science

Probabilistic logic programming

Probabilistic logic programming is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Probabilistic logic programming rather than just read about it. In short: Probabilistic logic programming is a programming paradigm that combines logic programming with probabilities. Most approaches to probabilistic logic programming are based on the distribution semantics, which splits a program into a set of probabilistic facts and a logic program.

Key takeaways

Probabilistic logic programming belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Probabilistic logic programming to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Probabilistic logic programming from memory before moving on to harder problems.

Reference excerpt

Probabilistic logic programming is a programming paradigm that combines logic programming with probabilities. Most approaches to probabilistic logic programming are based on the distribution semantics, which splits a program into a set of probabilistic facts and a logic program. It defines a probability distribution on interpretations of the Herbrand universe of the program.

Languages Most approaches to probabilistic logic programming are based on the distribution semantics, which underlies many languages such as Probabilistic Horn Abduction, PRISM, Independent Choice Logic , probabilistic Datalog, Logic Programs with Annotated Disjunctions, ProbLog, P-log, and CP-logic. While the number of languages is large, many share a common approach so that there are transformations with linear complexity that can translate one language into another.

Semantics Under the distribution semantics, a probabilistic logic program is interpreted as a set of independent probabilistic facts (ground atomic formulas annotated with a probability) and a logic program which can use the probabilistic facts in the bodies of its clauses. The probability of any assignment of truth values to the groundings of the formulas associated with probabilistic facts is given by the product of their probabilities; this is equivalent to assuming the choices of probabilistic facts to be independent random variables.

Stratified programs If for any choice of truth values for the probabilistic facts, the resulting logic program is stratified, it has a unique minimal Herbrand model which can be seen as the unique interpretation associated with that choice of truth values. Important subclasses of stratified programs are positive programs, which do not use negation, but may be recursive, and acyclic programs, which may use negation but have no recursive dependencies.

Answer set programs The stable model semantics underlying answer set programming gives meaning to unstratified programs by allocating potentially more than one answer set to every truth value assignment of the probabilistic facts. This raises the question of how to distribute the probability mass across the answer sets. The probabilistic logic programming language P-Log resolves this by dividing the probability mass equally between the answer sets, following the principle of indifference. Alternatively, probabilistic answer set programming under the credal semantics allocates a credal set to every query. Its lower probability bound is defined by only considering those truth value assignments of the probabilistic facts for which the query is true in every answer set of the resulting program (cautious reasoning); its upper probability bound is defined by considering those assignments for which the query is true in some answer set (brave reasoning).

Inference 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 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. 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. 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.

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.

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.

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. Common approaches to parameter learning are based on expectation–maximization or gradient descent, while structure learning can be performed by searching the space of possible clauses under a variety of heuristics.

See also Inductive logic programming Probabilistic database Probabilistic programming ProbLog Statistical relational learning

References

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. doi:10.3389/frobt.2014.00006. 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.

Worked examples

Example 1 — a first encounter with Probabilistic logic programming

Start with the simplest possible case. Write down what Probabilistic logic programming claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Probabilistic logic programming before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Probabilistic logic programming ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Probabilistic logic programming

In research: Probabilistic logic programming appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Probabilistic logic programming in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Probabilistic logic programming is common in secondary-school and first-year university syllabi. It links to neighbouring topics Logic programming, Probabilistic models, Programming paradigms, so understanding it makes those chapters shorter.
In everyday life: Look for Probabilistic logic programming outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Probabilistic logic programming in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Probabilistic logic programming means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Probabilistic logic programming out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Probabilistic logic programming in simple terms?

Why does Probabilistic logic programming matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Probabilistic logic programming?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Probabilistic logic programming.