Introduction to Logic
Term 1b 2020-2021
1 object 2 names, 2 object not one name.
Predicate symbol: used to express property of object or relation between objects.
Binary predicate symbol: two arguments, refer to binary relation.
First order logic, Propositional logic:
No inner structure
Predicate symboles and individual constants
Capital letters (P, Q, R, S)
B(a), R(c, d), Q(b, f, e, d, a),Loves(romeo, julia) or:
in infix notation: a = b, c < d, e ≥ f
John knows Mary
John knows mary
P : John knows mary
j : John
K(x, y) : x knows y
Augusta Ada Byron is Ada lovelace
a = l with Translation key:
a: Augusta Ada Byron.
l: Ada Lovelace
Augusta Ada Byron is a computer scientist.
C(a) with translation key:
C(x): x is a computer scientist.
a: Augusta Ada Byron
a identical to b? a&b same properties.
validity: argument valid iff it is impossible premises true and conclusion false.
Premises: you can see this as the conditions.
Formal proof: proof in formal language.
Let P1, P2, P3 premises of an argument c conclusion. Then a formal proof looks like:
Different types of formal proofs:
Not necessary, may help look proof more natural.
= introduction: and =introduction:
Based on fact of reflexive:
line order important
Every object identical to itself.
Properties of Identity:
When a = b then b = a
When a = b&b = c then a = c
a = for all a