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arxiv: 2504.01733 · v5 · pith:2CETZSTOnew · submitted 2025-04-02 · 💻 cs.AI · cs.CC· cs.LO

Epistemic Skills: Reasoning about Knowledge and Oblivion

Xiaolong Liang , Y\`i N. W\'ang This is my paper

Pith reviewed 2026-05-25 08:07 UTC · model grok-4.3

classification 💻 cs.AI cs.CCcs.LO
keywords epistemic logicweighted modelsknowledge dynamicsepistemic skillsupskillingdownskillinggroup knowledgeknowability
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0 comments X

The pith

Epistemic logics in weighted models treat knowledge acquisition as upskilling and oblivion as downskilling via an epistemic skills metric.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a class of epistemic logics built on weighted models to track how agents gain or lose knowledge over time. An epistemic skills metric assigns capacities that increase during acquisition and decrease during loss. This setup incorporates group knowledge and defines knowability as the potential for upskilling and forgettability as the potential for downskilling. It also distinguishes epistemic de re from de dicto expressions and studies the complexity of model checking and satisfiability. A reader would care because the approach supplies a formal mechanism for reasoning about epistemic change that standard static logics leave implicit.

Core claim

The paper presents a class of epistemic logics grounded in a system of weighted models that introduce an epistemic skills metric to represent the epistemic capacities tied to knowledge updates. Knowledge acquisition is modeled as a process of upskilling, whereas oblivion is represented as a consequence of downskilling. The framework enables exploration of knowability and forgettability, supports analysis of distinctions between epistemic de re and de dicto expressions, and examines the computational complexity of the model checking and satisfiability problems.

What carries the argument

The epistemic skills metric defined over weighted models, which quantifies capacities for knowledge updates and drives upskilling for acquisition and downskilling for oblivion.

If this is right

  • Knowledge acquisition is formally modeled as upskilling in the weighted models.
  • Oblivion is formally modeled as downskilling in the weighted models.
  • Knowability is defined as the potential to gain knowledge through upskilling.
  • Forgettability is defined as the potential to lapse into oblivion through downskilling.
  • Distinctions between epistemic de re and de dicto expressions receive detailed analysis within the framework.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The weighted-model approach could be applied to simulate collective knowledge changes across groups of artificial agents.
  • Complexity results for model checking might indicate feasible verification methods for dynamic epistemic systems.
  • The upskilling and downskilling processes could be tested against empirical data on human learning and forgetting rates.

Load-bearing premise

The dynamics of knowledge acquisition and oblivion can be adequately represented by upskilling and downskilling processes within weighted models using the epistemic skills metric.

What would settle it

An observed case of knowledge gain or loss that cannot be matched to any corresponding increase or decrease in the epistemic skills values assigned in the weighted model.

Figures

Figures reproduced from arXiv: 2504.01733 by Xiaolong Liang, Y\`i N. W\'ang.

Figure 1
Figure 1. Figure 1: Illustration of the model M. Curly brackets are omitted from set labels for brevity. Edges labeled with the empty set, such as between w1 and w4, indicate universal distinguishability—except by totally incompetent agents (those with an empty skill set)—and are not depicted in the diagram. 2.4.2. Model checking results. The following properties hold within the model M = (W, E, C, β). They are categorized be… view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of G0 = ({d1, d2, d3, d4}, {{d1, d3}, {d1, d4}, {d2, d4}, {d3, d4}}). Play alternates between Player I (starting at d) and Player II until a player cannot move. As an example, G0 = ({d1, d2, d3, d4}, {{d1, d3}, {d1, d4}, {d2, d4}, {d3, d4}}) represents an undirected graph. An illustration of G0 is given in [PITH_FULL_IMAGE:figures/full_fig_p020_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Illustration of the induced model MG0 , with G0 illustrated in [PITH_FULL_IMAGE:figures/full_fig_p021_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: These logics exclude common knowledge (CG), update modalities ((+S)a, (−S)a, (=S)a, (≡b)a), and quantifying modalities (⊞a, ⊟a, ✷a), focusing on logics based on subsets of LCDEF , such as L, LD and LDEF . The results will be shown by reductions to and from known complexity results, and are summarized in [PITH_FULL_IMAGE:figures/full_fig_p026_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Roadmap of proofs for the complexity of satisfiability problems for logics with common knowledge, excluding update and quantifying modalities. Boxed nodes display known complexity results. A solid arrow from one logic to another indicates that the satisfiability problem for the former logic is a subproblem for the latter. A dashed arrow labeled “PTIME” denotes a polynomial-time reduction from the satisfiab… view at source ↗
read the original abstract

