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We report an experimental evaluation of the “input−output surface” for a biochemical AND gate. The obtained data are modeled within the rate-equation approach, with the aim to map out the gate function and cast it in the language of logic variables appropriate for analysis of Boolean logic for scalability. In order to minimize “analog” noise, we consider a theoretical approach for determining an optimal set for the process parameters to minimize “analog” noise amplification for gate concatenation. We establish that under optimized conditions, presently studied biochemical gates can be concatenated for up to order 10 processing steps. Beyond that, new paradigms for avoiding noise buildup will have to be developed. We offer a general discussion of the ideas and possible future challenges for both experimental and theoretical research for advancing scalable biochemical computing. [ABSTRACT FROM AUTHOR]

It is commonly agreed that the well-known Lucas–Penrose arguments and even Penrose’s ‘new argument’ in [Penrose, R. (1994): Shadows of the Mind, Oxford University Press] are inconclusive. It is, perhaps, less clear exactly why at least the latter is inconclusive. This note continues the discussion in [Lindström, P. (2001): Penrose’s new argument, J. Philos. Logic 30, 241–250; Shapiro, S.(2003): Mechanism, truth, and Penrose’s new argument, J. Philos. Logic 32, 19–42] and elsewhere of this question. [ABSTRACT FROM AUTHOR]

We show how to interpret intuitionistic propositional logic into a predicative second-order intuitionistic propositional system having only the conditional and the universal second-order quantifier. We comment on this fact. We argue that it supports the legitimacy of using classical logic in a predicative setting, even though the philosophical cast of predicativism is nonrealistic. We also note that the absence of disjunction and existential quantifications allows one to have a process of normalization of proofs that avoids the use of "commuting conversions." [ABSTRACT FROM AUTHOR]

Le premier tractatus du commentaire d'Albert le Grand à l' Isagoge de Porphyre consiste en une manière de proème ou d'introduction à l'ensemble de la logique. Comme la plupart des textes d'Albert le Grand, ce traité est d'une très grande richesse, qu'atténuent toutefois son manque d'ordre et son obscurité d'expression. Étant donné que les aspects fondamentaux de la logique y sont touchés--son statut scientifique et philosophique, son utilité, son sujet, sa division, sa relation aux sciences du langage, etc.--, ce petit ouvrage est du plus haut intérêt pour quiconque cherche à mieux comprendre la logique et la philosophie de la logique du XIII e siècle. L'auteur présente ici une traduction annotée et expliquée de ce texte difficile, faite d'après la version provisoire de la nouvelle édition de Cologne. Le relevé des sources principales de l'ouvrage révèle, sur un fond aristotélicien permanent, une forte influence des traités logiques arabes nouvellement arrivés en Occident. The first tractatus of Albert the Great's commentary on Porphyry's Isagoge consists of a kind of proem or introduction to the whole of logic. As most of Albert the Great's texts, this tract is of great richness, though it lacks order and is sometimes obscure. Since the fundamental themes of logic are addressed therein--its scientific and philosophical status, its utility, its subject, its division, its relation to the linguistic arts, etc.--, this small work is of high interest for anyone trying to better understand thirteenth-century logic and philosophy of logic. The author presents a translation of this difficult text, made after a preliminary version of the new critical edition and enriched with an introduction and explanatory notes. The survey of the main sources of the tract reveals, apart from a permanent artistotelian background, the strong influence of the Arabic logical treatises which were then coming in the Western world. [ABSTRACT FROM AUTHOR]

The article cites a below chance performance on a verbal test using paired concepts. In the design of tests that have dichotomous response alternatives, the usual procedure is to balance the test so that it has as many items with one alternative correct as the other. That is, in a test with true-false type answers, there are genere ally as many items with correct true as correct false answers. The logic underlying this design is that when the respondent is not answering on the basis of his knowledge, he should be letting no more than half the answers correct on the basis of guessing, or by "chance."