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Various k-special functions such as k-gamma function, k-beta function and k-hypergeometric functions have been introduced and investigated. Recently, the k-gamma function of a matrix argument and k-beta function of matrix arguments have been presented and studied. In this paper, we aim to introduce an extended k-gamma function of a matrix argument and an extended k-beta function of matrix arguments and investigate some of their properties such as functional relations, inequality, integral formula, and integral representations. Also an application of the extended k-beta function of matrix arguments to statistics is considered.

Background Data from subjective patient-reported outcome measures (PROMs) are now being used in the health sector to make or support decisions about individuals, groups and populations. Contemporary validity theorists define validity not as a statistical property of the test but as the extent to which empirical evidence supports the interpretation of test scores for an intended use. However, validity testing theory and methodology are rarely evident in the PROM validation literature. Application of this theory and methodology would provide structure for comprehensive validation planning to support improved PROM development and sound arguments for the validity of PROM score interpretation and use in each new context. Objective This paper proposes the application of contemporary validity theory and methodology to PROM validity testing. Illustrative example The validity testing principles will be applied to a hypothetical case study with a focus on the interpretation and use of scores from a translated PROM that measures health literacy (the Health Literacy Questionnaire or HLQ). Discussion Although robust psychometric properties of a PROM are a pre-condition to its use, a PROM's validity lies in the sound argument that a network of empirical evidence supports the intended interpretation and use of PROM scores for decision making in a particular context. The health sector is yet to apply contemporary theory and methodology to PROM development and validation. The theoretical and methodological processes in this paper are offered as an advancement of the theory and practice of PROM validity testing in the health sector.

Argument schemes are abstractions substantiating the inferential connection between premise(s) and conclusion in argumentative communication. Identifying such conventional patterns of reasoning is essential to the interpretation and evaluation of argumentation. Whether studying argumentation from a theory-driven or data-driven perspective, insight into the actual use of argumentation in communicative practice is essential. Large and reliably annotated corpora of argumentative discourse to quantitatively provide such insight are few and far between. This is all the more true for argument scheme corpora, which tend to suffer from a combination of limited size, poor validation, and the use of ad hoc restricted typologies. In the current paper, we describe the annotation of schemes on the basis of two distinct classifications: Walton’s taxonomy of argument schemes, and Wagemans’ Periodic Table of Arguments. We describe the annotation procedure for each, and the quantitative characteristics of the resulting annotated text corpora. In doing so, we extend the annotation of the preexisting US2016 corpus of televised election debates, resulting in, to the best of our knowledge, the two largest consistently annotated corpora of schemes in argumentative dialogue publicly available. Based on evaluation in terms of inter-annotator agreement, we propose further improvements to the guidelines for annotating schemes: the argument scheme key, and the Argument Type Identification Procedure.

During the last decade, one source of debate in argumentation theory has been the notion that there are different modes of arguing that need to be distinguished when analyzing and evaluating arguments. Visual argument is often cited as a paradigm example. This paper discusses the ways in which it and modes of arguing that invoke non-verbal sounds, smells, tactile sensations, music and other non-verbal entities may be defined and conceptualized. Though some attempts to construct a ‘multimodal’ theory of argument are criticized, it advocates for an argumentation theory that makes room for visual arguing and for other non-verbal modes that have not been explored in depth. In the process, the paper provides a method for identifying the structure of multimodal arguments and argues that adding modes to our theoretical tool box is an important step toward a comprehensive account of argument.

In recent years, academics and educators have begun to use software mapping tools for a number of education-related purposes. Typically, the tools are used to help impart critical and analytical skills to students, to enable students to see relationships between concepts, and also as a method of assessment. The common feature of all these tools is the use of diagrammatic relationships of various kinds in preference to written or verbal descriptions. Pictures and structured diagrams are thought to be more comprehensible than just words, and a clearer way to illustrate understanding of complex topics. Variants of these tools are available under different names: \"concept mapping\", \"mind mapping\" and \"argument mapping\". Sometimes these terms are used synonymously. However, as this paper will demonstrate, there are clear differences in each of these mapping tools. This paper offers an outline of the various types of tool available and their advantages and disadvantages. It argues that the choice of mapping tool largely depends on the purpose or aim for which the tool is used and that the tools may well be converging to offer educators as yet unrealised and potentially complementary functions (HRK / Abstract übernommen).

Anonymous argumentation has recently been the focus of public controversy: flash points include the outing of pseudonymous bloggers by newspapers and the launch of an academic journal that expressly permits pseudonymous authorship. However, the controversy is not just a recent one—similar debates took place in the nineteenth century over the then common practice of anonymous journalism. Amongst the arguments advanced by advocates of anonymous argumentation in either era is the contention that it is essential if the widest range of voices are to be heard; amongst the counterarguments of its critics, that it weakens the credibility of individual arguments and irresponsibly cheapens the standard of public discourse. This paper explores some implications of the controversy for the ethics of argumentation in general and virtue theories of argumentation in particular.

This paper presents sufficient conditions involving limsup for the oscillation of all solutions of linear difference equations with general deviating argument of the formΔx(n)+p(n)x(τ(n))=0, n∈ℕ0 [∇x(n)−q(n)x(σ(n))=0, n∈ℕ],, where (p(n))n≥0 and (q(n))n≥1 are sequences of nonnegative real numbers and (τ(n))n≥0, (σ(n))n≥1 are (not necessarily monotone) sequences of integers. The results obtained improve all well-known results existing in the literature and an example, numerically solved in MATLAB, illustrating the significance of these results is provided.

This paper develops Mark D. Linville’s brief description of “a sort of moral fine-tuning argument”. I develop the argument in four ways: I unpack the argument and give it a clear formulation, I unpack the theistic explanation of why a somewhat reliable moral capacity is expected, I point to the significance of not seeking to explain a perfect moral capacity, and I put the argument up against the recent work on non-theistic moral epistemology by Derek Parfit, David Enoch, and Erik Wielenberg.