We explore a framework for argumentation (based on classical logic) in which an argument is a pair where the first item in the pair is a minimal consistent set of formulae that proves the second item (which is a formula). We provide some basic definitions for arguments, and various kinds of counter-arguments (defeaters). This leads us to the definition of canonical undercuts which we argue are the only defeaters that we need to take into account. We then motivate and formalise the notion of argument trees and argument structures which provide a way of exhaustively collating arguments and counter-arguments. We use argument structures as the basis of our general proposal for argument aggregation.

Chinese ways of dealing with seeming contradictions result in a dialectical or compromise approach---retaining basic elements of opposing perspectives by seeking a "middle way." European-American ways, on the other hand, deriving from a lay version of Aristotelian logic, result in a differentiation model that polarizes contradictory perspectives in an effort to determine which fact or position is correct. Empirical studies showed that dialectical thinking is a form of folk wisdom in Chinese culture: Chinese preferred dialectical proverbs containing seeming contradictions more than did Americans. Chinese were also found to prefer dialectical resolutions to social conflicts, and to prefer dialectical arguments over classical Western logical arguments. Furthermore, when two apparently contradictory propositions were presented, Americans polarized their views and Chinese were moderately accepting of both propositions. Origins of these cultural differences and their implications for human reasoning in general are discussed. 3 3 Consider the following statements about recent scientific discoveries: Statement A. Two mathematicians have discovered that the activities of a butterfly in Beijing, China, noticeably affect the temperature in the San Francisco Bay Area. Statement B. Two meteorologists have found that the activities of a local butterfly in the San Francisco Bay Area have nothing to do with temperature changes in the same San Francisco Bay Area. What would be your intuitive reaction to these statements? Do you see an implicit contradiction between the two pieces of information? What strategy would you use to deal with such contradictions? What is the rationale for using such a strategy? Does your cultural background affect your reasoning and judgments about contradicti...

There are a number of frameworks for modelling argumentation in logic. They incorporate a formal representation of individual arguments and techniques for comparing conflicting arguments. An example is the framework by Besnard and Hunter that is based on classical logic and in which an argument (obtained from a knowledgebase) is a pair where the first item is a minimal consistent set of formulae that proves the second item (which is a formula). In the framework, the only counter-arguments (defeaters) that need to be taken into account are canonical arguments (a form of minimal undercut) . Argument trees then provide a way of exhaustively collating arguments and counter-arguments. A problem with this set up is that some argument trees may be "too big" to have sufficient impact. In this paper, we address the need to increase the impact of argumentation by using pruned argument trees. We formalize this in terms of how arguments resonate with the intended audience of the arguments. For example, if a politician wants to make a case for raising taxes, the arguments used would depend on what is important to the audience: Arguments based on increased taxes are needed to pay for improved healthcare would resonate better with an audience of pensioners, whereas arguments based on increased taxes are needed to pay for improved transport infrastructure would resonate better with an audience of business executives. By

Numerous argumentation systems have been proposed in the literature. Yet there often appears to be a shortfall between proposed systems and possible applications. In other words, there seems to be a need for further development of proposals for argumentation systems before they can be used widely in decision-support or knowledge management. We believe that this shortfall can be bridged by taking a hybrid approach. Whilst formal foundations are vital, systems that incorporate some of the practical ideas found in some of the informal approaches may make the resulting hybrid systems more useful. In informal approaches, there is often an emphasis on using graphical notation with symbols that relate more closely to the real-world concepts to be modelled. There may also be the incorporation of an argument ontology oriented to the user domain. Furthermore, in informal approaches there can be greater consideration of how users interact with the models, such as allowing users to edit arguments and to weight influences on graphs representing arguments. In this paper, we discuss some of the features of argumentation, review some key formal argumentation systems, identify some of the strengths and weaknesses of these formal proposals, and finally consider some ways to develop formal proposals to give hybrid argumentation systems. To focus our discussions, we will consider some applications, in particular an application in analysing structured news reports.

