Is an origin function an ordinary independently sampled random property?

No. Its value is tied to the object's generating arguments rather than sampled separately in the same way as a usual random function.

Can one source generate several objects?

Yes. The associated number statement controls how many exist for that source.

Can an object's origin be uncertain during inference?

Yes. Different possible explanations of an observation may associate it with different generated objects or sources.

AI Glossary / Graphs and symbolic AI / Advanced

Origin function

Definition

An origin function, in the BLOG probabilistic modeling language, maps a generated object to an object that participated in its generation. Its value is established by the generating number statement. It links objects to their modeled origins when the number or identity of objects may be uncertain.

What it means

BLOG can describe worlds containing different numbers of objects. A number statement specifies how many objects arise for a particular combination of existing objects. An origin function lets the model recover those generating arguments from each resulting object.

For example, a model might generate inspection records separately for each production batch. The function BatchOf(record) identifies the batch associated with a generated record. The function returns an object, not a probability or a count.

This is a specialized probabilistic-modeling meaning. It is not the coordinate origin, a generic data-provenance field or the similarly named function in build tools. Generation describes construction of a possible world, not proof of real-world causation.

How it works

Declare the relevant types and an origin function with one input type and one return type. Attach that function to a number statement so that objects generated for a particular argument receive the corresponding origin value.

If records are generated for batch b, every record produced by that statement instance has BatchOf(record) = b. The count can be random, while the origin assignment is fixed by that generation history. Other random properties can then depend on the origin object.

An object may have more than one origin, represented by separate origin functions, such as a source and a time step. An origin is definite within a world but may be unknown to an observer. Inference compares possible worlds consistent with the evidence rather than repeatedly changing an origin inside one fixed world.

Three practical examples

A simulation generates a variable number of inspection records per batch and links each record back to its generating batch.
A sensor model generates observations for source-and-time combinations, preserving both kinds of origin.
A probabilistic data-association model considers alternative explanations for which modeled source produced an observation.

Think of it this way

Think of a folder that creates a varying number of numbered slips. Every slip keeps a reference to the folder that generated it, even when the number of slips differs across imagined scenarios.

The analogy captures the link and variable count. In probabilistic inference the folder assignment can itself be unknown to the observer, so a reference in a hypothetical world is not necessarily an observed fact.

Worked example

Counts are random; origins follow the generating group

Consider two guaranteed batch objects, A and B. For a toy model, the number of inspection records from A follows a Poisson distribution with mean 2, and the number from B follows a Poisson distribution with mean 1. Assume these two counts are independent. Each record has an origin function BatchOf returning its batch.

In one possible world, A generates two records and B generates one. Give them illustrative labels R1, R2 and R3. Then BatchOf(R1) = A, BatchOf(R2) = A and BatchOf(R3) = B. The count of records from A is 2, but BatchOf(R1) returns A, not 2.

The probability of this count combination is P(N_A = 2) times P(N_B = 1). The first factor is exp(−2) times 2 squared divided by 2 factorial, or 2 exp(−2). The second is exp(−1). Their product is 2 exp(−3), approximately 0.0996. This is a probability of counts, not a probability assigned by the origin function.

In another world, A may generate zero records and B may generate two. There is then no A-generated record on which to evaluate BatchOf. The expected total is 2 + 1 = 3, not a requirement for every world.

If a real observation identifies a record without revealing its batch, the model may need to infer that association. Illustrative labels are not independent evidence. These numbers are invented.

Illustrative case study

The fictional Maple Models team creates a BLOG-style simulation for the two batches. Its first report mixes the expected record count with the number sampled in a particular world, then mistakenly describes BatchOf as the function that predicts that count.

A reviewer separates the count distribution, generated records and origin links. The team checks a zero-record world as well as the two-plus-one world, and confirms that each existing record refers to its generating batch.

When adding observations, Maple distinguishes known batch labels from uncertain associations. This fictional exercise demonstrates the language concept.

Common misconceptions and mistakes

An origin function returns the number of generated objects. The number statement determines the count; the origin function returns a generating object.
Origins must be directly observed. They can be definite within a world yet uncertain given available evidence.
Every object has exactly one origin in every model. Multiple origin functions can describe different generating arguments.
The modeling link proves physical causation. Its validity depends on the model and supporting evidence.

Business use

Origin functions are useful when a model must keep generated entities associated with their sources while allowing their numbers to vary. This can support simulations and reasoning about uncertain object identity or data association.

For practical work, document which entities are guaranteed, which are generated and which associations are observed. Test zero counts, multiple generated objects and ambiguous evidence. Also separate the language's semantics from the quality of the chosen probability distributions. Correct syntax does not ensure a realistic model.

Check your understanding

In the two-plus-one world, why does BatchOf(R1) return A rather than 2?

Answer: It identifies R1's generating batch. The value 2 is the number of records generated for A, a separate quantity defined by the count statement.

Related terms

Open-universe probability model
Possible world
Generative model
BLOG
number statement
generated object
data association
random function

Learn next

Draw two batch objects and several possible generated-record sets. Label every origin link, then add a separate random record property. Explain which values are fixed by generation, which are sampled and which an observer might not know.

Sources

The BLOG language reference defines origin functions and their use in number statements: https://bayesianlogic.github.io/download/blog-langref.pdf

Milch and colleagues explain unknown objects and generation histories: https://people.csail.mit.edu/dsontag/papers/MilchEtAl_SRLbook07.pdf

The batch model, probability calculation and Maple Models case are original examples. The cited language reference describes BLOG version 0.9; this entry does not claim a current software feature audit.

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