Mathematical Logic - Stanford University

Mathematical Logic

Part Three

Recap from Last Time

What is First-Order Logic?

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First-order logic is a logical system for

reasoning about properties of objects.

Augments the logical connectives from

propositional logic with

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predicates that describe properties of

objects, and

functions that map objects to one another,

quantifiers that allow us to reason about

multiple objects simultaneously.

¡°For any natural number n,

n is even iff n2 is even¡±

?n. (n ¡Ê ? ¡ú (Even(n) ? Even(n2)))

?? isis the

the universal

universalquantifier

quantifier

and

and says

says ¡°for

¡°for any

any choice

choice of

of n,

n,

the

the following

following isis true.¡±

true.¡±

Some muggles are intelligent.

?m. (Muggle(m) ¡Ä Intelligent(m))

?? isis the

the existential

existentialquantifier

quantifier

and

and says

says ¡°for

¡°for some

some choice

choice of

of

m,

m, the

the following

following isis true.¡±

true.¡±

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