Non-monotonic logic is the study of ways of inferring new information from given information that do not satisfy the monotonicity property satisfied by all methods based on classical logic. In mathematics, if a conclusion is warranted on the basis of current premises, no additional premises will ever invalidate the conclusion. In everyday life, however it seems clear that we, human beings, draw sensible conclusions from what we know and that, on the face of new information we often have to take back previous conclusion. Argumentation is a way to formalize non-monotonic reasoning, using the construction and comparison of arguments for and against certain conclusions. Now one general question could be why the urge to implement non-monotonic reasoning in machines? Why is it auspicious that they are going to reason with each other to reach a goal? Jim Waldo the lead architect for Jini, was asked if faster processor, faster network and larger storage capacity could eventually diminish the need for distributed computing?[1] The trends to look at are those described by Moore's Law having to do with processors and the trends with network traffic. Moore's law as we all know said, the performance of the processor doubles every 18 months. Whereas the trends in network traffic, however, is that it doubles every 12 months. So the increase in network traffic is outpacing the increase in processor performance. Widespread distributed computing will force peer to peer applications to go beyond file sharing and gaming. As more and more different kinds of computing devices, from servers to cell phones to automobiles to refrigerators will be on the network, information will be frequently incomplete, incoherent or contradictory. It has therefore been proposed that automated decision making systems may benefit from the use of 'defeasible argumentation' [2], a relatively new paradigm in logical reasoning based upon sound theoretical concepts from the study of argument in order to support opinions, claims, proposals and ultimately decisions and conclusions.;In argumentation systems non-monotonicity arises from the fact that new premises may give rise to stronger counterarguments, which may defeat the original argument. It can be applied to any form of reasoning with contradictory information, whether the contradictions have to do with rules and exceptions or not. For instance, the contradictions may arise from reasoning with several sources of information, or they may be caused by disagreement about beliefs or about moral, ethical or political claims. When compared with traditional automated rule-based decision-making this approach is more in keeping with the way humans often deliberate and finally make a choice [3] and could prove extremely useful in real world software applications. However, research in argumentation has inherited the tendency from the non-monotonic reasoning community to focus the majority of attention on the theoretical issues, ignoring the practical details of algorithm implementation. Furthermore, many of the proposed algorithms lack a complexity analysis and therefore it remains unclear how well these algorithm perform in practice. This could be responsible for the lack of uptake of this type of logical reasoning formalism within existing software applications. This thesis contains an algorithm more practical to be implemented in software industry and an application of Argumentation in Reputation system.
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