In this paper we show how the defense relation among abstract arguments can be used to encode the reasons for accepting arguments. After introducing a novel notion of defenses and defense graphs, we propose a defense semantics together with a new notion of defense equivalence of argument graphs, and compare defense equivalence with standard equivalence and strong equivalence, respectively. Then...

Two transformations between the complex space and 2-dimensional Euclidian topological space are defined. By them, the concept of argument is induced to 2dimensional vectors using argument of complex number. Similarly, the concept of an angle is introduced using the angle of two complex numbers. The concept of a triangle and related concepts are also defined in n-dimensional Euclidian topologica...

Existing approaches to summarizing multi-party argumentative conversations in reader comment are extractive and fail to capture the argumentative nature of these conversations. Work on argument mining proposes schemes for identifying argument elements and relations in text but has not yet addressed how summaries might be generated from a global analysis of a conversation based on these schemes....

This paper fortifies and defends the so called Sufficiency Argument (SA) against Classical Invariantism. In Sect. 2, I explain the version of the SA formulated but then rejected by Brown (2008a). In Sect. 3, I show how cases described by Hawthorne (2004), Brown (2008b), and Lackey (forthcoming) threaten to undermine one or the other of the SA’s least secure premises. In Sect. 4, I buttress one ...

Systems of linear diierential equations with constant coeecients, as well as Lotka{Volterra equations, with delays in the oo{diagonal terms are considered. Such systems are shown to be asymptotically stable for any choice of delays if and only if the matrix has a negative weakly dominant diagonal.

We will call such adjuncts instances of the X or no X construction It was suggested in the middle 1980s by Alexis Manaster-Ramer that well-formed instances of X or no X involve a string X of unbounded length preceding or no, with an exact copy following (for a brief allusion to it in print, see Manaster-Ramer 1986). This claim has received hardly any discussion at all in the subsequent literatu...