Structural Rule of N-Coordinated Single Atomic Catalysts for Electrochemical CO2 Reduction

Metal single-atom catalysts (SACs) on nitrogen-doped carbons exhibit an attractive prospect in catalysis. However, how to quickly collocate various metal centers with diversified N-coordination topologic structures to maximize the catalytic...

From 2-Sequents and Linear Nested Sequents to Natural Deduction for Normal Modal Logics

We extend to natural deduction the approach of Linear Nested Sequents and of 2-Sequents. Formulas are decorated with a spatial coordinate, which allows a formulation of formal systems in the original spirit of natural deduction: only one introduction and one elimination rule per connective, no additional (structural) rule, no explicit reference to the accessibility relation of the intended Kripke models. We give systems for the normal modal logics from K to S4. For the intuitionistic versions of the systems, we define proof reduction, and prove proof normalization, thus obtaining a syntactical proof of consistency. For logics K and K4 we use existence predicates (à la Scott) for formulating sound deduction rules.

THE INTRODUCTION OF GRAMMIME: A NOVEL APPROACH IN TEACHING THE ENGLISH SENTENCE PATTERNS

The awareness of communicative way of teaching English comes in different forms. This paper discusses the grammime, a new form of TPR which is mainly designed for eight parts of speech. It is used in some English training schools in China and is seen effective because it helps young learners to be acquainted with grammatical structure of sentences thus helping them to construct well-structured sentences with the help of different hand gestures which represent a structural rule. Incorporating oral drill with hand movements can augment the opportunity of memorizing the words, their meanings, and structural rule which makes learning much easier, interactive, and fun. The results which were obtained through experimental approach and self-made assessment instrument for pretest and posttest were used to assess grammime’s influence and impact on young learner’s learning process and outcomes. It is explored that the intervention using grammime really has an impact on young learners’ learning outcomes. Most specifically, the results suggest that when young learners are exposed to grammime and they practice it, the acquisition of knowledge and the learning process and outcomes increase. <p> </p><p><strong> Article visualizations:</strong></p><p><img src="/-counters-/edu_01/0745/a.php" alt="Hit counter" /></p>

A note on the system GRW with the intensional contraction rule

In Ilić and Boričić (2014, Log. J. IGPL, 22, 673–695), the right-handed cut-free sequent calculus $GRW$ for the contraction-less relevant logic $RW$ is defined. In this paper, we show that the enlargement of the system $GRW$ with the structural rule of intensional contraction (WI) presents the sequent system for the principal relevant logic $R$ but the rule of cut cannot be eliminated in $GRW+$(WI).

Perceptual Tuning Influences Rule Generalization: Testing Humans With Monkey-Tailored Stimuli

Comparative research investigating how nonhuman animals generalize patterns of auditory stimuli often uses sequences of human speech syllables and reports limited generalization abilities in animals. Here, we reverse this logic, testing humans with stimulus sequences tailored to squirrel monkeys. When test stimuli are familiar (human voices), humans succeed in two types of generalization. However, when the same structural rule is instantiated over unfamiliar but perceivable sounds within squirrel monkeys’ optimal hearing frequency range, human participants master only one type of generalization. These findings have methodological implications for the design of comparative experiments, which should be fair towards all tested species’ proclivities and limitations.

A RECOVERY OPERATOR FOR NONTRANSITIVE APPROACHES

In some recent articles, Cobreros, Egré, Ripley, & van Rooij have defended the idea that abandoning transitivity may lead to a solution to the trouble caused by semantic paradoxes. For that purpose, they develop the Strict-Tolerant approach, which leads them to entertain a nontransitive theory of truth, where the structural rule of Cut is not generally valid. However, that Cut fails in general in the target theory of truth does not mean that there are not certain safe instances of Cut involving semantic notions. In this article we intend to meet the challenge of answering how to regain all the safe instances of Cut, in the language of the theory, making essential use of a unary recovery operator. To fulfill this goal, we will work within the so-called Goodship Project, which suggests that in order to have nontrivial naïve theories it is sufficient to formulate the corresponding self-referential sentences with suitable biconditionals. Nevertheless, a secondary aim of this article is to propose a novel way to carry this project out, showing that the biconditionals in question can be totally classical. In the context of this article, these biconditionals will be essentially used in expressing the self-referential sentences and, thus, as a collateral result of our work we will prove that none of the recoveries expected of the target theory can be nontrivially achieved if self-reference is expressed through identities.

The finite embeddability property for some noncommutative knotted extensions of FL

We consider the knotted structural rule x&lt;sup&gt;m&lt;/sup&gt;≤x&lt;sup&gt;n&lt;/sup&gt; for n different than m and m greater or equal than 1. Previously van Alten proved that commutative residuated lattices that satisfy the knotted rule have the finite embeddability property (FEP). Namely, every finite partial subalgebra of an algebra in the class can be embedded into a finite full algebra in the class. In our work we replace the commutativity property by some slightly weaker conditions. Particularly, we prove the FEP for the variety of residuated lattices that satisfy the equation xyx=x&lt;sup&gt;2&lt;/sup&gt;y and the knotted rule. Furthermore, we investigate some generalizations of this noncommutative property by working with equations that allow us to move variables. We also note that the FEP implies the finite model property. Hence the logics modeled by these residuated lattices are decidable.

FULL LAMBEK CALCULUS WITH CONTRACTION IS UNDECIDABLE

We prove that the set of formulae provable in the full Lambek calculus with the structural rule of contraction is undecidable. In fact, we show that the positive fragment of this logic is undecidable.