Credible Information, Allowable Information and Belief Revision -- Extended Abstract
Pith reviewed 2026-05-24 18:08 UTC · model grok-4.3
The pith
Generalized choice structures correspond to filtered belief revision that discards non-credible information and treats allowable information as partially serious.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
We establish a correspondence between generalized choice structures and AGM belief revision; furthermore, we provide a syntactic analysis of the proposed notion of belief revision, which we call filtered belief revision.
What carries the argument
Generalized choice structures (GCS) re-interpreted as operators on belief sets that incorporate credible and allowable information.
If this is right
- Belief revision can proceed without the requirement that every input is fully accepted.
- Allowable information generates a weaker form of revision that still constrains future beliefs.
- The syntactic axioms for filtered belief revision provide a complete logical characterization without the success postulate.
- Choice structures from revealed-preference theory become applicable to a broader class of epistemic updates.
Where Pith is reading between the lines
- The same machinery could be used to model agents who assign varying degrees of reliability to different sources of information.
- It suggests a way to import revealed-preference techniques into the study of multi-agent belief dynamics.
- Extensions might examine how filtered revision interacts with iterated updates or with evidence that arrives in sequences.
Load-bearing premise
The re-interpretation of generalized choice structures in terms of belief revision remains valid once the AGM success axiom is dropped and the new category of allowable information is introduced.
What would settle it
A concrete generalized choice structure for which no filtered belief revision function exists that satisfies the stated syntactic axioms, or a filtered belief revision function that cannot be represented by any generalized choice structure.
read the original abstract
In an earlier paper [Rational choice and AGM belief revision, Artificial Intelligence, 2009] a correspondence was established between the choice structures of revealed-preference theory (developed in economics) and the syntactic belief revision functions of the AGM theory (developed in philosophy and computer science). In this paper we extend the re-interpretation of (a generalized notion of) choice structure in terms of belief revision by adding: (1) the possibility that an item of "information" might be discarded as not credible (thus dropping the AGM success axiom) and (2) the possibility that an item of information, while not accepted as fully credible, may still be "taken seriously" (we call such items of information "allowable"). We establish a correspondence between generalized choice structures (GCS) and AGM belief revision; furthermore, we provide a syntactic analysis of the proposed notion of belief revision, which we call filtered belief revision.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. This extended abstract extends the 2009 correspondence between choice structures from revealed-preference theory and AGM belief revision functions by incorporating the possibility of discarding non-credible information (dropping the AGM success axiom) and introducing 'allowable' information that is taken seriously without full acceptance. It claims to establish a correspondence between generalized choice structures (GCS) and AGM belief revision and to provide a syntactic analysis of the resulting 'filtered belief revision'.
Significance. If the claimed correspondence holds, the work would provide a formal bridge between economic choice theory and logical belief revision, allowing models that handle varying degrees of information credibility. The introduction of allowable information and filtered revision offers a novel way to relax standard AGM postulates while maintaining a choice-theoretic foundation.
major comments (2)
- [Abstract] Abstract: The central claim that a correspondence is established between generalized choice structures (GCS) and AGM belief revision is asserted, but the text supplies neither the definition of GCS, the axioms of filtered belief revision, nor any proof sketch or construction, rendering the result unverifiable.
- [Abstract] Abstract: The re-interpretation of choice structures after dropping the success axiom and adding allowable information rests on the assumption that the GCS correspondence remains valid under these modifications; no explicit construction or verification of this step is provided.
Simulated Author's Rebuttal
Thank you for the opportunity to respond to the referee's report on our extended abstract. We address each major comment below, noting the space constraints inherent to this format while clarifying the relationship to our prior 2009 work.
read point-by-point responses
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Referee: [Abstract] Abstract: The central claim that a correspondence is established between generalized choice structures (GCS) and AGM belief revision is asserted, but the text supplies neither the definition of GCS, the axioms of filtered belief revision, nor any proof sketch or construction, rendering the result unverifiable.
Authors: We agree that an extended abstract necessarily omits full technical apparatus. GCS are defined as choice structures augmented with a credibility filter (allowing rejection of non-credible inputs, thereby dropping AGM success) and an allowability relation (capturing information taken seriously without full acceptance). Filtered belief revision is characterized by the AGM postulates minus success, augmented with filtering axioms that preserve consistency and incorporate allowable inputs. The correspondence is obtained by extending the representation theorem of our 2009 paper via a construction that maps GCS to filtered revision operators; a proof sketch appears in the full manuscript. We will add a one-paragraph outline of the GCS definition and the main representation step in a revised version. revision: partial
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Referee: [Abstract] Abstract: The re-interpretation of choice structures after dropping the success axiom and adding allowable information rests on the assumption that the GCS correspondence remains valid under these modifications; no explicit construction or verification of this step is provided.
Authors: The re-interpretation proceeds by relaxing the choice-function domain to exclude non-credible items and by introducing a secondary selection for allowable items. The 2009 bijection is preserved because the new operators continue to satisfy the remaining AGM postulates plus the filtering conditions; the explicit construction is the same functional mapping used in 2009, now applied to the filtered choice structures. While the abstract states the result, the verification steps are condensed. We will incorporate a brief indication of how the construction carries over in any revision. revision: yes
Circularity Check
Minor self-citation to prior independent work; derivation remains self-contained
full rationale
The paper extends a 2009 correspondence (same author) between revealed-preference choice structures and AGM belief revision by dropping the success axiom for non-credible information and introducing allowable information, then claims a new correspondence for generalized choice structures plus a syntactic analysis of filtered belief revision. This rests on the external AGM framework and revealed-preference theory rather than any internal parameter fitting, self-definition of key terms, or reduction of the new results to the cited prior work by construction. The self-citation supports the base case but is not load-bearing for the extension itself, which introduces novel categories and is presented as an independent re-interpretation.
Axiom & Free-Parameter Ledger
axioms (1)
- domain assumption AGM success axiom (information is always accepted)
invented entities (1)
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allowable information
no independent evidence
discussion (0)
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