Probabilistic logic programming
Probabilistic logic programming is a programming paradigm that combines logic programming with probabilities.
Distribution semantics
Most approaches to probabilistic logic programming are based on the distribution semantics.[1]
Under the distribution semantics, a probabilistic logic program defines a probability distribution over interpretations of its predicates on its Herbrand universe. The probability of a ground query Q is then obtained from the joint distribution of the query and the worlds: it is the sum of the probability of the worlds where the query is true.[2][3][4]
Languages
The distribution semantics underlies many languages such as Probabilistic Horn Abduction, PRISM, Independent Choice Logic , probabilistic Datalog, Logic Programs with Annotated Disjunctions (Vennekens et al., 2004), ProbLog, P-log, and CP-logic. While the number of languages is large, all share a common approach so that there are transformations with linear complexity that can translate one language into another.[2]
Recursion and negation
Stratified programs
Answer set programs
Inference
The problem of computing the probability of queries is called (marginal) inference. Solving it by computing all the worlds and then identifying those that entail the query is impractical as the number of possible worlds is exponential in the number of ground probabilistic facts.[2] In fact, already for acyclic programs and atomic queries, computing the conditional probability of a query given a conjunction of atoms as evidence is #P-complete.[5]
Exact inference
Usually, exact inference is performed by resorting to knowledge compilation: according to this, a propositional theory and a query are compiled into a “target language”, which is then used to answer queries in polynomial time. The compilation becomes the main computational bottleneck, but considerable effort has been devoted to the development of efficient compilers. The compilation methods differ in the compactness of the target language and the class of queries and transformations that they support in polynomial time.[2]
Approximate inference
Since the cost of inference may be very high, approximate algorithms have been developed. They either compute subsets of possibly incomplete explanations or use random sampling. In the first approach, a subset of the explanations provides a lower bound and the set of partially expanded explanations provides an upper bound. In the second approach, the truth of the query is repeatedly checked in an ordinary logic program sampled from the probabilistic program. The probability of the query is then given by the fraction of the successes.[2][6]
Learning
Probabilistic inductive logic programming aims to learn probabilistic logic programs from data. This includes parameter learning, which estimates the probability annotations of a program while the clauses themselves are given by the user, and structure learning, in which the clauses themselves are induced by the probabilistic inductive logic programming system.[2]
Common approaches to parameter learning are based on expectation–maximization or gradient descent, while structure learning van beperformed by searching the space of possible clauses under a variety of heuristics.[2]
Applications
See also
References
- ^ Riguzzi, Fabrizio; Swift, Theresa (2018-09-01), "A survey of probabilistic logic programming", Declarative Logic Programming: Theory, Systems, and Applications, ACM, pp. 185–228, retrieved 2023-10-25
- ^ a b c d e f g Riguzzi, Fabrizio; Bellodi, Elena; Zese, Riccardo (2014). "A History of Probabilistic Inductive Logic Programming". Frontiers in Robotics and AI. 1. doi:10.3389/frobt.2014.00006/full. ISSN 2296-9144.
{{cite journal}}: CS1 maint: unflagged free DOI (link) - ^ Poole, David (1993). "Probabilistic Horn abduction and Bayesian networks". Artificial Intelligence. 64 (1): 81–129. doi:10.1016/0004-3702(93)90061-f. ISSN 0004-3702.
- ^ Sato, Taisuke (1995), "A Statistical Learning Method for Logic Programs with Distribution Semantics", Proceedings of the 12th International Conference on Logic Programming, The MIT Press, retrieved 2023-10-25
- ^ Riguzzi, Fabrizio (2023). Foundations of probabilistic logic programming: Languages, semantics, inference and learning (2nd ed.). Gistrup, Denmark: River Publishers. p. 180. ISBN 978-87-7022-719-3.
- ^ Kimmig, Angelika; Demoen, Bart; Raedt, Luc De; Costa, Vítor Santos; Rocha, Ricardo (2011). "On the implementation of the probabilistic logic programming language ProbLog". Theory and Practice of Logic Programming. 11 (2–3): 235–262. doi:10.1017/S1471068410000566. ISSN 1475-3081.
As of 3 February 2024, this article is derived in whole or in part from Riguzzi, Fabrizio; Bellodi, Elena; Zese, Riccardo (2014). "A History of Probabilistic Inductive Logic Programming". Frontiers in Robotics and AI. 1.. The copyright holder has licensed the content in a manner that permits reuse under CC BY-SA 3.0 and GFDL. All relevant terms must be followed.