There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Traditional engineering instruction is deductive, beginning with theories and progressing to the applications of those theories Alternative teaching approaches are more inductive Topics are introduced by presenting specific observations, case studies or problems, and theories are taught or the students are helped to discover them only after the need to know them has been established This study reviews several of the most commonly used inductive teaching methods, including inquiry learning, problem-based learning, project-based learning, case-based teaching, discovery learning, and just-in-time teaching The paper defines each method, highlights commonalities and specific differences, and reviews research on the effectiveness of the methods While the strength of the evidence varies from one method to another, inductive methods are consistently found to be at least equal to, and in general more effective than, traditional deductive methods for achieving a broad range of learning outcomes

Inductive Teaching and Learning Methods: Definitions, Comparisons, and Research Bases

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Qualitative Research in Information Systems

Thank you for reading software product line engineering foundations principles and techniques. Maybe you have knowledge that, people have look numerous times for their favorite books like this software product line engineering foundations principles and techniques, but end up in malicious downloads. Rather than reading a good book with a cup of coffee in the afternoon, instead they are facing with some infectious bugs inside their desktop computer.

Software Product Line Engineering Foundations Principles And Techniques

It represents a universally applicable attitude and skill set everyone, not just computer scientists, would be eager to learn and use.

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Computational Thinking 計算論的思考

The principle of truth-functionality (or compositionality) is a basic principle in many-valued logic in general, and in classical logic in particular. According to this principle, the truth-value of a complex formula is uniquely determined by the truth-values of its subformulas. However, real-world information is inescapably incomplete, uncertain, vague, imprecise or inconsistent, and these phenomena are in an obvious conflict with the principle of truth-functionality. One possible solution to this problem is to relax this principle by borrowing from automata and computability theory the idea of non-deterministic computations, and apply it in evaluations of truth-values of formulas. This leads to the introduction of non-deterministic matrices (Nmatrices) — a natural generalization of ordinary multi-valued matrices, in which the truth-value of a complex formula can be chosen nondeterministically out of some non-empty set of options. There are many natural motivations for introducing non-determinism into the truth-tables of logical connectives.

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Non-deterministic semantics for logical systems

We define in precise terms the basic properties that an `ideal propositional paraconsistent logic' is expected to have, and investigate the relations between them. This leads to a precise characterization of ideal propositional paraconsistent logics. We show that every three-valued paraconsistent logic which is contained in classical logic, and has a proper implication connective, is ideal. Then we show that for every n > 2 there exists an extensive family of ideal n-valued logics, each one of which is not equivalent to any k-valued logic with k < n.

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Ideal Paraconsistent Logics

Maximality is a desirable property of paraconsistent logics, motivated by the aspiration to tolerate inconsistencies, but at the same time retain from classical logic as much as possible. In this paper we introduce the strongest possible notion of maximal paraconsistency, and investigate it in the context of logics that are based on deterministic or non-deterministic three-valued matrices. We show that all reasonable paraconsistent logics based on three-valued deterministic matrices are maximal in our strong sense. This applies to practically all three-valued paraconsistent logics that have been considered in the literature, including a large family of logics which were developed by da Costa's school. Then we show that in contrast, paraconsistent logics based on three-valued properly nondeterministic matrices are not maximal, except for a few special cases (which are fully characterized). However, these non-deterministic matrices are useful for representing in a clear and concise way the vast variety of the (deterministic) three-valued maximally paraconsistent matrices. The corresponding weaker notion of maximality, called premaximal paraconsistency, captures the "core" of maximal paraconsistency of all possible paraconsistent determinizations of a non-deterministic matrix, thus representing what is really essential for their maximal paraconsistency.

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Maximal and Premaximal Paraconsistency in the Framework of Three-Valued Semantics

In the paper Cut-free ordinary sequent calculi for logics having generalized finite-valued semantics by A. Avron, J. Ben-Naim, and B. Konikowska. (Logica Universalis, 1:41–69, 2006), a general method was developed for generating cut-free ordinary sequent calculi for logics that can be characterized by finite-valued semantics based on non-deterministic matrices (Nmatrices). In this paper, a substantial step towards automation of paraconsistent reasoning is made by applying that method to a certain crucial family of thousands of paraconsistent logics, all belonging to the class of C-systems. For that family, the method produces in a modular way uniform Gentzen-type rules corresponding to a variety of axioms considered in the literature.

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Cut-free sequent calculi for C-systems with generalized finite-valued semantics

Behavioural studies revealed that the dog–human relationship resembles the human mother–child bond, but the underlying mechanisms remain unclear. Here, we report the results of a multi-method approach combining fMRI (N = 17), eye-tracking (N = 15), and behavioural preference tests (N = 24) to explore the engagement of an attachment-like system in dogs seeing human faces. We presented morph videos of the caregiver, a familiar person, and a stranger showing either happy or angry facial expressions. Regardless of emotion, viewing the caregiver activated brain regions associated with emotion and attachment processing in humans. In contrast, the stranger elicited activation mainly in brain regions related to visual and motor processing, and the familiar person relatively weak activations overall. While the majority of happy stimuli led to increased activation of the caudate nucleus associated with reward processing, angry stimuli led to activations in limbic regions. Both the eye-tracking and preference test data supported the superior role of the caregiver’s face and were in line with the findings from the fMRI experiment. While preliminary, these findings indicate that cutting across different levels, from brain to behaviour, can provide novel and converging insights into the engagement of the putative attachment system when dogs interact with humans.

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Anna Zamansky

Papers

Non-deterministic semantics for logical systems

Ideal Paraconsistent Logics

Maximal and Premaximal Paraconsistency in the Framework of Three-Valued Semantics

Cut-free sequent calculi for C-systems with generalized finite-valued semantics

Exploring the dog-human relationship by combining fMRI, eye-tracking and behavioural measures.