Semantic Logic Notes

 LOGIC

 LOGIC
 Logic is a word that means many things to different people.
 LOGIC deals with meanings in a language system, not with actual
behaviour (partial) of any sort.
 Logic deals most centrally with PROPOSITIONS.
 RATIONAL BEHAVIOUR
 Rational behaviour involves:
(a) goals
(b) assumptions and knowledge about existing states of affairs
(c) calculations, based on these assumptions and knowledge, leading to
ways of achieving the goals.
 RATIONAL BEHAVIOUR
 Example:

 Goal: to alleviate my hunger
 Assumptions and knowledge:
Hunger is alleviated by eating food.
Cheese is food.
There is a piece of cheese in front of me.
I am able to eat this piece of cheese
 Calculations:
If hunger is alleviated by eating food and cheese is food, then hunger
is alleviated by eating cheese.
If hunger is alleviated by eating cheese, then my own hunger would be
alleviated by eating this piece of cheese in front of me, and eating this
piece of cheese would alleviate my hunger, and my goal is to alleviate
my hunger, so therefore eating this piece of cheese would achieve my
goal.
 (Rational) action: eating the cheese
 LOGICAL FORMULAE
 John and Mary are married is ambiguous, being paraphrasable either as:
 John and Mary are married to each other .
 John is married to someone and Mary is married to someone.


 Logical Formulae:
 (j MARRIED TO m) & (m MARRIED TO j)
 ( x (j MARRIED TO x)) & ( y (m MARRIED TO y))

 MODUS PONENS
 MODUS PONENS is a rule stating that if a proposition P entails a
proposition Q, and P is true, then Q is true.