Existential Concept Graphs of Power Context Families

Abstract

The aim of this paper is to show how existential concept graphs may be introduced on the semantic level. For this the “free extension” of a power context family $\mathbb{K}$ by a given set X of variables is constructed as a power context family “freely” enlarged by X. Then, an existential concept graph of $\mathbb{K}$ can be appropriately defined as a concept graph of the free extension of $\mathbb{K}$ that can be projected onto a concept graph of $\mathbb{K}$ by some mapping induced by an interpretation of the variables of X by basic objects of $\mathbb{K}$ . The introduced conceptual content of existential concept graphs allows a simple description of the generalization order between those graphs. All this can be generalized to existential protoconcept graphs for also including negations. In this way, the actual development of Contextual Judgment Logic disposes of (implicit) existential quantifiers as well as negations and negating inversions (cf. [Wi01a]).