Statistical Statements in Probabilistic Logic Programming

Self Cite

Probabilistic Answer Set Programming under the credal semantics (PASP) describes an uncertain domain through an answer set program extended with probabilistic facts. The PASTA language leverages PASP to express statistical statements. A solver with the same name allows to perform inference in PASTA programs and, in general, in PASP. In this paper, we investigate inference in PASP, propose a new inference algorithm called aspcs based on Second Level Algebraic Model Counting (2AMC), and implement it into the aspmc solver. Then, we compare it with PASTA on a set of benchmarks: the empirical results show that, when the program does not contain aggregates, the new algorithm outperforms PASTA. However, when we consider PASTA statements and aggregates, we need to replace aggregates with a possibly exponential number of rules, and aspcs is slower than PASTA.

“…We are interested in the probability of smokes (1). Increasing instances are: i2 = i1 ∪ {person (3). }, i3 = i2 ∪ {person (4).…”

Section: Methodsmentioning

confidence: 99%

“…}, i4 = i3 ∪ {0.2::influences(2, 3). }, i5 = i4 ∪ {0.7::influences (3,4). }, i6 = i5 ∪ {0.9::influences(4, 1).}.…”

Section: Methodsmentioning

confidence: 99%

Section: Statistical Statementsmentioning

confidence: 99%

Section: Statistical Statementsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Inference in Probabilistic Answer Set Programming Under the Credal Semantics

Azzolini,

Riguzzi

2023

Self Cite

MAP Inference in Probabilistic Answer Set Programs

Azzolini

Bellodi

Riguzzi

2023

Reasoning with uncertain data is a central task in artificial intelligence. In some cases, the goal is to find the most likely assignment to a subset of random variables, named query variables, while some other variables are observed. This task is called Maximum a Posteriori (MAP). When the set of query variables is the complement of the observed variables, the task goes under the name of Most Probable Explanation (MPE). In this paper, we introduce the definitions of cautious and brave MAP and MPE tasks in the context of Probabilistic Answer Set Programming under the credal semantics and provide an algorithm to solve them. Empirical results show that the brave version of both tasks is usually faster to compute. On the brave MPE task, the adoption of a state-of-the-art ASP solver makes the computation much faster than a naive approach based on the enumeration of all the worlds.

Approximate Inference in Probabilistic Answer Set Programming for Statistical Probabilities

Azzolini

Bellodi

Riguzzi

2023

Abstract“Type 1” statements were introduced by Halpern in 1990 with the goal to represent statistical information about a domain of interest. These are of the form “x% of the elements share the same property”. The recently proposed language PASTA (Probabilistic Answer set programming for STAtistical probabilities) extends Probabilistic Logic Programs under the Distribution Semantics and allows the definition of this type of statements. To perform exact inference, PASTA programs are converted into probabilistic answer set programs under the Credal Semantics. However, this algorithm is infeasible for scenarios when more than a few random variables are involved. Here, we propose several algorithms to perform both conditional and unconditional approximate inference in PASTA programs and test them on different benchmarks. The results show that approximate algorithms scale to hundreds of variables and thus can manage real world domains.