This paper provides practical operationalizations of criteria for evaluating scientific theories, such as the consistency and falsifiability of theories and the soundness of inferences, that take into account definitions. The precise formulation of these criteria is tailored to the use of automated theorem provers and automated model generators—generic tools from the field of automated reasoning. The use of these criteria is illustrated by applying them to a first order logic representation of a classic organization theory, Thompson’s Organizations in Action.

set theory' [12] as his source, and another refers to Barrow `Theories of everything' [2]. One contents himself with references to two earlier unpublished papers of his own. Others give no source. For definiteness let me write down a proof, not in Cantor's words, which contains all the points we shall need to comment on. (1) We claim first that for every map f from the set {1, 2, . . . } of positive integers to the open unit interval (0, 1) of the real numbers, there is some real number which is in (0, 1) but not in the image of f. (2) Assume that f is a map from the set of positive integers to (0, 1). (3) Write 0 . a n1 a n2 a n3 . . . for the decimal expansion of f(n), where each a ni is a numeral between 0 and 9. (Where it applies, we choose the expansion which is eventually 0, not that which is eventually 9.) (4) For each positive integer n, let b n be 5 if a nn #= 5, and 4 otherwise. (5) Let b be the real number whose decimal expansion is 0 . b 1 b 2 b 3 . . . . (6...

Abstract. The call for a “focus on content ” in ontology research by Nicola Guarino and Mark Musen in their launching statement of the journal Applied Ontology has quite some implications and ramifications. We reflectively discuss ontology engineering as a scientific discipline, and we put this into the wider perspective of debates in other fields, including the methodology of social and natural sciences, and of Information Systems and design science research. We outline how ontologies provide us with a (new) scientific method for theory formation. This positioning allows for stronger concepts and techniques for theoretical, empirical and practical validation that in our view are now needed in the field. A prerequisite for this is an emphasis on ontology as a (domain) content oriented concept, rather than as primarily a computer representation notion. Taking application domain theories and the associated content reference of ontologies really seriously as first-class citizens will actually increase the contribution of ontology engineering to the development of scientific method in general. Next, ontologies should develop from the current static representations of relatively stable domain content into actionable theories-in-use, and a possible way forward is to build in capabilities for self-organization of ontologies as service-oriented knowledge utilities (SOKUs) that can be delivered over the Web.

This vision paper reflects on the nature and status of Requirements Engineering as a science, based on recent RE journal articles on methodological foundations and research classification such as [18]. We put this discussion into the wider perspective of ongoing debates in other areas, including social and natural sciences methodology, IS and design research. We propose a new categorization of the notions of validity and evaluation, and suggest a criterial framework inspired by work on the structure of scientific argument.

Abstract: This article emphasizes the need to encourage undergraduate students to develop arguments, which involves enhancing their analytical skills and capacity for critical thinking, across disciplines regardless of level. It argues that these skills, required by the Quality Assurance Agency’s (QAA) benchmarks, are developed not by instruction but by engaging with the philosophic process that leads to the deep learning. This process of learning is based on a dialectical approach, viewing dialogue with colleagues, primary texts and written assignments, as central to developing an inductive argument and a critical perspective. This article proposes an analytical framework to analyze the extent to which a tutor is facilitating the development of argument. It suggests that while, if required one must provide students with explicit guidelines about this process, nevertheless this practice is problematic because of the inherent tension between explicit teaching and deep learning, which facilitates the acquisition of these analytical skills. Key words: analytical skills; critical thinking; deduction; deep learning; development of argument; dialectic; explicit teaching; formative assessment; induction; implicit teaching

Weighted Factors Analysis (WeFA) has been proposed as a new approach for elicitation, representation, and manipulation of knowledge about a given problem, generally at a high and strategic level. Central to this proposal is that a group of experts in the area of the problem can identify a hierarchy of factors with positive or negative influences on the problem outcome.