Stylistic Variants and Translation Scheme
Stylistic variants: when 2 sentences of a natural language have the same logical form relative to a single translation scheme
Natural languages like English has many stylistic variants to convey the same idea. It is one of the things that makes poetry beautiful. Natural languages has conversational implications. However, all variants have the same logical form.
ex.2 When someone asks you if you are happy and you say no, they might say that they are sorry that you are sad. However, you might not be sad, you are just not happy. In contrast, artificial intelligence robots like Siri interprets I am not happy as ~H.
Conjunction
ex.
Natural languages like English has many stylistic variants to convey the same idea. It is one of the things that makes poetry beautiful. Natural languages has conversational implications. However, all variants have the same logical form.
Negation
ex.1 P = John is conscious and ~P can be....
John is not conscious.
John is unconscious.
It is not the case that John is conscious.
It is false that John is conscious.
ex.2 When someone asks you if you are happy and you say no, they might say that they are sorry that you are sad. However, you might not be sad, you are just not happy. In contrast, artificial intelligence robots like Siri interprets I am not happy as ~H.
Conjunction
ex.
M = Tony is Mexican.
C = Tony is a diligent citizen.
Logical form: M & C
Natural language:
Tony is Mexican and a diligent citizen.
Tony is a diligent citizen but he is also Mexican ?
Disjunction
ex.
ex.
1. S --> C
You are in California if you are in San Francisco.
2. C --> S
You are in California only if you are in San Francisco.
Only difference in the natural language is the addition of the word only, but it changes the whole truth value of the sentences. 1 makes S is precedent and 2 makes C the precedent.
Neither/nor
ex.
Neither Φ & Ψ
Logical form: ~(Φ v Ψ) or (~Φ & ~Ψ)
Tenses
In natural languages, "Mary is dancing" has a different meaning than "Mary will dance."
In translation schemes, tenses are ignored because they are noninfluential in validity.
ex.
1 If Bill dies, then he won't talk.
2 Bill died.
C Bill ain't talking
1 If I deposit $500 into my bank account, then I will have $500 available to spend.
2 I deposited $500 into my account this morning.
C I have $500 available now.
ex.
You can pass the calculus course only if you both pass the final exam and have a passing quiz average. You did pass the final exam, but you didn't have a passing quiz average. You did not, therefore, pass calculus.
Pass calculus = P
Pass final = F
Pass quiz average = Q
F&Q --> P
F&~Q
~P
You are in California if you are in San Francisco.
2. C --> S
You are in California only if you are in San Francisco.
Only difference in the natural language is the addition of the word only, but it changes the whole truth value of the sentences. 1 makes S is precedent and 2 makes C the precedent.
Neither/nor
ex.
Neither Φ & Ψ
Logical form: ~(Φ v Ψ) or (~Φ & ~Ψ)
Tenses
In natural languages, "Mary is dancing" has a different meaning than "Mary will dance."
In translation schemes, tenses are ignored because they are noninfluential in validity.
ex.
1 If Bill dies, then he won't talk.
2 Bill died.
C Bill ain't talking
1 If I deposit $500 into my bank account, then I will have $500 available to spend.
2 I deposited $500 into my account this morning.
C I have $500 available now.
ex.
You can pass the calculus course only if you both pass the final exam and have a passing quiz average. You did pass the final exam, but you didn't have a passing quiz average. You did not, therefore, pass calculus.
Pass calculus = P
Pass final = F
Pass quiz average = Q
F&Q --> P
F&~Q
~P
Comments
Post a Comment