Epistemic Disturbance in the Graph Model for Conflict Resolution: State-Preserving Actions, Four-Valued Assessments, and the Distinction between Capability and Intention

Yukiko Kato

cs.GTOct 8, 2026

Epistemic Disturbance in the Graph Model for Conflict Resolution: State-Preserving Actions, Four-Valued Assessments, and the Distinction between Capability and Intention

Authors: Yukiko Kato

Organizations: Lynx Technologies Inc., Tokyo, Japan · Institute of Science Tokyo, Tokyo, Japan

Abstract

In the graph model for conflict resolution (GMCR), a decision maker (DM) either moves the conflict to another state or does nothing. The basic definitions leave inaction implicit, so every action that leaves the state unchanged is treated as doing nothing. Yet announcements, exercises, leaks and selective disclosures are neither moves nor inaction: they leave the state unchanged but change what other DMs believe about which moves are available and which moves others would want to make. We introduce such state-preserving actions by augmenting states with the DMs' epistemic states: a physical move changes the physical state, a state-preserving action changes only the epistemic state, and inaction is the absence of a transition. Actions generate evidence through observer-specific interpretation maps. Building on a four-valued extension of GMCR from the author's earlier work, which separates evidence for and against, we show that evidence for a move can only enable perceived moves and evidence against can only disable them, that two of the four reduction operators ignore one kind of evidence, and that contradictory assessments are absorbing under monotone accumulation. With the monotonicity of stability in move sets, this fixes the direction in which any action moves a DM's stability judgements and characterizes when actions can enable provocation or deterrence. Capability assessments affect all sanction-based stability concepts, and on the DM's own side also Nash stability, whereas intention assessments affect only sequential stability. Hedging between two candidate types weakly expands or shrinks an observer's sequentially stable set according to how it reads contradiction. In the 1995 DVD format negotiation, general metarationality cannot distinguish its phases, since the computer industry group could always sanction; sequential stability, which asks whether it would, can.

Figures & tables

Assessment disturbed	Concepts affected	Counterpart in [ 16 ]
Own capability ( $\psi$ on $O_{i}$ )	Nash, GMR, SMR, SEQ (available improvements and escapes)	—
Opponents’ capability ( $\psi$ on $O\setminus O_{i}$ )	GMR, SMR, SEQ; Nash unchanged (existence of sanctioning paths)	structural admissibility
Opponents’ intention ( $\chi$ )	SEQ only (credibility of sanctioning paths)	preferential credibility

Table 1: Effects of capability and intention assessments on stability concepts.

$\psi^{1}(o)$	Action and induced change	$\delta_{1}(\mathsf{YN})=\mathsf{Y}$ ( $\delta_{\mathsf{N}\mathsf{Y}}$ , $\delta_{\mathsf{Y}\mathsf{Y}}$ )	$\delta_{1}(\mathsf{YN})=\mathsf{N}$ ( $\delta_{\mathsf{Y}\mathsf{N}}$ , $\delta_{\mathsf{N}\mathsf{N}}$ )
$\mathsf{N}$ (threat not believed)	$d_{2}$ : $\mathsf{N}\to\mathsf{YN}$	threat perceived; $d_{2}$ is deterrence-enabling for DM 2	no effect
$\mathsf{Y}$ (threat believed)	$d_{3}$ : $\mathsf{Y}\to\mathsf{YN}$	no effect	threat no longer perceived; $d_{3}$ is provocation-enabling for DM 3

Table 2: Effect of state-preserving actions on DM 1’s judgement at

s

	observers with $\delta(\mathsf{YN})=\mathsf{Y}$	observers with $\delta(\mathsf{YN})=\mathsf{N}$
$H$ reveals $\theta_{A}$	$P_{2}$ judges $s$ SEQ, $P_{1}$ not	$P_{2}$ judges $s$ SEQ, $P_{1}$ not
$H$ reveals $\theta_{B}$	$P_{1}$ judges $s$ SEQ, $P_{2}$ not	$P_{1}$ judges $s$ SEQ, $P_{2}$ not
$H$ hedges	both judge $s$ SEQ	neither

Table 3: SEQ judgements of the status quo in Example 9.4 .

DM	Option	Meaning
$M$	$L_{M}$	launch the MMCD format unilaterally
	$A_{M}$	accept a unified format
$S$	$L_{S}$	launch the SD format unilaterally
	$A_{S}$	accept a unified format
$T$	$E_{M}$	endorse MMCD
	$E_{S}$	endorse SD

Table 4: Decision makers and options of the DVD model.

