Operator grammar is a
mathematical theory of human language that explains how language carries
information. This theory is the culmination of the life work of
Zellig Harris, with major
publications toward the end of the last century. Operator grammar proposes that each human language is a
self-organizing system in which both the
syntactic
In linguistics, syntax () is the study of how words and morphemes combine to form larger units such as phrases and sentences. Central concerns of syntax include word order, grammatical relations, hierarchical sentence structure (constituency), ...
and
semantic
Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy, linguistics and comput ...
properties of a word are established purely in relation to other words. Thus, no external system (
metalanguage
In logic and linguistics, a metalanguage is a language used to describe another language, often called the ''object language''. Expressions in a metalanguage are often distinguished from those in the object language by the use of italics, quot ...
) is required to define the rules of a language. Instead, these rules are learned through exposure to usage and through participation, as is the case with most
social behavior. The theory is consistent with the idea that
language evolved gradually, with each successive generation introducing new complexity and variation.
Operator grammar posits three
universal constraints:
dependency (certain words depend on the presence of other words to form an utterance),
likelihood (some combinations of words and their dependents are more likely than others) and
reduction (words in high likelihood combinations can be reduced to shorter forms, and sometimes omitted completely). Together these provide a theory of
language information: dependency builds a
predicate–argument structure; likelihood creates distinct meanings; reduction allows compact forms for communication.
Dependency
The fundamental mechanism of operator grammar is the