Conditional Deduction Under Uncertainty

Abstract

Abstract. Conditional deduction in binary logic basically consists of deriving new statements from an existing set of statements and conditional rules. Modus Ponens, which is the classical example of a conditional deduction rule, expresses a conditional relationship between an antecedent and a consequent. A generalisation of Modus Ponens to probabilities in the form of probabilistic conditional inference is also well known. This paper describes a method for conditional deduction with beliefs which is a generalisation of probabilistic conditional inference and Modus Ponens. Meaningful conditional deduction requires a degree of relevance between the antecedent and the consequent, and this relevance can be explicitly expressed and measured with our method. Our belief representation has the advantage that it is possible to represent partial ignorance regarding the truth of statements, and is therefore suitable to model typical real life situations. Conditional deduction with beliefs thereby allows partial ignorance to be included in the analysis and deduction of statements and hypothesis.

Subjective logic operators in trust assessment: an empirical study

“…and McAnally 2004;Jøsang et al 2005Jøsang et al , 2006McAnally and Jøsang 2004;Jøsang 2008) satisfies the combination requirements described previously.…”

“…As discussed in (Jøsang 2001), a Subjective Logic opinion admits a geometrical representation inside a triangle, and, as shown in (Jøsang et al 2005), operators can be defined in order to satisfy graphical properties 3 .…”

“…Given opinions about two propositions from different frames of discernment, it is possible to combine them in various ways using SL's various operators, as detailed in (Jøsang 2001;Jøsang and McAnally 2004;Jøsang et al 2005Jøsang et al , 2006McAnally and Jøsang 2004). In this work we concentrate on Jøsang's discount and fusion operators, which we review next.…”

“…(Jøsang et al 2005) shows how the deduction operator affects the space of possible derived opinions.…”

Optimal Trust Network Analysis with Subjective Logic

“…Subjective logic defines a number of operators [3,8]. Some operators represent generalisations of binary logic and probability calculus operators, whereas others are unique to belief theory because they depend on belief ownership.…”