Panel of Figure 1 — Figure 1: Option-level transitions of the three DMs. Every arrow is one-way: all transitions are irreversible. $E_{M}$ ( $E_{S}$ ) is unavailable once $M$ ( $S$ ) has accepted, $E_{C}$ requires that a camp has accepted, and no DM moves once the format is unified.

Panel of Figure 2 — Figure 2: Integrated graph of the DVD model. States are grouped by the positions of the two camps (columns: $M$ ; rows: $S$ ); within a group, the centre position is the state in which $T$ has made no statement, and the other positions correspond to $E_{M}$ (upper left), $E_{S}$ (right), $B$ (lower left) and $E_{C}$ (lower right). All arcs are irreversible. The status quo is state $1$ and the unified format state $33$ ; the option form of every state is given in Table 6 .

Live TWG types	$M$ judges $s_{0}$ stable (SEQ / GMR)	$S$ judges $s_{0}$ stable (SEQ / GMR)
$\{\theta_{B}\}$ , $\{\theta_{U}\}$ or $\{\theta_{US}\}$	yes / yes	yes / yes
$\{\theta_{S}\}$	yes / yes	no / yes
$\{\theta_{M}\}$	no / yes	yes / yes
$\{\theta_{M},\theta_{S}\}$	yes / yes	yes / yes

Table 5: Stability judgements of the status quo

s_{0}

against unilateral launch.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

	$M$		$S$		$T$				camps		types of $T$
State	$L_{M}$	$A_{M}$	$L_{S}$	$A_{S}$	$E_{M}$	$E_{S}$	$B$	$E_{C}$	$M$	$S$	$\theta_{B}$	$\theta_{U}$	$\theta_{US}$	$\theta_{S}$	$\theta_{M}$
1	–	–	–	–	–	–	–	–	6	6	3	4	4	4	4
2	–	–	–	–	Y	–	–	–	6	6	4	5	5	6	2
3	–	–	–	–	–	Y	–	–	6	6	4	5	3	2	6
4	–	–	–	–	–	–	Y	–	6	6	3	4	4	5	5
5	–	–	Y	–	–	–	–	–	8	5	5	6	6	5	5

Appendix

Table 6: Feasible states (option form) and preference rankings of the DVD model. Y: the option is taken; –: it is not.

		Statement of $T$
Own camp	Rival camp	none	endorses own	endorses rival	refusal	endorses compromise
not moved	not moved	6 [1/1]	6 [2/3]	6 [3/2]	6 [4/4]	–
not moved	launched	8 [5/13]	5 [6/15]	12 [7/14]	6 [8/16]	–
not moved	accepted	3 [9/25]	2 [10/26]	–	3 [11/27]	10 [12/28]
launched	not moved	5 [13/5]	1 [14/7]	10 [15/6]	9 [16/8]	–
launched	launched	10 [17/17]	5 [18/19]	12 [19/18]	11 [20/20]	–

Appendix

Table 7: Ranks of the camps by situation, from the viewpoint of the own camp. Each cell gives the rank (1: most preferred) and, in brackets, the state number when the own camp is

M

/ when it is

S

; –: infeasible.

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Provenance-Enhanced Statements in Knowledge Graphs

Fabio Vitali, Valentina Pasqual

University of Bologna, Italy

Logical Reasoning Data Provenance Knowledge Representation Graph Reasoning Knowledge Graphs Epistemic Logic

Open paper AskPDF arXiv

Provenance-enhanced statements of the form "according to

X

\varphi

" are pervasive in contemporary knowledge graphs, especially in domains where graph content primarily represents claims, interpretations, and hypotheses (\emph{capta}) rather than observer-independent facts (\emph{data}). Current provenance models can record who asserted what, but they typically treat provenance as semantically neutral, leaving underspecified how attributed claims relate to factual commitment, to one another, and to reasoning. In this paper we introduce DEC, a framework that interprets provenance predicates as indicators of epistemic stance and groups provenance-homogeneous sets of statements into \emph{cognitive worlds}. Drawing on cognitive modal logics (doxastic, epistemic, and conjectural), DEC characterizes locality, rationality, and controlled permeation between cognitive worlds and a distinguished factual core ("reality"), thereby enabling principled reasoning over attributed content without collapsing disagreements into inconsistencies. We formalize a DEC interpretation for RDF datasets that is conservative over RDF~1.2 semantics, clarify the role of intensionality and identity (including the Superman paradox), and illustrate the approach on common Semantic Web representations (named graphs, quoted triples/RDF-star, and reification). Finally, we describe our prototype DEC reasoner implemented as a Fuseki dataset module, supporting controlled factualisation and explicit detection of disagreements and delusions.

Abstract

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