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Probabilistic logic programming
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.
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.
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.
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.
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.
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Probabilistic logic programming AI simulator
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Probabilistic logic programming
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.
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.
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.
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.
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.