The paper studies semantics that evaluate arguments in argumentation graphs, where each argument has a basic strength, and may be attacked by other arguments. It starts by defining a set of principles, each of which is a property that a semantics could satisfy. It provides the first formal analysis and comparison of existing semantics. Finally, it defines three novel semantics that satisfy more principles than existing ones.
One of the most prominent tools for abstract argumentation is the Dung's framework, AF for short. It is accompanied by a variety of semantics including grounded, complete, preferred and stable. Although powerful, AFs have their shortcomings, which led to development of numerous enrichments. Among the most general ones are the abstract dialectical frameworks, also known as the ADFs. They make use of the so-called acceptance conditions to represent arbitrary relations. This level of abstraction brings not only new challenges, but also requires addressing existing problems in the field. One of the most controversial issues, recognized not only in argumentation, concerns the support cycles. In this paper we introduce a new method to ensure acyclicity of the chosen arguments and present a family of extension-based semantics built on it. We also continue our research on the semantics that permit cycles and fill in the gaps from the previous works. Moreover, we provide ADF versions of the properties known from the Dung setting. Finally, we also introduce a classification of the developed sub-semantics and relate them to the existing labeling-based approaches.
Temporal patterns of running velocity is of profound interest for coaches and researchers involved in sprint racing. In this study, we applied a nonhomogeneous differential equation for the motion with resistance force proportional to the velocity for the determination of the instantaneous velocity and instantaneous and average acceleration in the sprinter discipline at 100 m. Results obtained for the instantaneous velocity in this study using the presented model indicate good agreement with values measured directly, which is a good verification of the proposed procedure. To perform a comprehensive analysis of the applicability of the results obtained, the harmonic canon of running for the 100-m sprint discipline was formed. Using the data obtained by the measurement of split times for segments of 100-m run of the sprinters K. Lewis (1988), M. Green (2001), and U. Bolt (2009), the method described yielded results that enable comparative analysis of the kinematical parameters for each sprinter. Further treatment allowed the derivation of the ideal harmonic velocity canon of running, which can be helpful to any coach in evaluating the results achieved at particular distances in this and other disciplines. The method described can be applied for the analysis of any race.
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