• README ⤓ .txt 2026-10-22T165042.936 000000000000800
  Logics individuated by dropping monotony — the rule that adding premises never removes conclusions. Monotony is the consequence-relation form of weakening, as transitivity is the consequence-relation form of cut, so this subdivision stands to weakening as Nontransitive stands to cut: the structural rule is withdrawn at the level of the relation itself, and everything local stays classical.
• Nonmonotonic Consequence Relations ⤓ .md 2026-10-22T165042.936 000000000001016
  Dov Gabbay, "Theoretical foundations for non-monotonic reasoning in expert systems" (in Krzysztof R. Apt, ed., Logics and Models of Concurrent Systems, Springer 1985), asked what minimal conditions a consequence relation must satisfy to represent a nonmonotonic logic and answered with three: reflexivity, cut, and weak monotonicity — the last renamed cautious monotony by David Makinson, whose "General theory of cumulative inference" (2nd International Workshop on Non-Monotonic Reasoning, Grassau 1988; LNCS, Springer 1989) independently developed the Tarski-style theory and gave Gabbay's postulates a semantics with a completeness proof. Sarit Kraus, Daniel Lehmann and Menachem Magidor, "Nonmonotonic reasoning, preferential models and cumulative logics" (Artificial Intelligence 44, 1990, 167–207), combined Gabbay's proof-theoretic line with the preference semantics Yoav Shoham had advocated and proved the representation theorems; Lehmann and Magidor, "What does a conditional knowledge base entail?" (Artificial Intelligence 55, 1992, 1–60), added the rational relations — rational monotony imported from the conditional axiom CV at Makinson's suggestion — and the rational closure. Makinson's Bridges from Classical to Nonmonotonic Logic (College Publications, 2005) is the monograph treatment.
• Preferential Logic ⤓ .md 2026-08-20T061920.000 000000000038664
  Kraus, Lehmann, Magidor (1990). KLM framework. Ranked models. Non-monotonic consequence. Foundation of defeasible reasoning.
• CRITERIA ⤓ .txt 2026-10-22T165042.936 000000000000816
  Not sufficient: A knowledge-representation formalism individuated by its representation problem — default rules, minimized predicates, stable models — which belongs in Applications/Knowledge however nonmonotonic its consequence relation is. A belief-change operation (Modal/Epistemic and Applications/Knowledge hold revision). A conditional logic individuated by its object-language conditional (Modal/Alethic), even though the flat fragment of such logics and preferential consequence coincide. Paraconsistency or paracompleteness, which drop different things.