On the Structure of Game Provenance and its Applications

TL;DR

This paper explores the detailed structure of game-based provenance models for first-order queries, introducing new provenance types and demonstrating their computation and applications in areas like argumentation.

Contribution

It introduces a fine-grain analysis of game provenance, identifying seven edge types and their roles, advancing understanding of query provenance in database theory.

Findings

Seven new edge types in game provenance models.

Provenance can be computed during game solving.

Applications demonstrated in argumentation frameworks.

Abstract

Provenance in databases has been thoroughly studied for positive and for recursive queries, then for first-order (FO) queries, i.e., having negation but no recursion. Query evaluation can be understood as a two-player game where the opponents argue whether or not a tuple is in the query answer. This game-theoretic approach yields a natural provenance model for FO queries, unifying how and why-not provenance. Here, we study the fine-grain structure of game provenance. A game $G=(V,E)$ consists of positions $V$ and moves $E$ and can be solved by computing the well-founded model of a single, unstratifiable rule: \[ \text{win}(X) \leftarrow \text{move}(X, Y), \neg \, \text{win}(Y). \] In the solved game $G^{\lambda}$, the value of a position $x\,{\in}\,V$ is either won, lost, or drawn. This value is explained by the provenance $\mathscr{P}$(x), i.e., certain (annotated) edges reachable from $x$. We identify seven edge types that give rise to new kinds of provenance, i.e., potential, actual, and primary, and demonstrate that "not all moves are created equal". We describe the new provenance types, show how they can be computed while solving games, and discuss applications, e.g., for abstract argumentation frameworks.