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Diffstat (limited to 'linguistics/semantics.md')
| -rw-r--r-- | linguistics/semantics.md | 34 |
1 files changed, 28 insertions, 6 deletions
diff --git a/linguistics/semantics.md b/linguistics/semantics.md index 96bbb17..a590de3 100644 --- a/linguistics/semantics.md +++ b/linguistics/semantics.md @@ -33,12 +33,34 @@ With basic logic and the lambda calculus under our belt, we may simply get strai ### Entities and Functions -> I am Alice. -> Alice is bad. -> The blue pigeon flew away. +> *I am Alice.* <br> +> *Alice is bad.* <br> +> *The blue pigeon flew away.* + +- Noun: $⟨e,t⟩ ↝ λx.Noun(x)$ +- Verb (intransitive): $⟨e,t⟩ ↝ λx.Verb(x)$ +- Verb (transitive): $⟨e,⟨e,t⟩⟩ ↝ λy.λx.Verb(x, y)$ +- Verb (meaningless): $⟨⟨e,t⟩,⟨e,t⟩⟩ ↝ λP.λx.P(x)$ +- Adj: $⟨⟨e,t⟩,⟨e,t⟩⟩ ↝ λNoun.λx.[Adj(x) ∧ Noun(x)]$ + +- or (clausal): $⟨t,⟨t,t⟩⟩ ↝ λq.λp.[p ∨ q]$ +- and (clausal): $⟨t,⟨t,t⟩⟩ ↝ λq.λp.[p ∧ q]$ +- or (verbal): $⟨⟨e,t⟩,⟨⟨e,t⟩,⟨e,t⟩⟩⟩ ↝ λQ.λP.λx.[P(x) ∨ Q(x)]$ +- and (verbal): $⟨⟨e,t⟩,⟨⟨e,t⟩,⟨e,t⟩⟩⟩ ↝ λQ.λP.λx.[P(x) ∧ Q(x)]$ +- or (quantifiers): $⟨⟨e,⟨e,t⟩⟩,⟨⟨e,⟨e,t⟩⟩,⟨e,⟨e,t⟩⟩⟩⟩ ↝ λQ.λP.λy.λx.[P(x,y) ∨ Q(x,y)]$ +- and (quantifiers): $⟨⟨e,⟨e,t⟩⟩,⟨⟨e,⟨e,t⟩⟩,⟨e,⟨e,t⟩⟩⟩⟩ ↝ λQ.λP.λy.λx.[P(x,y) ∧ Q(x,y)]$ + +- not: $⟨⟨e,t⟩,⟨e,t⟩⟩ ↝ λP.λx.¬P(x)$ ### Quantification +- every: $⟨⟨e,t⟩,⟨⟨e,t⟩,t⟩⟩ ↝ λQ.λP.∀x.[P(x) → Q(x)]$ + - everything: $⟨⟨e,t⟩,t⟩ ↝ λP.∀x.P(x)$ +- 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 $λP.∀x.¬P(x))$ + ### Reference ### Numbers and Plurality @@ -53,9 +75,9 @@ With basic logic and the lambda calculus under our belt, we may simply get strai ### Command, Request, Obligation -> Alice, run!<br> -> Alice, please run.<br> -> Alice should run. +> *Alice, run!* <br> +> *Alice, please run.* <br> +> *Alice should run.* ### Questions ## Resources |