The Bousi$\sim$Prolog Language

The language we call Bousi$\sim$Prolog (BPL for short) is an extension of the standard Prolog language with a similarity relation defined on a syntactic domain. Therefore, the syntax of the extended language is easy. It is mainly the Prolog syntax but enriched with a built-in symbol ``~~'' used for describing similarity relations by means of similarity equations of the form:

 <alphabet symbol> ~~ <alphabet symbol> = <degree>

meaning that two constants, n-ary function symbols or n-ary predicate symbols are similar with a certain degree.

A BPL program is mainly a sequence of Prolog facts and rules followed by a sequence of similarity equations.

As an example, this BPL program fragment specify features and preferences on books stored in a data base. The preferences are specified by means of similarity equations:

% FACTS
adventures(treasure_island).
adventures(the_call_of_the_wild).
mystery(the_murders_in_the_rue_morgue).
horror(dracula).
science_fiction(the_city_and_the_stars).
science_fiction(the_martian_chronicles).

% RULES
good(X) :- interesting(X).

% SIMILARITY EQUATIONS
adventures ~~ mystery = 0.5
adventures ~~ science_fiction = 0.8
adventures ~~ interesting = 0.9
mystery ~~ horror = 0.9
mystery ~~ science_fiction = 0.5
science_fiction ~~ horror = 0.5

Bousi$\sim$Prolog implements a weak unification operator, also denoted by ``$\sim\sim$'', which is the fuzzy counterpart of the syntactical unification operator ``='' of standard Prolog. It can be used, in the source language, to construct expressions like ``Term1 ~~ Term2 =:= Degree'' which is interpreted as follows: The expression is true if Term1 and Term2 are unifiable by similarity with approximation degree AD equal to Degree. In general, we can construct expressions ``Term1 ~~ Term2 <op> Degree'' where ``<op>'' is a comparison arithmetic operator or the symbol ``=''. In the last case, the construction ``Term1 ~~ Term2 = Degree'' success if Term1 and Term2 are weak unifiable with approximation degree Degree. These expressions may be introduced in a query as well as in the body of a clause.