# Acyclic Graph of Definitions of a Language

Given a certain language L, let's define it's language graph G as the graph where nodes correspond to words and a directed edge between node B and node A implies that the word referenced by B belongs to the definition of the word referenced by A.

My question is, can we construct a set of definitions that still reflect the semantic meaning of the words of L while also resulting in G being acyclic? If it is not the case, can we construct an artificial language that follows this property?

An acyclic definition graph would imply the existence of certain words without a definition but such a graph can result in a topological sort of words. Thus an ordered hierarchy for learning the words of the language.

• The Natural Semantic Metalanguage is one attempt to solve the problem of circular definitions. – curiousdannii Mar 14 at 22:58
• I don't understand the idea of a word "belonging to the definition" of another word. Also, how do we know if a definition "reflects" the meaning of a word? – user6726 Mar 14 at 23:55
• @user6726 Let's take for example the oxford's definition of the word "Person" : "A human being regarded as an individual." Since the word "human" belongs to the definition of the word "person" then there is a directed edge from the node corresponding to "human" to that of "person". A definition reflects the meaning if it succeeds in defining it. I do not know of any formal way of expressing this statement. – Mirowsky Mar 15 at 0:07
• @curiousdannii Thanks ! This is an interesting read. – Mirowsky Mar 15 at 0:10
• In other words, "contains", i.e. that definition of "person" contains the word "human". I would say a definition states the meaning of a word α iff it identifies all and only the referents of α. And you want all words to be defined by propositions composed only of other words (non-circularly). – user6726 Mar 15 at 1:00