Seven kinds of equivalent models for generalized coalition logics

TL;DR

This paper explores six different types of models that determine the validity of eight coalition logics, expanding understanding of models in strategic reasoning and coalition logic.

Contribution

It introduces six new model types that characterize the validity of eight coalition logics, broadening the modeling framework beyond previous assumptions.

Findings

Each of the eight logics is characterized by six alternative model types.

The models include single-coalition-first, neighborhood, and tree-like structures.

These models generalize and refine previous assumptions in coalition logic modeling.

Abstract

Coalition Logic is an important logic in logical research on strategic reasoning. In two recent papers, Li and Ju argued that generally, concurrent game models, models of Coalition Logic, have three too strong assumptions: seriality, independence of agents, and determinism. They presented eight coalition logics based on eight classes of general concurrent game models, determined by which of the three assumptions are met. In this paper, we show that each of the eight sets of valid formulas of the eight logics is determined by six other kinds of models, that is, single-coalition-first action models, single-coalition-first actual neighborhood models, clear grand-coalition-first action models, clear single-coalition-first actual neighborhood models, tree-like grand-coalition-first action models, and tree-like single-coalition-first actual neighborhood models.