Text, Duality and the Bidirectional Semantic Knowledge: An EpistemicMathematical Model for Semantics

Source abstract

In this article, we present an epistemic-mathematical duality frame for universality-to-text and text-into-text semantics from our approach with focus on the nature of semantic knowledge implying hypotheses and results of computational brain dimensions of the latter. Thus, starting from a space mathematical organization of language on the linguistic object, especially duality of self-expansion/self-reduction, a threefold attempt enables the following: First, we rely on axiomatic frames of abstract semantic algebra and its representation-induction model. Secondly, by means of demonstration, a test along with two major components is proposed in which the first component verifies SOP (conceptual)/POS (compositional) logical-semantic implications of syntax-semantic duality: a model of state/term absorption is applied (XConceptual compositional). Furthermore, we present a graph model of duality based on perfect elimination ordering PEO between conceptual and compositional dualities endowed with polarity and reversibility. Moreover, a model of participational duality entails an experimental/empirical framework through conversational interactions. From diplo/haplo-arguments, cognitive duality of intelligibility/comprehension yields an epistemic function from Conceptual Wholes and Conceptual absorption/inversion specified by Labeled or regressive Constatives Lco and interpretive primitives IP (through Gamma function). Lastly, a debate on semantic holism and duality suggests a dual oriented holism of the bidirectional text OTO.