What is a genuine variable?
Is a free variable, the universal quantification of which yields a true formula. For example. Ax.x + x = 2x
What is an unknown?
An unknown is a free variable, the existential quantification of which yields a true formula. Ex.adult(x)
What is the introduction of (for all symbol) universal quantifier called?
generalization
What is the introduction of (for some symbol) existential quantifier called?
specialization
What is the another name for the elimination stage of a predicate logic proof?
Instantiation
List Nissanke’s Rules for Variable Handling:
- Do not assume that a property holds for a particular
individual on the basis that it holds for at least one
individual: i.e. when eliminating the existential quantifier, do
not instantiate its variable with a constant.
2.When eliminating the existential quantifier, do not instantiate
its variable with an existing free variable.
- Do not generalise, that is, introduce the universal quantifier, on the basis of an individual (a constant).
- Do not generalise, that is, introduce the universal quantifier, on the basis of an unknown.
- Do not generalise on the basis of a variable
appearing in a formula obtained by eliminating the
existential quantifier, irrespective of whether that variable is
a genuine variable. - Within the scope of an assumption, do not
generalise on the basis of the variable appearing in
the assumption. - Every instantiation, whether following the elimination of a universal or an existential quantifier, must always be done with a free variable.
- Beware of binding of any newly quantified variable,
that is, as a result of the introduction of either universal or
existential, by an unintended quantifier.
What is a predicate?
Objects in term of their attributes/properties and their relationships with each other. Predicates correspond to attributes or relationships.
What is a unary predicate?
A predicate that takes one identifier/object as an argument and gives attributes to that identifier/object. Doesn’t describe relationships between identifiers.
What is a binary predicate?
Binary predicates take two objects/identifiers as arguments so can describe the relationship between objects/identifiers. Can also describe attributes of objects.
What is an n-ary predicate?
An n-ary predicate is a predicate involving n objects expressing a relationship among them.
When does a predicate become a proposition?
A predicate is initially an incomplete proposition that only becomes a proposition it is applied to some entity or multiple entities where necessary. A predicate is not a proposition until the correct number of arguments have been assigned, otherwise a truth value cannot be determined.
What is the ‘for all’ symbol?
Universal quantifier. ‘For all’. Applies a predicate to all objects/things in a defined universe.
What is the ‘there exists’ symbol?
Existential quantifier. ‘There exists some’. Applies a predicate to at least one object/thing in a defined universe, but we don’t know how many.
