An Algebraic Prolog for Reasoning about Possible Worlds
By Angelika Kimmig, Guy Van den Broeck, Luc De Raedt. 2011
69 citations recorded by the source corpus.
We introduce aProbLog, a generalization of the probabilistic logic programming language ProbLog. An aProbLog program consists of a set of definite clauses and a set of algebraic facts; each such fact is labeled with an element of a semiring. A wide variety of labels is possible, ranging from probability values to reals (representing costs or utilities), polynomials, Boolean functions or data structures. The semiring is then used to calculate labels of possible worlds and of queries. We formally define the semantics of aProbLog and study the aProbLog inference problem, which is concerned with computing the label of a query. Two conditions are introduced that allow one to simplify the inference problem, resulting in four different algorithms and settings. Representative basic problems for each of these four settings are: is there a possible world where a query is true (SAT), how many such possible worlds are there (#SAT), what is the probability of a query being true (PROB), and what is the most likely world where the query is true (MPE). We further illustrate these settings with a number of tasks requiring more complex semirings.
Subfields: Artificial Intelligence, Computational Theory and Mathematics
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Sebastijan Dumancic
- Angelika Kimmig
- Robin Manhaeve
- Luc De Raedt
- Thomas Demeester
- Lise Getoor
- Matthias Broecheler
- Stephen H. Bach
In Computational Theory and Mathematics
- Angelika Kimmig
- Luc De Raedt
- Thomas Demeester
- Lise Getoor
- Matthias Broecheler
- Stephen H. Bach
- Sebastijan Dumancic
- Bert Huang
Citations in the corpus
- DeepProbLog: Neural Probabilistic Logic Programming (2018, methodology): “More specifically, to compute the gradient with respect to the probabilistic logic program part, we rely on Algebraic ProbLog (aProbLog, [Kimmig et al., 2011]), a generalization of the ProbLog language and inference to arbitrary commutative semirings, including the gradient semiring [Eisner, 2002].”
- Hinge-Loss Markov Random Fields and Probabilistic Soft Logic (2015, background): “Another related formalism is aProbLog (Kimmig et al., 2011), which generalizes ProbLog to allow clauses to be annotated with elements from a”
- Probabilistic (logic) programming concepts (2015, methodology): “Prominent examples of Prolog-based languages using this semantics include ICL (Poole, 2008), PRISM (Sato and Kameya, 2001) and ProbLog (De Raedt et al, 2007; Kimmig et al, 2011b), even though there exist subtle differences between these languages as we will illustrate later.”