Basic question: Translating from English to PL

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Estaran
 
Reply Tue 10 Feb, 2009 03:37 am
Hi, I just have a couple of quick questions about translating from English to propositional logic using symbols. They seem pretty simple, but I can't find the answers anywhere specifically.

1) Is it sometimes necessary to break paragraphs up into multiple separate arguments?
eg. "Either John will wear a shirt and be cold, or the sun will shine. John will not both wear a shirt and be cold. So, the sun will shine."
The only way I can see to translate this is:
" (J&C) v S; ~(J&C); S" with ; separating discrete arguments. Is that correct, or is there a way to express all of that in a single argument?

2) What is the meaning of a statement such as "AB"? Is it the same as "A&B"?

Thanks!
 
Victor Eremita
 
Reply Wed 11 Feb, 2009 03:28 am
@Estaran,
1.
Let A = John will wear a shirt
Let B = [He'll] be cold
Let C = The sun will shine
(A&B) V C
~(A&B)
-----------
C

The third sentence is a conclusion, so it needs to be distinguished.

This would work: (A&B) V C ; ~(A&B) ∴ C


2. AB is short for A&B, it's taken from college algebra, where one omits the multiply sign: a * b = ab
 
VideCorSpoon
 
Reply Wed 11 Feb, 2009 09:45 am
@Victor Eremita,
For #1, it is usually necessary to break up paragraphs into separate arguments. They serve as the premises for your conclusion, the function of the entire proof that you want to evaluate.

In your example, I translated it like this.

(J & C) v S
~ (W v C)___
S

The problem you gave was a classic disjunctive syllogism. However, the second line (i.e. ~ (P v Q) ) can be either ~(WvC) or ~W&~C because if anything it is an extension of the DeMorgan replacement rule.

As to your second statement, in propositional logic if a syntactical composition is missing a connective, it usually means that it is not a WFF (well formed formula). This is a definite rule in propositional logic that as far as I am aware of is non debatable.
 
 

 
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