Compositional semantics addresses how the meanings of complex expressions are built from the meanings of their parts combined according to syntactic structure — Frege's principle of compositionality. Truth-conditional semantics analyzes sentence meaning as the conditions under which a sentence would be true. Key phenomena include entailment (if A is true, B must follow necessarily), presupposition (background assumptions that survive negation), and scope ambiguity (when quantifiers or negation interact in multiple ways).
Practice writing truth conditions for simple sentences. Work through scope ambiguity examples with quantifiers like 'every' and 'some'. Distinguish entailment from presupposition by testing what happens when the sentence is negated.
If you have studied lexical semantics, you know the meaning of individual words. But knowing that "dog" means dog and "chased" means chased does not tell you what "Every dog chased some cat" means — or why that sentence is ambiguous in a way that "The dog chased the cat" is not. Compositional semantics is the study of how sentential meaning is built from word meanings and grammatical structure. Frege's foundational insight, called the principle of compositionality, states that the meaning of a complex expression is a function of the meanings of its parts and the way those parts are combined. Structure matters: "The dog bit the man" and "The man bit the dog" contain the same words but mean different things because the syntactic roles differ.
A key tool in compositional semantics is truth-conditional meaning: to know the meaning of a sentence is to know under what conditions it would be true. "Snow is white" is true if and only if snow is white. This may seem trivially obvious, but it gives a precise, testable handle on meaning. We can now ask whether sentence A entails sentence B — does B have to be true in every situation where A is true? "Fido is a dog" entails "Fido is an animal," because there is no possible situation in which the first is true and the second is false. Entailment is strictly logical: it holds necessarily, in virtue of meaning alone, not just in most cases.
Presuppositions are a subtler phenomenon. They are background assumptions that a sentence takes for granted rather than asserts. "My sister stopped going to the gym" presupposes that my sister was going to the gym before. The diagnostic is negation: negate the sentence ("My sister didn't stop going to the gym") and the presupposition survives — we still assume she had been going. Regular assertions and entailments, by contrast, are cancelled by negation. This survival under negation is what makes presuppositions unusual and worth studying separately.
Scope ambiguity shows how syntactic structure and semantic interpretation can come apart. The sentence "Every professor read some student's paper" has two readings: one where a single paper was read by all professors (existential quantifier takes wide scope), and one where each professor read a (possibly different) paper (existential takes narrow scope under the universal). These are genuine differences in logical content. Formal semantics handles them by explicitly representing which quantifier takes scope over which, using tools like lambda calculus or logical form representations.
The reason compositional semantics feels challenging at first is that natural language is extraordinarily efficient — a small vocabulary and grammar generates an infinite range of meanings. The machinery behind that efficiency is what this field makes explicit. As you move into pragmatics, you will discover that truth conditions are only part of the story: what we communicate goes well beyond what we literally say. But compositional semantics gives you the baseline — the literal meaning relative to which all other communicative enrichments operate.