resolution
1. the maximum number of {pixels} that can be
displayed on a {monitor}, expressed as (number of horizontal
pixels) x (number of vertical pixels), i.e., 1024x768. The
ratio of horizontal to vertical resolution is usually 4:3, the
same as that of conventional television sets.
2. A mechanical method for proving statements of
{first order logic}, introduced by J. A. Robinson in 1965.
Resolution is applied to two {clauses} in a {sentence}. It
eliminates, by {unification}, a {literal} that occurs
"positive" in one and "negative" in the other to produce a new
clause, the {resolvent}.
For example, given the sentence:
(man(X) ◦> mortal(X)) AND man(socrates).
The literal "man(X)" is "negative". The literal
"man(socrates)" could be considered to be on the right hand
side of the degenerate implication
True ◦> man(socrates)
and is therefore "positive". The two literals can be unified
by the binding X ◦ socrates.
The {truth table} for the implication function is
A | B | A ◦> B
--:---:-------
F | F | T
F | T | T
T | F | F
T | T | T
(The implication only fails if its premise is true but its
conclusion is false). From this we can see that
A ◦> B ◦◦ (NOT A) OR B
Which is why the left hand side of the implication is said to
be negative and the right positive. The sentence above could
thus be written
((NOT man(socrates)) OR mortal(socrates))
AND
man(socrates)
Distributing the AND over the OR gives
((NOT man(socrates)) AND man(socrates))
OR
mortal(socrates) AND man(socrates)
And since (NOT A) AND A ◦◦ False, and False OR A ◦◦ A we can
simplify to just
mortal(socrates) AND man(socrates)
So we have proved the new literal, mortal(socrates).
Resolution with {backtracking} is the basic control mechanism
of {Prolog}.
See also {modus ponens}, {SLD Resolution}.
3. {address resolution}.
(1996-02-09)