L6 - Predicate Logic Flashcards
one of the pinnacles of the development in Logic for it aims to address the limits of Propositional Logic.
Predicate Logic
propositions could also be broke down to subatomic parts:
subject and predicate
any proper noun
subject
indicate property of a subject
predicate
function of predicates
adjective, noun, verb, relation
indicate the subject of a proposition
individual constants
Italicized lowercase Roman alphabet is used for this
individual constants
indicate the predicate. Italicized uppercase Roman alphabet is used.
predicate letters
In cases when propositions contain no definite subject the letters used are called
individual variables
This WFF is called an _______ serving as the blueprint of basic propositions in Predicate Logic.
Open Formula or Propositional Formula
It is neither true nor false and will only gain truth-value once the individual variable is supplied by an individual constant.
Open Formula or Propositional Formula
In using individual variables and constants, three possible instances/combinations
- 1-place arity singulary/unary
- 2-place arity Binart
- 3-place arity Ternary
makes use of only x with the predicate functioning as the property of x.
1-place arity singulary/unary
makes use of x and y with the predicate functioning as the relation between x and y.
binary
makes use of x, y, and z with the predicate functioning as
the relation of x to y and z.
ternary
Going back to individual variables, analysis of propositions with uncertain subjects is guided by the
Square of Oppositions.
there are two quantifying symbols used in Predicate Logic:
universal quantifier and existential quantifier
indicates that a predicate is attributed to all possible subjects (everyone, everything, everywhere, etc.)
universal quantifier
indicates that a predicate is attributed only to some subjects
existential quantifier
A contradicts
O
I contradicts
E
possible instances/combinations
arity
A
universal affirmation
( ∀x ) ( Kx )
E
(Universal Negation) Everyone is not kind ( ∀x ) ~ ( Kx )
I
(Existential Affirmation) Someone is kind
( ∃x ) ( Kx )
O
(Existential Negation) Someone is not kind ( ∃x ) ~ ( Kx )
Relation between A and E: at most one must be true.
Contrary
Relation between I and O: at least one must be true
Subcontrary
Relation between the subaltern (universal proposition) and its superaltern (existential proposition): if A is true then I is necessarily true, if E is true then O is necessarily true, but not the converse for both.
Sublaternative
in which it is asserted that a particular individual has some specified attribute
Affirmative singular proposition
an expression that contains an individual variable and becomes a statement when that instantiated. A propositional function can also become a statement by the process of generalization
Propositional function
used
before a propositional function to assert that the predicate following the symbol is true of everything
Universal quantifier | a symbol,
used before a propositional function to assert that the function has one or more true substitution instances
Existential quantifier
