12.1. A brief introduction to clausal logic¶

Solution 1.2

Construct the proof trees for the query

?-nearby(W,charing_cross).

There are six answers to this query:

{ W→green_park }
{ W→leicester_square }
{ W→bond_street }
{ W→oxford_circus }

The proof trees for the first three answers are analogous to Figure 1.2. The proof tree for the fourth answer is given below (the two remaining proof trees are similar):

Solution 1.4

A list is either the empty list [], or a non-empty list [First|Rest] where Rest is a list. Define a predicate list(L), which checks whether L is a list. Adapt it such that it succeeds only for lists of (1) even length and (2) odd length.

The first specification can immediately be translated to Prolog:

list([]).
list([_First|Rest]):-list(Rest).

A list of even length is either the empty list, or a non-empty list with two more elements than the next shorter list of even length:

evenlist([]).
evenlist([_First,_Second|Rest]):-evenlist(Rest).

In order to adapt this definition for lists of odd length, only the non-recursive clause needs to be changed:

oddlist([_One]).
oddlist([_First,_Second|Rest]):-oddlist(Rest).

Notice that oddlist can also be defined in terms of evenlist (or vice versa):

oddlist([_First|Rest]):-evenlist(Rest).

Solution 1.5

Construct a query asking for a route from Bond Street to Piccadilly Circus with at least two intermediate stations.