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Diffstat (limited to 'linguistics')
| -rw-r--r-- | linguistics/semantics.md | 11 |
1 files changed, 8 insertions, 3 deletions
diff --git a/linguistics/semantics.md b/linguistics/semantics.md index a590de3..96638aa 100644 --- a/linguistics/semantics.md +++ b/linguistics/semantics.md @@ -20,6 +20,11 @@ This framework is [first-order/predicate logic](../mathematics/logic) and the [s ### Compositionality +The *Principle of Compositionality* states that the meaning of a *constituent* is determined entirely by its *components*. This is *the* fundamental underlying principle behind formal logic and subsequently semantics. It holds for not just sentence composition (syntax), but also *word formation* (morphology), and what's of interest to us here - meaning (semantics). + +### Substitution + +The *Principle of Substitution* states that substituting one part of an expression with something else of the same meaning *preserves* the meaning of the expression as a whole. This might be thought of as a given, but semantics has its roots in philosophy, and philosophers care very much about enumerating their givens. ### Predicate Logic & The Lambda Calculus @@ -37,8 +42,8 @@ With basic logic and the lambda calculus under our belt, we may simply get strai > *Alice is bad.* <br> > *The blue pigeon flew away.* -- Noun: $⟨e,t⟩ ↝ λx.Noun(x)$ -- Verb (intransitive): $⟨e,t⟩ ↝ λx.Verb(x)$ +- Noun $↝ λx.Noun(x)$ $: ⟨e,t⟩$ +- Verb (intransitive) ↝ $λx.Verb(x)$: $⟨e,t⟩$ - Verb (transitive): $⟨e,⟨e,t⟩⟩ ↝ λy.λx.Verb(x, y)$ - Verb (meaningless): $⟨⟨e,t⟩,⟨e,t⟩⟩ ↝ λP.λx.P(x)$ - Adj: $⟨⟨e,t⟩,⟨e,t⟩⟩ ↝ λNoun.λx.[Adj(x) ∧ Noun(x)]$ @@ -59,7 +64,7 @@ With basic logic and the lambda calculus under our belt, we may simply get strai - some: $⟨⟨e,t⟩,⟨⟨e,t⟩,t⟩⟩ ↝ λQ.λP.∃x.[P(x) ∧ Q(x)]$ - something: $⟨⟨e,t⟩,t⟩ ↝ λP.∃x.P(x)$ - no: $⟨⟨e,t⟩,⟨⟨e,t⟩,t⟩⟩ ↝ λQ.λP.∀x.[P(x) → ¬Q(x)] (or λQ.λP.¬∃x.[P(x) ∧ Q(x)])$ - - nothing: $⟨⟨e,t⟩,t⟩ ↝ λP.¬∃x.P(x)$ (or $λP.∀x.¬P(x))$ + - nothing: $⟨⟨e,t⟩,t⟩ ↝ λP.¬∃x.P(x)$ (or $λP.∀x.¬P(x)$) ### Reference |