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I have 3 statements I want to convert into symbolic logic (P, Q, etc.)

 All men are people.  Some men are clever.  Therefore, all people are clever.

First of all, I know this is illogical, but I'm trying to figure out how to show this using symbolic logic. Can I say:

 P = men
 Q = people
 R = clever

 (All) P -> Q
 (Exist) P -> R
 ----------------
 (All) Q -> R

It's easy to see that Q->R doesn't follow from this.

I realize the statements aren't in the "if, then" format, but it can be modified that way can't it? That is, if you are a man, then you are a person....etc.

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1  
What kind of symbolic logic do you mean? Propositional calculus? or predicate logic? The "(P,Q, etc.)" indicates that you wish a conversion into propositional calculus. Your example, however, is somewhat a mixture between the two. In propositional calculus one only considers propositions as a whole, i.e. the variables P, Q, etc. denote propositions. So your example would be "P ∧ Q → R". When you want to look at the structure of the proposition you can use predicate logic as it is demonstrated by Tyler's answer. – AndreasS Nov 8 '12 at 16:50

2 Answers

up vote 3 down vote accepted 
∀x (Man(x) → Person(x))
∃x (Man(x) ∧ Clever(x))
--------------------------------
∀x (Person(x) → Clever(x))
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up vote 0 down vote 
∀x ∈ Man : x ∈ People
∃x ∈ Man : x ∈ Clever
---------
∀x ∈ People : x ∈ Clever

Typing hint:
∀ - "for every" (HTML: ∀ Unicode: ∀)
∃ - "exists" (HTML: ∃; Unicode: ∃)
∈ - "element of" (HTML: ∈; Unicode: ∈)
: - "such that"; in different Math schools you may find a plain colon as above or ⊩ (Unicode: ⊩), "forces"

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I think the OP was looking for propositional logic notation rather than set notation. – smartcaveman Nov 2 '12 at 14:22
1  
Also, you might want to look at Ian Mercer's blog - he has a lot of NLP articles and an open source .NET engine : nlp.abodit.com , blog.abodit.com/category/nlp – smartcaveman Nov 2 '12 at 14:24

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