Statistical Statements in Probabilistic Logic Programming

Probabilistic Logic Programs under the distribution semantics (PLPDS) do not allow statistical probabilistic statements of the form "90% of birds fly", which were defined "Type 1" statements by Halpern. In this paper, we add this kind of statements to PLPDS and introduce the PASTA ("Probabilistic Answer set programming for STAtistical probabilities") language. We translate programs in our new formalism into probabilistic answer set programs under the credal semantics. This approach differs from previous proposals, such as the one based on "probabilistic conditionals" as, instead of choosing a single model by making the maximum entropy assumption, we take into consideration all models and we assign probability intervals to queries. In this way we refrain from making assumptions and we obtain a more neutral framework. We also propose an inference algorithm and compare it with an existing solver for probabilistic answer set programs on a number of programs of increasing size, showing that our solution is faster and can deal with larger instances.