implicit attitude towards independence and interdependence. Consistent with the previous findings, as compared to Japanese, Americans were significantly higher in multiple indices of implicit independence (vs. interdependence) including personal (vs. social) self‐definition, experience of disengaging (vs. engaging) emotions and personal (vs. social) form of happiness. Furthermore, as compared to Japanese, Americans had a significantly more positive implicit attitude towards independence assessed with the IAT. As also observed in the previous research, explicit measures showed inconsistent cross‐cultural patterns. Lastly, we observed little statistical within‐culture coherence among the implicit measures of independence (vs. interdependence), consistent with a view that the implicit indices capture alternative ways for individuals to achieve the cultural mandate of independence or interdependence.     

Melioration revisited: a systematic replication of Vaughan (1981)

Organisms that behave so as to forfeit a relatively higher overall rate of reinforcement in favor of a relatively lower rate are said to engage in suboptimal choice. Suboptimal choice has been linked with maladaptive behavior in humans. Melioration theory offers one explanatory framework for suboptimal choice. Melioration theory suggests behavior is controlled by differences in local reinforcer rates between alternatives. Vaughan (1981) arranged two experimental conditions in which maximizing the overall rate of reinforcement required behavior that was compatible, or incompatible, with melioration. Vaughan found pigeons allocated more time to a locally richer alternative even when doing so resulted in suboptimal choice. However, Vaughan did not show whether these effects could systematically reverse and did not provide within‐session data to show that choice across short time spans remains under the control of differences in local reinforcer rates. The present study used pigeons to replicate and extend Vaughan's findings. We investigated shifts in overall‐ and within‐session choice across repeated conditions, according to arranged local contingencies. Behavior systematically followed changes in local contingencies for most pigeons. Within‐session data suggests that, providing differences in local reinforcer rates are discriminated, pigeons will allocate more time to a locally richer alternative, even if this leads to suboptimal choice. These findings facilitate the more confident use of similar procedures that investigate how melioration contributes to suboptimal choice.     

Visual field x response hand interactions and level priming in the processing of laterally presented hierarchical stimuli

Hemisphere-specific processing of laterally presented global and local stimulus levels was investigated by (a) examining interactions between the visual field of stimulus presentation and the response hand and (b) comparing intra- with inter-hemispheric effects of level priming (i.e. faster and more accurate performance when the target level repeats). Although in Experiment 1, which involved two-choice responses with left and right hands, performance costs occurred when the same hemisphere received the stimulus and controlled the response hand, further analyses suggest that these effects reflect spatial compatibility rather than intra-hemispheric interference. Consistent with the spatial compatibility interpretation, in Experiment 2 a similar visual field x response interaction was obtained with regard to left and right responses given with the same hand. Trial-to-trial level priming occurred in both experiments and was unaffected by the intra-hemispheric sequence of target levels. Implications regarding hemispheric processing mode are discussed.     

Power affects basic cognition: Increased attentional inhibition and flexibility

The present article examines effects of power on basic cognition. It proposes that power bolsters the ability to attend to information selectively; enhancing the processing of information that is related to accessible constructs in detriment of peripheral, less accessible information. In contrast, powerlessness increases attunement to peripheral information, inducing greater distractibility and less attentional flexibility. Experiment 1 focuses on attention to an object and its context. Experiment 2 examines attentional focus and readiness to act. Experiment 3 examines attention to global vs. local aspects of a focal target. Powerful individuals, relative to powerless individuals, showed greater ability to inhibit peripheral information, and greater ability to focus attention in line with the demands of the task. Furthermore, inhibiting peripheral information facilitated action. The consequences of these findings for different domains are discussed.