# Statements in sybolic logic

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.

• 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. Nov 8 '12 at 16:50

``````∀x (Man(x) → Person(x))
∃x (Man(x) ∧ Clever(x))
--------------------------------
∀x (Person(x) → Clever(x))
``````
``````∀x ∈ Man : x ∈ People
∃x ∈ Man : x ∈ Clever
---------
∀x ∈ People : x ∈ Clever
``````

Typing hint:
`∀` - "for every" (HTML: `&forall;` Unicode: `&#8704;`)
`∃` - "exists" (HTML: `&exist;`; Unicode: `&#8707;`)
`∈` - "element of" (HTML: `&isin;`; Unicode: `&#8712;`)
`:` - "such that"; in different Math schools you may find a plain colon as above or `⊩` (Unicode: `&#8873;`), "forces"

• I think the OP was looking for propositional logic notation rather than set notation. Nov 2 '12 at 14:22
• 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 Nov 2 '12 at 14:24