Intro Logic
2nd Ph.D. student. (Germany) 6 and 3 and another one on the way.
Text book:
Logic is the study of methods for evaluating whether the premises of an argument adequately support its conclusion.
An argument is a set of propositions where some of the propositions are intended to support another one in the set.
A proposition a truth or falsehood that may or may not be expressed in a sentence.
Examples:
There is a table in a room.
Em Tisch rst im Zimmer.
predicate logic: $\exists x, T x \wedge R x$
True/False def:
True: a proposition is true it represents things as they are
False: a proposition is true it represents things as they are not.
Examples:
Premises: a proposition in an argument that is intended to support conclusion.
Conlusion: a proposition in a argument that is intended to be supported by the premises.
Deductive argument: arguments where the premises guarrentte that the coclusion is true.
Inductive argument: arguments where the premises make the conclusion probable.
Vague.
Deductive arguments.
Valid argument: is valid when it is necessary that if the premises are true then the conclusion must be true.
Invalid argument: is invalid when it is not necessary that
(Valid and invalid is specificly used for arguments. Not for statements, etc..)
Modus ponens.
Valid arguments:
1. If A then B; ( if grass is purple, then the moon is made of cheese)
2. A. (grass is purple)
Therefore,
3. B.
Validity: don’t care whether the premises are true or not; only care if the premises are true, can we reach the conclusion from the premises.
Invalid arguments:
1. If A, then B (if we are in a classroom, then we are having class)
2. B. (we are having class)
Therefore,
A. (we are in classroom)
Sound argument: is a valid argument with true premises.
Unsound argument: is invalid argument or valid argument with false premises.
Logic: study of methods to evaluating arguments.
Argument form: A pattern of reasoning from premises to a conclusion.
Substitution instance: An argument that results from uniformly replacing variables of an argument form with propositions.
(Statement vs. Propersition. Same propersition can have different statements.)
Formally Valid: an argument is formally valid when it is valid … of its form.
I am a rhino.
Truth-functional operator: An operator that takes propositions as input and the output values depends only on the truth values of the input.
Operators: if-then; negation;
Conditional: An if-then proposition, it states that the ‘then-part’ is true if the ‘if-part’ is true.
If True then True; // true statement
If True then False; // false statement
If F then F; // true statement
If F then T; // true statement
if A then B: A is called antecedent; B is called consequent.
Negation: the negation of proposition states the denial of the negated proposition.
How to show an argument form is invalid?
By counter example, first substitute.
1. if A, then not B; (if you study, you won't fail)/(if we are having an afternoon shower, it is not early morning)
2. not A; (you don't study)/(we are not having an afternoon shower)
Therefore,
3. B. (you will fail)/(it is early morning)next time: truth tables.
Pythagoras /pi’θægÓ™ræs/ theorem.
If you could revise
the fundmental principles of
computer system design
to improve security...
... what would you change?