Chapter 7 Three Principles of Compositionality

Abstract

This paper is a theoretical reflection on syntax and two kinds of semantics: (i) intensional (conceptual)—semantics comprising of the relationship between language and cognition (conceptual reality) and (ii) extensional (denotational)— semantics describing the relationships between language and reality (ontological reality) to which the language refers. The paper outlines a formal theory of compositionality and presents some methatheoretical results that can be regarded as a sample of the metatheory of syntax, meaning and interpretation (denotation). The theory of compositionality assumes as the basic axioms three formulas which formalise three different ways of understanding the so-called Principle of Compositionality, taking into account one syntactic and two semantic, both intensional (conceptual) and extensional (denotational), aspects. The formalisation of the syntactic principle of compositionality is connected with the rule of cancellation of categorial indices used by Ajdukiewicz [1] in his algorithm of checking the syntactic connection of language expressions. The formalisation of the two remaining principles takes into consideration Carnap’s dualism: intension-extension in the meaning of linguistic expressions. All three axioms as proposed in this paper have the same scheme and define suitable homomorphisms of a partial algebra of language into three partial algebras determined by 1) syntactic categorial indices (types), 2) intensional (conceptual) semantics and 3) extensional (denotational) semantics. Fundamental theorems of the theory as given refer to some replacement principles and truth value principles. The theory is presented as a modification and development of the author’s axiomatic Theory of Language Syntax and its expansion on semantic components ([32], [34], [35], [36], [37], [39], [40], [41], [42]).