Tree-Like Justification Systems are Consistent

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.