arXiv subjects

Yukiko Kato

Publications and source records attributed to Yukiko Kato.

3 recordsLinked to original sources

arXiv2026

A Four-Valued Graph Model for Conflict Resolution: Core Framework and a Machine-Checked Formalization in Lean 4

This note consolidates the core of the Quasi-Closed World Graph Model for Conflict Resolution (QCW-GMCR), which extends the standard Graph Model for Conflict Resolution with Belnap's four-valued logic to represent option-level epistemic ambiguity, and pairs the framework with a machine-checked Lean 4 formalization. QCW-GMCR combines: (1) FOUR-valued option assignments with compositional propagation to state-level feasibility; (2) graded reachability (definite, credible, possible) based on an FDE-inspired transition-warrant semantics, with definite reachability related to FDE consequence in the Boolean fragment; (3) axiomatized deterministic reductions from four-valued assessments to binary decisions, including four canonical operators reflecting distinct risk attitudes; and (4) catastrophe-avoiding equilibrium concepts with a quasi-closed-world safety invariant. A four-valued hypergame extension captures heterogeneous subjective assessments across decision makers. We state the core definitions and results and report the parts verified in Lean 4 with mathlib, including the classical GMCR stability hierarchy, algebraic and compositional properties of FOUR-valued conjunction, properties of the canonical reductions, and the graded reachability hierarchy. The formalization also helped identify and correct earlier claims, including a knowledge-monotonicity axiom replaced by truth monotonicity. This preprint provides a stable, citable record of the framework and its current formal verification status.

cs.LO↗

arXiv2023

Categorical Approach to Conflict Resolution: Integrating Category Theory into the Graph Model for Conflict Resolution

This paper introduces the Categorical Graph Model for Conflict Resolution (C-GMCR), a novel framework that integrates category theory into the traditional Graph Model for Conflict Resolution (GMCR). The C-GMCR framework provides a more abstract and general way to model and analyze conflict resolution, enabling researchers to uncover deeper insights and connections. We present the basic concepts, methods, and application of the C-GMCR framework to the well-known Prisoner's Dilemma and other representative cases. The findings suggest that the categorical approach offers new perspectives on stability concepts and can potentially lead to the development of more effective conflict resolution strategies.

cs.AI↗

arXiv2022

State Definition for Conflict Analysis with Four-valued Logic

We examined a four-valued logic method for state settings in conflict resolution models. Decision-making models of conflict resolution, such as game theory and graph model for conflict resolution (GMCR), assume the description of a state to be the outcome of a combination of strategies or the consequence of option selection by the decision-makers. However, for a framework to function as a decision-making system, unless a clear definition of the task of placing information out of an infinite world exists, logical consistency cannot be ensured, and thus, the function may be incomputable. The introduction of paraconsistent four-valued logic can prevent incorrect state setting and analysis with insufficient information and provide logical validity to analytical methods that vary the analysis resolution depending on the degree of coarseness of the available information. This study proposes a GMCR stability analysis with state configuration based on Belnap's four-valued logic.

cs.AI↗