Tree-Like Justification Systems are Consistent

TL;DR

This paper proves that all reasonable tree-like justification systems are consistent, resolving a key problem in justification theory related to non-monotonic logics.

Contribution

It establishes that in the tree-like setting of justification theory, all systems satisfying reasonable conditions are guaranteed to be consistent.

Findings

All reasonable tree-like justification systems are consistent.

The result unifies understanding of justification systems in non-monotonic logics.

Addresses a longstanding open problem in justification theory.

Abstract

Justification theory is an abstract unifying formalism that captures semantics of various non-monotonic logics. One intriguing problem that has received significant attention is the consistency problem: under which conditions are justifications for a fact and justifications for its negation suitably related. Two variants of justification theory exist: one in which justifications are trees and one in which they are graphs. In this work we resolve the consistency problem once and for all for the tree-like setting by showing that all reasonable tree-like justification systems are consistent.