Beginner's guide

For those not familiar with preferences in logic programming, it might already be instructive to compare the results obtained on a simple example with and without preferences:

• Consider the well-known penguin-birds-example without preferences.
  $$\begin{eqnarray*} penguin(tweety) &\leftarrow& \\ bird(tweety) &\leftarrow& ... ...g flies(tweety) &\leftarrow& penguin(tweety), not flies(tweety) \end{eqnarray*}$$
  
  
  
  
  
  This program is expressed in our syntax as follows:

      penguin(tweety).
      bird(tweety).
      flies(tweety) :- not neg flies(tweety), bird(tweety).
  neg flies(tweety) :- not     flies(tweety), penguin(tweety).
  

  Compiling the file, named penguin.lp, and piping the result into dlv yields two answer sets:

  dlv [build BEN/Nov 24 1999   gcc egcs-2.91.66 19990314 (egcs-1.1.2 release)]
  
  Reading "Examples/penguin.dlv"
  
  
  {true, penguin(tweety), bird(tweety), flies(tweety)}
  
  {true, penguin(tweety), bird(tweety), neg_flies(tweety)}
  

• Consider now the well-known penguin-birds-example with preferences.

  For this, we name the two last rules:
  

  $$\begin{array}{lrcl} &penguin(tweety) &\leftarrow& \\ &bi... ...not flies(tweety) \\ &n_1\prec n_2 &\leftarrow& \end{array}$$
  
  
  Rules $r_1$ and $r_2$ are associated with names $n_1$ and $n_2$, which are constants in the object language. Fact expresses, intuitively, that $r_2$ has ``higher priority'' than $r_1$.

  This program is expressed in our syntax as follows:

      penguin(tweety).
      bird(tweety).
      flies(tweety) :- name(1), not neg flies(tweety), bird(tweety).
  neg flies(tweety) :- name(2), not     flies(tweety), penguin(tweety).
  
      1 < 2.
  

  Compiling the file penguin.lp and piping the result into dlv yields now only one answer set:

  dlv [build BEN/Nov 24 1999   gcc egcs-2.91.66 19990314 (egcs-1.1.2 release)]
  
  Reading "Examples/penguin.dlv"
  
  
  {true, name(1), name(2), penguin(tweety), bird(tweety), ok(2), oko(1,1),
  oko(2,1), oko(2,2), prec(1,2), neg_prec(2,1), ap(2), neg_flies(tweety),
  oko(1,2), ok(1), bl(1)}
  

  Here we obtain a single answer set that corresponds to the second answer set above; it includes further atoms that stem from the additional preference-handling rules.