A categorical approach to the semantics of argumentation

1996 ◽  
Vol 6 (2) ◽  
pp. 167-188 ◽  
Author(s):  
Simon Ambler
Keyword(s):  
Large Scale ◽  
Formal Semantics ◽  
Reasoning Under Uncertainty ◽  
Enriched Category ◽  
Closed Category ◽  
Dempster Shafer Theory ◽  
Medical Expert System ◽  
Shafer Theory ◽  
Theory Of Evidence ◽  
Cartesian Closed

Argumentation is a proof theoretic paradigm for reasoning under uncertainty. Whereas a ‘proof’ establishes its conclusion outright, an ‘argument’ can only lend a measure of support. Thus, the process of argumentation consists of identifying all the arguments for a particular hypothesis φ, and then calculating the support for φ from the weight attached to these individual arguments. Argumentation has been incorporated as the inference mechanism of a large scale medical expert system, the ‘Oxford System of Medicine’ (OSM), and it is therefore important to demonstrate that the approach is theoretically justified. This paper provides a formal semantics for the notion of argument embodied in the OSM. We present a categorical account in which arguments are the arrows of a semilattice enriched category. The axioms of a cartesian closed category are modified to give the notion of an ‘evidential closed category’, and we show that this provides the correct enriched setting in which to model the connectives of conjunction (&) and implication (⇒).Finally, we develop a theory of ‘confidence measures’ over such categories, and relate this to the Dempster-Shafer theory of evidence.

scholarly journals Plato's Cave in the Dempster-Shafer land--the Link between Pignistic and Plausibility Transformations

2017 ◽  
Author(s):  
Chunlai Zhou ◽  
Biao Qin ◽  
Xiaoyong Du
Keyword(s):  
Statistical Inference ◽  
Belief Function ◽  
Belief Functions ◽  
Reasoning Under Uncertainty ◽  
Function Model ◽  
Probability Functions ◽  
Degree Of Belief ◽  
Dempster Shafer Theory ◽  
Shafer Theory ◽  
Theory Of Evidence

In reasoning under uncertainty in AI, there are (at least) two useful and different ways of understanding beliefs: the first is as absolute belief or degree of belief in propositions and the second is as belief update or measure of change in belief. Pignistic and plausibility transformations are two well-known probability transformations that map belief functions to probability functions in the Dempster-Shafer theory of evidence. In this paper, we establish the link between pignistic and plausibility transformations by devising a belief-update framework for belief functions where plausibility transformation works on belief update while pignistic transformation operates on absolute belief. In this framework, we define a new belief-update operator connecting the two transformations, and interpret the framework in a belief-function model of parametric statistical inference. As a metaphor, these two transformations projecting the belief-update framework for belief functions to that for probabilities are likened to the fire projecting reality into shadows on the wall in Plato's cave.

REASONING UNDER UNCERTAINTY FOR SHILL DETECTION IN ONLINE AUCTIONS USING DEMPSTER–SHAFER THEORY

2010 ◽  
Vol 20 (07) ◽  
pp. 943-973 ◽  
Author(s):  
FEI DONG ◽  
SOL M. SHATZ ◽  
HAIPING XU
Keyword(s):  
Decision Making ◽  
Online Auctions ◽  
Single Source ◽  
Reasoning Under Uncertainty ◽  
Multiple Sources ◽  
Dempster Shafer Theory ◽  
Shafer Theory ◽  
Theory Of Evidence ◽  
Positive Results

This paper describes the design of a decision support system for shill detection in online auctions. To assist decision making, each bidder is associated with a type of certification, namely shill, shill suspect, or trusted bidder, at the end of each auction's bidding cycle. The certification level is determined on the basis of a bidder's bidding behaviors including shilling behaviors and normal bidding behaviors, and thus fraudulent bidders can be identified. In this paper, we focus on representing knowledge about bidders from different aspects in online auctions, and reasoning on bidders' trustworthiness under uncertainties using Dempster–Shafer theory of evidence. To demonstrate the feasibility of our approach, we provide a case study using real auction data from eBay. The analysis results show that our approach can be used to detect shills effectively and efficiently. By applying Dempster–Shafer theory to combine multiple sources of evidence for shill detection, the proposed approach can significantly reduce the number of false positive results in comparison to approaches using a single source of evidence.

scholarly journals A MODIFIED D NUMBERS METHODOLOGY FOR ENVIRONMENTAL IMPACT ASSESSMENT

2017 ◽  
Vol 24 (2) ◽  
pp. 653-669 ◽  
Author(s):  
Ningkui WANG ◽  
Daijun WEI
Keyword(s):  
Environmental Impact ◽  
Impact Assessment ◽  
Environmental Impact Assessment ◽  
Previous Method ◽  
Combination Process ◽  
Dempster Shafer Theory ◽  
Shafer Theory ◽  
Theory Of Evidence ◽  
D Numbers ◽  
Commutative Property

Environmental impact assessment (EIA) is usually evaluated by many factors influenced by various kinds of uncertainty or fuzziness. As a result, the key issues of EIA problem are to rep­resent and deal with the uncertain or fuzzy information. D numbers theory, as the extension of Dempster-Shafer theory of evidence, is a desirable tool that can express uncertainty and fuzziness, both complete and incomplete, quantitative or qualitative. However, some shortcomings do exist in D numbers combination process, the commutative property is not well considered when multiple D numbers are combined. Though some attempts have made to solve this problem, the previous method is not appropriate and convenience as more information about the given evaluations rep­resented by D numbers are needed. In this paper, a data-driven D numbers combination rule is proposed, commutative property is well considered in the proposed method. In the combination process, there does not require any new information except the original D numbers. An illustrative example is provided to demonstrate the effectiveness of the method.

Knowledge reduction in random information systems via Dempster–Shafer theory of evidence

2005 ◽  
Vol 174 (3-4) ◽  
pp. 143-164 ◽  
Author(s):  
Wei-Zhi Wu ◽  
Mei Zhang ◽  
Huai-Zu Li ◽  
Ju-Sheng Mi
Keyword(s):  
Information Systems ◽  
Knowledge Reduction ◽  
Dempster Shafer Theory ◽  
Shafer Theory ◽  
Theory Of Evidence

A Framework for Decision Fusion in Image Forensics Based on Dempster–Shafer Theory of Evidence

2013 ◽  
Vol 8 (4) ◽  
pp. 593-607 ◽  
Author(s):  
Marco Fontani ◽  
Tiziano Bianchi ◽  
Alessia De Rosa ◽  
Alessandro Piva ◽  
Mauro Barni
Keyword(s):  
Image Forensics ◽  
Decision Fusion ◽  
Dempster Shafer Theory ◽  
Shafer Theory ◽  
Theory Of Evidence
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