This article sets up a graph-theoretical framework for argumentation-analysis (dialectical analysis) which expands classical argument-analysis. Within this framework, a main theorem on the existence of inconsistencies in debates is stated and proved: the vicious circle theorem. Subsequently, two corollaries which generalize the main theorem are derived. Finally, a brief outlook is given on further expansions and possible applications of the developed framework.

This paper develops concepts and procedures for the evaluation of complex debates. They provide means for answering such questions as whether a thesis has to be considered as proven or disproven in a debate or who carries a burden of proof. While being based on classical logic, this framework represents an (argument-based) approach to non-monotonic, or defeasible reasoning. Debates are analysed as dialectical structures, i.e. argumentation systems with an attack- as well as a support-relationship. The recursive status assignment over the (...) arguments is conditionalised on proponents in a debate. The problem of multiple status assignments arising on circular structures is solved by showing that uniqueness can be guaranteed qua reconstruction of a debate. The notion of burden of proof as well as other discursive aims rational proponents pursue in a debate is defined within the framework. (shrink)

Different inferences in probabilistic logics of conditionals 'preserve' the probabilities of their premisses to different degrees. Some preserve certainty, some high probability, some positive probability, and some minimum probability. In the first case conclusions must have probability I when premisses have probability 1, though they might have probability 0 when their premisses have any lower probability. In the second case, roughly speaking, if premisses are highly probable though not certain then conclusions must also be highly probable. In the third case (...) conclusions must have positive probability when premisses do, and in the last case conclusions must be at least as probable as their least probable premisses. Precise definitions and well known examples are given for each of these properties, characteristic principles are shown to be valid and complete for deriving conclusions of each of these kinds, and simple trivalent truthtable 'tests' are described for determining which properties are possessed by any given inference. Brief comments are made on the application of these results to certain modal inferences such as "Jones may own a car, and if he does he will have a driver's license. Therefore, he may have a driver's license.". (shrink)

There was a long tradition in philosophy according to which good reasoning had to be deductively valid. However, that tradition began to be questioned in the 1960’s, and is now thoroughly discredited. What caused its downfall was the recognition that many familiar kinds of reasoning are not deductively valid, but clearly confer justification on their conclusions. Here are some simple examples.

The question addressed in this paper is how the degree of justification of a belief is determined. A conclusion may be supported by several different arguments, the arguments typically being defeasible, and there may also be arguments of varying strengths for defeaters for some of the supporting arguments. What is sought is a way of computing the “on sum” degree of justification of a conclusion in terms of the degrees of justification of all relevant premises and the strengths of all (...) relevant reasons. (shrink)

This major work challenges some widely held positions in epistemology - those of Peirce and Popper on the one hand and those of Quine and Kuhn on the other.

"A sequel to Pollock's How to Build a Person, this volume builds upon that theoretical groundwork for the implementation of rationality through artificial ...

Degrees of belief; Dempster's rule of combination; Simple and separable support functions; The weights of evidence; Compatible frames of discernment; Support functions; The discernment of evidence; Quasi support functions; Consonance; Statistical evidence; The dual nature of probable reasoning.

Logical models of argument formalize commonsense reasoning while taking process and computation seriously. This survey discusses the main ideas which characterize di erent logical models of argument. It presents the formal features of a few main approaches to the modeling of argumentation. We trace the evolution of argumentationfrom the mid-80's, when argumentsystems emerged as an alternative to nonmonotonic formalisms based on classical logic, to the present, as argument is embedded in di erent complex systems for real-world applications, and allows more (...) formal work to be done in different areas, such as AI & Law, case-based reasoning and negotiation among intelligent agents. (shrink)