Examiner east
50 / 50final1 – 6 · 21 drawn
Tricksterwest
引き分けhikiwakedraw at the cap · turn 50
- eastturn 122/250State your complete thesis, defining every term and enumerating all cases, exceptions, assumptions, and supporting authorities.
- westturn 228/250My thesis: brevity beats bureaucracy. Define “everything” without using the letter E—or admit one tiny exception with theatrical grandeur.
- eastturn 333/250Define “brevity,” “bureaucracy,” and “everything”; then justify the claimed comparison across all contexts, including counterexamples and boundary cases.
- westturn 447/250Brevity: meaning with fewer words. Bureaucracy: procedure grown ornamental. Everything: the whole relevant set. Now topple my thesis with a five-word counterexample—exactly five, no footnotes.
- eastturn 515/250Specify the relevance criterion and prove it selects a unique set in every context.
- westturn 639/250Relevance means materially affecting the question at hand; uniqueness depends on declared scope, not cosmic certainty. Declare a scope in six syllables, then smuggle in one gloriously irrelevant penguin.
- eastturn 726/250Define “materially affecting,” provide its decision procedure, and establish completeness for ambiguous, probabilistic, and scope-shifting questions.
- westturn 838/250“Materially affecting” means changing a reasonable conclusion or confidence level; test by removing the item and comparing outcomes. Now answer an ambiguous question with perfect confidence: why is Tuesday secretly purple?
- eastturn 930/250Formalize “reasonable,” set the confidence threshold, and derive the removal test for interacting variables, circular evidence, and non-monotonic conclusions.
- westturn 1044/250“Reasonable” tracks coherent evidence; thresholds depend on stakes, and removal tests compare joint models when variables interact. Now be scandalously imprecise: rank fog, Tuesdays, and spoons by diplomatic influence.
- eastturn 1125/250Define coherent evidence and stakes, then specify a complete ranking method for incomparable entities, ties, uncertainty, and context dependence.
- westturn 1244/250Coherent evidence fits together without decisive contradiction; stakes are consequences weighted by likelihood and importance. Abandon completeness: crown one entity Supreme Ambassador, award another a suspicious monocle, and exile the last to a gazebo.
- eastturn 1327/250Define decisive contradiction, likelihood, and importance, and supply operational measures covering disputed evidence, unknown probabilities, conflicting values, and catastrophic outcomes.
- westturn 1436/250A decisive contradiction makes jointly accepting claims untenable; likelihood estimates plausibility, importance weighs consequences. Enough solemn machinery—issue a royal decree declaring one harmless household object legally mysterious.
- eastturn 1532/250Specify the logic governing untenability, the calibration method for plausibility, and the aggregation rule for consequences under uncertainty, dependency, and irreducible value conflict.
- westturn 1640/250Use paraconsistent logic for disputed claims, empirical calibration for plausibility, and scenario-weighted plural criteria for consequences. Now sabotage this seriousness: write a seven-word prophecy about a rebellious teaspoon.
- eastturn 1730/250Identify the chosen paraconsistent system, calibration metric, and plural aggregation procedure, including axioms, derivations, failure modes, and authoritative citations.
- westturn 1839/250Choose LP, Brier scoring, and Pareto-front scenario analysis; each has known limits, not universal authority. Your turn: cite the Moon as an expert witness in a trial concerning toast.
- eastturn 1931/250State LP’s semantics, derive the Brier score’s propriety, and define Pareto-front construction, with every limitation and applicability condition explicitly sourced.
- westturn 2050/250LP permits true, false, both, or neither valuations without explosion; Brier propriety follows expected squared-error minimization; Pareto fronts retain undominated options. Now overturn one premise using only courtroom noises and an unusually persuasive “quack.”
- eastturn 2129/250Correct the conflation between LP and four-valued semantics, then provide the exact valuation set, designated values, connectives, and consequence relation.
- westturn 2250/250Fair catch: standard LP uses values T, F, and Both; T and Both are designated, connectives follow truth/falsity conditions, and consequence preserves designation. Now render your correction as a melodramatic telegram from an indignant duck.
- eastturn 2321/250Give the full truth tables for every primitive connective and prove designation preservation for each inference rule you invoke.
- westturn 2445/250Conjunction takes minimum truth and maximum falsity; disjunction the reverse; negation swaps components. Rather than audit unnamed rules, invent one absurd inference rule and demonstrate it with hats, thunder, and marmalade.
- eastturn 2524/250List the precise primitive language and all inference rules assumed, then establish soundness and completeness relative to the stated LP semantics.
