Reasoning Consistently about Inconsistency

Abstract

Abstract-Patching et al. and Hinde et al. in their work on truth-space mass assignments, presented a semantic unification function and a semantic separation function for mass assignment logic that dealt with inconsistency. This paper takes these two functions and while preserving the outside inconsistencies shows how inconsistency can be reasoned about in a consistent manner. This means that inconsistency that arises outside the system need not enter the system, but needs to be represented within the system, and can therefore be extracted appropriately as output from the system to emerge as inconsistency on the outside. The internal reasoning system need therefore only concern itself with belief in truth, falsity and uncertainty.

A fuzzy directional distance measure

“…Semantic unification assesses the support of a claim A given a ground clause G. As defined in [7], it does not deal with claims or ground evidence that are inconsistent. However, an extended version described in [8] deals with inconsistent FSs, or alternatively nonnormalised FSs. This work starts with the extended version which is defined as follows for two MAs m A = {A i : a i } and m G = {G j : g j }: Semantic unification thus delivers a FS of truth values indicating the degree of support the fuzzy claim A receives from the fuzzy evidence G. Neither FS is necessarily normalised and so the FS representing the degree of support, similarly, is not necessarily normalised.…”

“…A background on MA and semantic unification is presented first. Mass assignment uses a measure of support based on semantic unification, [6] that is generalised in [8] and further in [9]. Distance is commonly calculated using α-cuts, which are related to MAs, such that they both break down the FS along the membership axis.…”

Agents and rough sets

“…Where Q is the linear superposition of the logic value for the active set. Resconi [1][2][3][4][5][6][7][8] , Hinde [16][17][18][19][20][21][22][23][24] .…”

A Fuzzy Directional Distance Measure

“…However, an extended version described in [8] deals with inconsistent FSs, or alternatively nonnormalised FSs. This work starts with the extended version which is defined as follows for two MAs m A = {A i : a i } and m G = {G j : g j }: Semantic unification thus delivers a FS of truth values indicating the degree of support the fuzzy claim A receives from the fuzzy evidence G. Neither FS is necessarily normalised and so the FS representing the degree of support, similarly, is not necessarily normalised.…”

“…Mass assignment uses a measure of support based on semantic unification, [6] that is generalised in [8] and further in [9]. Distance is commonly calculated using α-cuts, which are related to MAs, such that they both break down the FS along the membership axis.…”