Must a world describe every physical detail?

No. It specifies the relevant language or variables of the chosen abstraction.

Are all possible worlds equally probable?

No. Probability requires additional modeling assumptions or evidence.

Is a world the same as a scenario narrative?

A narrative can describe a world, but it may leave facts unspecified and therefore represent several worlds.

AI Glossary / Graphs and symbolic AI / Advanced

Possible world

Definition

A possible world is a specified way a situation could be, used to evaluate whether statements are true or false. In classical logic, each relevant statement has a definite truth value within a world, even when an agent does not know which world describes reality. In AI, a world is normally a mathematical representation of the details relevant to a task, rather than a description of everything in the universe.

What it means

An order might be paid or unpaid, stocked or unstocked, and dispatched or undispatched. A possible world assigns definite values to those facts. The agent may initially consider several worlds because its information is incomplete. Rules and observations restrict which worlds remain compatible with what it knows. This separates a fact's truth within one situation from the agent's uncertainty across several situations. A statement can be true in one compatible world and false in another, making it unresolved by the knowledge base.

How it works

For n Boolean propositions, there are 2^n truth assignments before constraints are applied. Evaluate the knowledge base in each assignment; an assignment satisfying every statement is a model of that knowledge base. A conclusion is entailed when it holds in every such model. One compatible world where the conclusion is false is enough to refute an entailment claim.
This describes the meaning of inference, not a requirement to enumerate every assignment in practical software. Solvers can reason symbolically. In probabilistic models, worlds can additionally carry weights, and an event corresponds to the worlds where its proposition holds. The probability of an event in a finite model is the sum of those weights. Logical compatibility alone does not supply them.

Three practical examples

A rule-based order checker tests whether the known facts guarantee that an order can proceed. A counterexample world can reveal an unaddressed condition without claiming that the counterexample is what actually happened.
A scheduling system considers different complete assignments of tasks to times. Constraints exclude assignments that violate dependencies or capacity, leaving feasible alternatives.
A probabilistic diagnostic model represents combinations of component states. It can distribute probability across compatible combinations rather than treating the number of listed combinations as evidence of their relative frequency.

Think of it this way

Imagine several completed forms, each telling one internally specified version of an incident. Your evidence rules some forms out. A conclusion is guaranteed by that evidence only if it appears on every remaining form. Finding it on one form establishes compatibility, not certainty.

Worked example

Use three Boolean facts at one fixed snapshot: S means 'stock is available,' P means 'payment is cleared,' and D means 'the order is dispatched.' Impose the fictional rule D if and only if both S and P. This includes both requirements for dispatch and the additional assumption that their joint presence guarantees dispatch at the snapshot.
There are eight assignments before the rule is applied. Exactly four satisfy it. In the order (S, P, D), they are (false, false, false), (false, true, false), (true, false, false), and (true, true, true).
Now observe that D is false. Three worlds remain: neither requirement holds; payment alone holds; or stock alone holds. The knowledge base entails that at least one of S and P is false. It does not entail that stock is absent, because the third world has stock. It does not entail that payment is uncleared, because the second world has cleared payment.
If a reliable observation additionally establishes S as true, only (true, false, false) remains. The model then entails that payment is uncleared. This conclusion depends on the complete stated rule. With only 'dispatch requires stock and payment,' failure to dispatch would not justify the same inference.
For illustration, assign the three undispatched worlds weights 0.2, 0.3 and 0.5 in the order listed. The probability that stock is available is 0.5, and the probability that payment is cleared is 0.3. Counting worlds would give one third for each, which would require a different, uniform weighting assumption. These weights are stipulated for demonstration, not inferred from the logical rule.

Illustrative case study

In a fictional fulfillment company, a dashboard labels every undispatched order 'payment missing.' A reviewer constructs the second world in the example: payment is cleared, stock is unavailable and dispatch is false. That world satisfies the simplified rule and observation, so the dashboard's conclusion is unsupported.
The team changes the message to indicate that a required condition remains unresolved, then requests the stock record. It also reviews whether the equivalence is realistic: real orders may remain undispatched because of processing delays even when both requirements hold. If so, the model needs another condition or a weaker rule. Correct reasoning from an oversimplified rule can still produce an unreliable operational conclusion.

Common misconceptions and mistakes

A possible world is not necessarily a likely world or the actual world. A logical model is also not necessarily a trained machine-learning model; here it means an interpretation satisfying stated formulas.
Unknown does not automatically mean false. Individual classical worlds assign truth values, while uncertainty arises from not knowing which world applies. Nor does one illustrative scenario establish a universal conclusion. Finally, inconsistent classical assumptions have no satisfying worlds; that situation requires attention rather than being presented as ordinary unresolved information.

Business use

Possible-world reasoning helps analysts ask precise questions: Is a proposed outcome compatible with the facts? Is it guaranteed by them? Which counterexample defeats the claim? Keep these questions separate from how likely an outcome is. Define the time and scope of each proposition, document rules and distinguish observations from assumptions. When a conclusion matters operationally, inspect both the inference and the adequacy of the representation. A missing delay variable in the order example changes what a non-dispatch observation can establish.

Check your understanding

How many worlds satisfy the example's equivalence?

Answer: Four.

After observing no dispatch, is cleared payment impossible?

Answer: No; the stock-unavailable, payment-cleared world remains.

Why does one counterexample matter?

Answer: Entailment requires the conclusion in every compatible model, so a single exception defeats it.

Related terms

Interpretation
Model
Satisfiability
Knowledge base
Joint probability distribution
logical entailment
truth assignment
counterexample
possible-world semantics

Learn next

Replace the equivalence with only D implies S and P. Enumerate the assignments again and check which conclusions remain valid after observing D false and S true.

Sources

Poole and Mackworth, Propositions, interpretations and models: https://artint.info/3e/html/ArtInt3e.Ch5.S1.html Poole and Mackworth, Probability and possible-world semantics: https://artint.info/3e/html/ArtInt3e.Ch9.S1.html AIMA glossary, possible world: https://github.com/aimacode/aima-glossary/blob/master/glossary.md

Previous: Possibility theory Next: Post-editing