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
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 ( ψ on Oi )
Nash, GMR, SMR, SEQ (available improvements and escapes)
—
Opponents’ capability ( ψ on O∖Oi )
GMR, SMR, SEQ; Nash unchanged (existence of sanctioning paths)
structural admissibility
Opponents’ intention ( χ )
SEQ only (credibility of sanctioning paths)
preferential credibility
Table 1: Effects of capability and intention assessments on stability concepts.
ψ1(o)
Action and induced change
δ1(YN)=Y ( δNY , δYY )
δ1(YN)=N ( δYN , δNN )
N (threat not believed)
d2 : N→YN
threat perceived; d2 is deterrence-enabling for DM 2
no effect
Y (threat believed)
d3 : Y→YN
no effect
threat no longer perceived; d3 is provocation-enabling for DM 3
Table 2: Effect of state-preserving actions on DM 1’s judgement at s .
observers with δ(YN)=Y
observers with δ(YN)=N
H reveals θA
P2 judges s SEQ, P1 not
P2 judges s SEQ, P1 not
H reveals θB
P1 judges s SEQ, P2 not
P1 judges s SEQ, P2 not
H hedges
both judge s SEQ
neither
Table 3: SEQ judgements of the status quo in Example 9.4 .
DM
Option
Meaning
M
LM
launch the MMCD format unilaterally
AM
accept a unified format
S
LS
launch the SD format unilaterally
AS
accept a unified format
T
EM
endorse MMCD
ES
endorse SD
Table 4: Decision makers and options of the DVD model.
Figure 1: Option-level transitions of the three DMs. Every arrow is one-way: all transitions are irreversible. EM ( ES ) is unavailable once M ( S ) has accepted, EC requires that a camp has accepted, and no DM moves once the format is unified.
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 EM (upper left), ES (right), B (lower left) and EC (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 s0 stable (SEQ / GMR)
S judges s0 stable (SEQ / GMR)
{θB} , {θU} or {θUS}
yes / yes
yes / yes
{θS}
yes / yes
no / yes
{θM}
no / yes
yes / yes
{θM,θS}
yes / yes
yes / yes
Table 5: Stability judgements of the status quo s0 against unilateral launch.
Appendix figures & tables2 assets
Supplementary material from the paper’s appendix.
Appendix
M
S
T
camps
types of T
State
LM
AM
LS
AS
EM
ES
B
EC
M
S
θB
θU
θUS
θS
θM
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.
Provenance-enhanced statements of the form "according to X, φ" 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.
In noisy social dilemmas, intended actions are stochastically corrupted before execution, so an observed defection may reflect hostile intent or action error. Standard Markov Decision Process (MDP) formulations treat executed actions as states, structurally precluding this distinction and causing systematic over-retaliation. We introduce a Partially Observable MDP (POMDP) formulation encoding opponent intentions as latent states and executed actions as noisy observations, solved within the active inference (AIF) framework with a cost function that decomposes into epistemic and pragmatic components that jointly address inferring current intent and learning how intent evolves. In the Iterated Prisoner's Dilemma with symmetric noise, we derive a critical noise threshold governing cooperation collapse, connecting it to a fixed-point condition on learned priors. Experiments reveal that the value of intention inference is context-dependent: the POMDP provides consistent advantages against conditionally cooperative opponents, but mutual intention inference under sufficient noise produces correlated belief-driven collapse. The advantage is specific to games where intent attribution is decision-relevant.
Kival Mahadew, Jonathan Shock
Dept. of Computer Science, University of Cape Town · Neuroscience Institute, University of Cape Town · Dept. of Mathematics & Applied Mathematics, University of Cape Town +2
Tool-using agents make consequential changes to external state, yet correct outcomes do not guarantee that their actions were supported by evidence established beforehand. We study where this evidence-to-action chain breaks as agents move from deciding whether to act to executing single actions and dependent workflows. Across ten model-harness configurations, strong static action assessment can coexist with much weaker interactive execution. Failures often begin before execution: agents stop with incomplete investigation or act before required evidence is established. Once required evidence is obtained, single-action execution is usually reliable, while multi-action workflows additionally expose unresolved prerequisites and incomplete execution. For this analysis, we introduce SafeActBench, comprising 656 cases across six operational domains and five protocols that progress from static action judgment and investigated non-action to single- and multi-action workflows. A provenance-bound Evidence Ledger and deterministic trajectory evaluator track what information was established, when actions occurred, and whether downstream dependencies were satisfied. These results show that failures arise not only from missing information, but also from how agents use established evidence when deciding and executing actions.
Hongzhan Lin, Shidong Cao, Ziyang Luo +3
National University of Singapore · Hong Kong Baptist University · Amazon Web Services +1