Over the last two and a half millennia of logical and linguistic research, a set of intuitions behind the notion of ‘sentence’ have accumulated not all of which can be accounted for in a coherent definition. One of these is the idea that a sentence can be used as a complete utterance. Since larger chunks of discourse like paragraphs and text are not generated by a grammar, a sentence is also the minimum unit that can be used as an utterance. The requirement that a sentence be usable as a complete utterance includes the condition that it possess an illocutionary force.

Another intuition behind the notion of ‘sentence’ is that it has a semantic structure: Its meaning is composed of a predicate and its arguments. These should be represented syntactically in the form of a syntactic (verbal nor non-verbal) predicate and minimally those dependents required by its valency, as in Aristotle's ‘the man walks’.

This intuitive requirement excludes most actually occurring utterances from the concept of ‘sentence’, like Yes. Oh. Hmhm. Fire! What? Gosh! and so on. There are various ways of solving this dilemma. One is to introduce the concept of the clause. This may be taken as the syntactic counterpart of the Aristotelian proposition.

A further problem is presented by syntactic complexity. The construction The man walks. is usable as a complete utterance, but the construction that the man walks is not, although it represents the same proposition. This has usually been solved by saying that a clause represents a proposition, but may be independent or subordinate. In the latter case, it is not usable as an utterance.

In English grammar, a construction comprising an independent and a dependent clause like The woman believes that the man walks. has traditionally been called ‘complex sentence’. This, however, is not a possible basis for a consistent definition of ‘complex sentence’ (Haspelmath 2020). The construction the woman who believes that the man walks contains the same two propositions combined into a complex of two clauses, but is not a sentence, but at most part of a sentence like This is the woman who believes that the man walks.

One way out of this is the following: We maintain the requirement that a sentence be a clause with an illocutionary force, but drop the requirement that a clause be simple, i.e. that it represent just one proposition. Then we can define:

• A proposition is a semantic object consisting of one predicate and at least its arguments (and possibly further components combining with a single predicate and its arguments).
• A clause is either a simple or a complex clause.
• A simple clause is a construction designating a proposition.
• A complex clause is a construction consisting of clauses.
• A sentence is a minimum utterance consisting of clauses.

This set of definitions has certain implications:

• The parenthesized expression in the definition of ‘proposition’ allows for quantifiers, determiners and modifiers.
• The internal structure of a clause is posited at the semantic level. This allows subsuming a construction like Latin ambulat (walk(PRS):3.SG) ‘(he) walks’ under the concept of clause although there is no subject or other verb dependent.
• The construction who believes that the man walks is a complex clause, but not a complex sentence since it is not a sentence.
• Utterances like Gosh!, but also elliptical utterances are still no sentences.

Reference

Haspelmath, Martin 2020, "On the difference between a clause and a sentence." Kibrik, Andrej A. et al. (eds.), VAProsy jazykoznaija: Megasbornik nanostatej. Sb. st. k jubileju V.A. Plungjana. Moskva: Buki Vedi; 597-605.