Prolegomenon on The Ontology of Complete or Partial Homomorphisms in The Syntax-Semantics Interface in Grammars
The formalization of the syntax-semantics interface in natural and formal languages subsumes a number of homomorphisms which are assumed to exist which should be tested and made explicit in Algebraic Linguistic systems. This paper examines selected grammar formalisms in philosophy (model theory) and mainstream linguistics (especially in Generative Grammars). Homomorphisms in the algebraic systems are subject to metaphysical and epistemological assumptions of full or partial access to reality. The paper argues that the homomorphisms should be partial due to the hierarchical nature of linguistic subconstituents in the syntax which are antisymmetrical, and should be implemented entirely using partial algebras in order to meet the constraint of compositionality.This paper notes the failure of some systems to account for the assymetries between perception and reality which are implied by the notions of homomorphisms espoused with reference to analytic and generative context free and context sensitive grammars.
Key Terms - Algebraic Linguistics, Formal Languages, Natural Languages, Analytic Grammars, Generative Grammars, Graph Theory, compositionality