Paired structures in knowledge representation

Abstract

In this position paper we propose a consistent and unifying view to all those basic knowledge representation models that are based on the existence of two somehow opposite fuzzy concepts. A number of these basic models can be found in fuzzy logic and multi-valued logic literature. Here it is claimed that it is the semantic relationship between two paired concepts what determines the emergence of different types of neutrality, namely indeterminacy, ambivalence and conflict, widely used under different frameworks (possibly under different names). It will be shown the potential relevance of paired structures, generated from two paired concepts together with their associated neutrality, all of them to be modelled as fuzzy sets. In this way, paired structures can be viewed as a standard basic model from which different models arise. This unifying view should therefore allow a deeper analysis of the relationships between several existing knowledge representation formalisms, providing a basis from which more expressive models can be later developed.Recent advances in Psychology and Neurology are providing relevant results for the development of decision making models. The human brain has specifically and successfully evolved to manage complex, uncertain, incomplete, and even apparently inconsistent information. For example, neurologists have shown that the part of the brain taking care of making up the last decision is different to the part of the brain in charge of the previous rational analysis of alternatives, being the first part associated to emotions (see, e.g., [6],[7]). A number of similar results within neurology (see, e.g.

Paired Structures and other opposites-based models

“…where X is our universe of discourse and each object x X  is assigned up to a degree ( ) Although more details will be found in [17], we should stress that, consistently with [16], an appropriate logic (or logics if [14] and [15] are taken into account), should be then associated to this structure (X, L, A L ). It is important to point out that, consistently with [1] and…”

Paired fuzzy sets: A unifying model for early knowledged acquisition

“…In this section we recall the basic definitions proposed in [16]. These definitions were justified on the basis of a semantic argument, which tries to explore our knowledge representation process: from a given predicate (for instance, one we consider relevant in a given context), we are able to generate its negation.…”

“…and any object x X ∈ , being n a strong negation function, i.e., a strictly decreasing continuous function : [21], [22] and [23]). The basic definitions proposed in [16] are the following:…”

“…The following definition of antagonism as a different kind of opposite has been also proposed in [16], noticing that we can find opposites that are neither antonyms nor antagonisms.…”

“…This paper pursues to stress the relevance of the notion of paired fuzzy sets, as proposed in a joint work between this team and other researchers at the Public University of Navarra, Spain [16]. Our approach should be considered also a continuation of a paper already published in the Fuzzy Sets and Systems journal [17].…”