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Calculusinlogicoponal

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Unformatted text preview: y
megabytes.”
   Let
C(m)
denote
“Mail
message
m
will
be
compressed.”
   Let
A(u)
represent
“User
u
is
active.”
   Let
S(n,
x)
represent
“Network
link
n
is
state
x.
   Now
we
have:
 Lewis
Carroll
Example
 Charles
Lutwidge
Dodgson
 


(AKA
Lewis
Caroll)
 







(1832‐1898)
   The
first
two
are
called
premises
and
the
third
is
called
the
 conclusion.

 1.  2.  3.    “All
lions
are
fierce.”
 “Some
lions
do
not
drink
coffee.”
 “Some
fierce
creatures
do
not
drink
coffee.”

 Here
is
one
way
to
translate
these
statements
to
predicate
 logic.
Let
P(x),
Q(x),
and
R(x)
be
the
propositional
functions
 “x
is
a
lion,”
“x
is
fierce,”
and
“x
drinks
coffee,”
respectively.
 ∀x (P(x)→ Q(x)) 2.  ∃x (P(x) ∧ ¬R(x)) 3.  ∃x (Q(x) ∧ ¬R(x)) 1.    Later
we
will
see
how
to
prove
that
the
conclusion
follows
 from
the
premises.
 Some
Predicate
Calculus
 Defini*ons
(op#onal)
   An
assertion
involving
predicates
and
quantifiers
is
valid
if
 it
is
true

     for
all
domains

 every
propositional
function

substituted
for
the
predicates
in
the
 assertion.
 Example:


   An
assertion
involving
predicates
is
satisfiable
if
it
is
true

     for
some
domains

 some
propositional
functions
that
can
be
substituted
for

the
 predicates
in
the
assertion.

 



Otherwise
it
is
unsatisfiable.
 



Example:




































not
valid
but
satisfiable

 



Example:
...
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