This paper presents a class of epistemic logics that captures the dynamics of acquiring knowledge and descending into oblivion, while incorporating concepts of group knowledge. The approach is grounded in a system of weighted models, introducing an ``epistemic skills'' metric to represent the epistemic capacities tied to knowledge updates. Within this framework, knowledge acquisition is modeled as a process of upskilling, whereas oblivion is represented as a consequence of downskilling. The framework further enables exploration of ``knowability'' and ``forgettability,'' defined as the potential to gain knowledge through upskilling and to lapse into oblivion through downskilling, respectively. Additionally, it supports a detailed analysis of the distinctions between epistemic de re and de dicto expressions. The computational complexity of the model checking and satisfiability problems is examined, offering insights into their theoretical foundations and practical implications.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The paper introduces a class of epistemic logics based on weighted models equipped with an epistemic-skills metric. Knowledge acquisition is formalized as upskilling operations and oblivion as downskilling operations; the framework also expresses group knowledge, knowability/forgettability, and the de-re/de-dicto distinction, while providing complexity results for model checking and satisfiability.

Significance. If the constructions are internally consistent, the work supplies a uniform semantic setting in which both positive and negative epistemic change can be represented via a single metric, extending standard dynamic epistemic logic to include graded forgetting. The explicit complexity analysis is a concrete strength that supports practical applicability.

minor comments (2)
  1. [Abstract] The abstract states that complexity results are obtained but does not preview the classes (e.g., PSPACE-complete); the introduction or § on complexity should state the precise bounds for both problems.
  2. Notation for the weighted models and the upskilling/downskilling operators should be introduced with a single running example that illustrates both an individual and a group update.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary and significance assessment of our paper introducing epistemic logics on weighted models with an epistemic-skills metric. The framework models knowledge acquisition via upskilling and oblivion via downskilling, while covering group knowledge, knowability/forgettability, de re/de dicto distinctions, and complexity results for model checking and satisfiability. The recommendation for minor revision is noted.

Circularity Check

0 steps flagged

No significant circularity detected in framework definition

full rationale

The paper introduces a new semantic framework consisting of weighted epistemic models equipped with an epistemic-skills metric, where knowledge acquisition is defined as upskilling and oblivion as downskilling. All subsequent notions (group knowledge, knowability, forgettability, de re / de dicto distinctions) are expressed inside these models by construction. No step claims an independent prediction, theorem, or empirical result that reduces to a fitted parameter or prior self-citation; the work is a definitional exercise whose internal consistency is not asserted via external load-bearing citations. The derivation chain is therefore self-contained and does not exhibit any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 3 invented entities

Review conducted from abstract only; the paper introduces several new modeling concepts whose grounding is not detailed here.

axioms (1)
  • standard math Standard axioms and semantics of epistemic logic
    The new logics extend existing epistemic logic systems as stated in the abstract.
invented entities (3)
  • epistemic skills metric no independent evidence
    purpose: to represent the epistemic capacities tied to knowledge updates
    Newly introduced to ground the weighted models.
  • upskilling no independent evidence
    purpose: modeling knowledge acquisition as skill improvement
    Defined in the framework as the process of acquiring knowledge.
  • downskilling no independent evidence
    purpose: modeling oblivion as skill decline
    Defined as the consequence of descending into oblivion.

pith-pipeline@v0.9.0 · 5677 in / 1355 out tokens · 45312 ms · 2026-05-25T08:07:39.859796+00:00 · methodology

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discussion (0)

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