Here's a basic example of a program written in Prolog that demonstrates logical programming:

```prolog
/* Facts */
parent(bob, alice).
parent(bob, john).
parent(jane, alice).
parent(jane, john).

/* Rules */
sibling(X, Y) :- parent(Z, X), parent(Z, Y), X \= Y.

/* Query */
?- sibling(alice, john).
```

In this example, we define a family tree using facts that specify the parent-child relationships between individuals. Then, we define a rule called "sibling" which is true if two individuals share a common parent. Finally, we query whether "alice" and "john" are siblings, which should return "true" as they share the same parents "bob" and "jane".

This program demonstrates logical programming because we're defining relationships between individuals in terms of logical rules, and we can query the program to infer new relationships based on those rules. In other words, we're expressing our knowledge of the world in terms of logical statements, and the Prolog interpreter is using that knowledge to make logical deductions and answer queries.
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