# Resolution

1. <hardware> 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. <logic> 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.

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