Tree-Like Justification Systems are Consistent
This work addresses a foundational problem in non-monotonic logic for researchers in formal AI and logic, providing a definitive solution for tree-like justification systems.
The paper tackled the consistency problem in justification theory for tree-like systems, proving that all reasonable tree-like justification systems are consistent, thereby resolving this long-standing issue.
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.