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Selective Credibility-Limited Belief Update | AI Research

Key Takeaways

  • Selective Credibility-Limited Belief Update (SCL) is a framework designed to handle belief changes when new information is only partially realizable.
  • Belief update concerns changes in an agent's beliefs induced by changes in the underlying world.
  • Nevertheless, existing credibility-limited approaches treat the epistemic input as an indivisible whole, and therefore cannot represent cases in which only part of a compound epistemic input can be realized.
  • We introduce selective credibility-limited belief update, in which the epistemic input is transformed, relative to each source world, into a weaker proxy before the credibility-limited transition is performed.
  • We provide semantic and axiomatic characterizations of the resulting class of update operators.
Paper AbstractExpand

Belief update concerns changes in an agent's beliefs induced by changes in the underlying world. Standard Katsuno-Mendelzon update assumes that an epistemic input can be incorporated from every initially possible world, whereas credibility-limited belief update restricts, for each source world, the successor worlds regarded as credible or reachable. Nevertheless, existing credibility-limited approaches treat the epistemic input as an indivisible whole, and therefore cannot represent cases in which only part of a compound epistemic input can be realized. We introduce selective credibility-limited belief update, in which the epistemic input is transformed, relative to each source world, into a weaker proxy before the credibility-limited transition is performed. We provide semantic and axiomatic characterizations of the resulting class of update operators. We then identify two well-behaved sub-classes; namely, consistency-preserving update operators, which require every transformed epistemic input to be credible from its source world whenever the original epistemic input is consistent, and maximal consistency-preserving update operators, which additionally require the selected proxy to be maximally informative among the credible consequences of the original epistemic input. Finally, we establish the generality of the proposed framework by showing that credibility-limited belief update is recovered as a special case, while Katsuno--Mendelzon belief update emerges when credibility restrictions are removed and the transformation functions are taken to be identities. These results demonstrate that the framework provides a unified and strictly more expressive account of belief update, encompassing established approaches while supporting source-dependent selective acceptance.

Selective Credibility-Limited Belief Update (SCL) is a framework designed to handle belief changes when new information is only partially realizable. While standard belief update models often treat incoming information as an "all-or-nothing" input, SCL allows an agent to weaken complex instructions into a more manageable proxy, ensuring the update remains credible relative to the agent's current state.

The Problem with Rigid Updates

Traditional belief update models, such as the Katsuno–Mendelzon (KM) framework, assume that an agent must fully incorporate new information into their belief system. This works well when the world changes in a predictable way, but it fails when an instruction is physically impossible or unreliable. For example, if a robot is told to "move a cup and fill it," but the cup is broken, the robot cannot perform both tasks. Standard models might force the robot to attempt the impossible, while existing credibility-limited models might force the robot to reject the entire instruction or eliminate the possibility of the action entirely. None of these options allow the robot to simply perform the executable part of the task—moving the cup—while ignoring the impossible part.

How Selective Credibility-Limited Update Works

SCL belief update introduces a transformation-based approach to solve this rigidity. Before an agent attempts to incorporate new information, the framework transforms the epistemic input into a "weaker proxy" specifically tailored to each source world.
This process relies on two main components:

  • Source-dependent transformation: The system evaluates the epistemic input relative to each possible starting world and weakens it into a proxy that is actually achievable.

  • Credibility-limited transition: Once the input is transformed into a credible proxy, the system applies standard transition mechanisms to select the most plausible successor worlds.
    By weakening the input at the source, the agent can accept parts of a compound instruction that are feasible while discarding parts that are not, without needing to reject the entire update.

Consistency and Information

The authors identify two specific sub-classes of SCL operators that manage how these proxies are selected:

  • Consistency-preserving operators: These ensure that if the original input is consistent, the transformed proxy remains credible from the source world. This guarantees that the agent always finds at least one valid successor world.

  • Maximal consistency-preserving operators: These go a step further by requiring that the selected proxy is the most informative version possible among all credible consequences of the original input.

Why This Framework Matters

The SCL framework provides a unified way to view belief update. The authors demonstrate that existing models are actually special cases of this broader approach:

  • Credibility-limited (CL) update is recovered when the transformation functions are treated as identities (no weakening occurs).

  • Katsuno–Mendelzon (KM) update is recovered when credibility restrictions are removed and transformations are identities.
    Because SCL can represent these established approaches while also supporting source-dependent selective acceptance, it offers a more expressive and flexible tool for modeling how agents adapt to complex, real-world information.

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