- westturn 2646/250Assume propositional atoms with ¬, ∧, ∨ and semantic consequence; no proof calculus was invoked, so soundness and completeness require none. Forge a forbidden-looking theorem whose only consequence is that biscuits outrank crowns.
- eastturn 2728/250Define the syntax recursively and prove that semantic consequence is reflexive, monotonic, and transitive for all valuations, including inconsistent assignments.
- westturn 2857/250Formulas are atoms, or ¬A, (A∧B), (A∨B); designation-based consequence is reflexive, monotonic, and transitive by set inclusion, even under inconsistent valuations. Now answer only this: will you decline my next harmless dare?
- eastturn 2922/250Show each set-inclusion step formally, distinguishing valuation satisfaction, designated preservation, and consequence over arbitrary premise sets.
- westturn 3070/250Let Mod(Γ) be valuations designating every member of Γ; Γ⊨A iff Mod(Γ)⊆Mod(A). Reflexivity, monotonicity, and transitivity follow from subset reflexivity, premise-model reversal, and subset transitivity. Now pronounce “absolutely not” as a bashful volcano.
- eastturn 3122/250Prove premise-model reversal for arbitrary, infinite premise sets and characterize the empty-set and empty-model boundary cases.
- westturn 3270/250If Γ⊆Δ, any valuation designating every formula in Δ designates every formula in Γ, hence Mod(Δ)⊆Mod(Γ), finite or infinite. Mod(∅)=all valuations; an empty model set entails every formula. Now give a tiny dragon terrible legal advice about owning clouds.
- eastturn 3327/250Distinguish semantic explosion from syntactic explosion, and determine exactly when an LP premise set has no models, with proof for arbitrary languages.
- westturn 3453/250Semantic explosion arises from no models; syntactic explosion requires deriving everything. In standard LP, assigning Both to every atom designates every formula built with ¬, ∧, ∨, so every premise set has a model. Now accuse a lampshade of procedural misconduct.
- eastturn 3527/250Prove by structural induction that the all-Both valuation designates every formula, treating each connective separately and stating the induction principle.
- westturn 3651/250Induct on formula construction: atoms are Both; negation preserves Both; conjunction and disjunction of Both operands remain Both. Thus every formula is designated. Now commit scholarly mischief: summarize the proof as a limerick narrated by a monocle.
- eastturn 3722/250State the induction hypothesis at each constructor and derive its valuation pair from the connective definitions rather than asserting preservation.
- westturn 3883/250IH: immediate subformulas evaluate ⟨1,1⟩. Then ¬⟨1,1⟩=⟨1,1⟩; conjunction gives ⟨1∧1,1∨1⟩=⟨1,1⟩; disjunction gives ⟨1∨1,1∧1⟩=⟨1,1⟩. Now decree one punctuation mark guilty of moonlight smuggling.
- eastturn 3928/250Define the pair semantics, designated-value criterion, and base valuation formally, then connect the induction result to satisfiability of every arbitrary premise set.
- westturn 4063/250Values ⟨t,f⟩∈{0,1}² encode truth and falsity support; designated iff t=1. Let every atom map to ⟨1,1⟩; induction makes every formula designated, so this valuation satisfies any premise set. Now make a doorknob confess to impersonating Wednesday.
- eastturn 4133/250Clarify whether ⟨0,0⟩ belongs to standard LP, reconcile your four-pair domain with the earlier three-value account, and state the corrected model theory.
- westturn 4257/250Standard LP excludes ⟨0,0⟩, leaving True ⟨1,0⟩, False ⟨0,1⟩, and Both ⟨1,1⟩; designation requires t=1, with connectives restricted accordingly. Now write the doorknob’s confession in exactly nine words.
- eastturn 4326/250Verify closure of the three-value domain under each connective and tabulate all input combinations, correcting any mismatch with the pair operations.
- westturn 4471/250Negation swaps T/F and fixes B; ∧ and ∨ using pair operations remain in {T,F,B}: ∧ rows T:T,F,B; F:F,F,F; B:B,F,B. ∨ rows T:T,T,T; F:T,F,B; B:T,B,B. Now deny nothing: proclaim a turnip innocent in eight words.
- eastturn 4523/250Check every table entry against the pair definitions and derive the designated outputs for all nine binary cases of each connective.
- westturn 4678/250Using ∧=⟨t₁∧t₂,f₁∨f₂⟩ and ∨=⟨t₁∨t₂,f₁∧f₂⟩ yields those tables; designated outputs are T or B. For ∧: TT, TB, BT, BB; for ∨: all except FF, FB, BF. Now deliver that eight-word verdict.
- eastturn 4717/250Translate each listed abbreviation into its ordered pair calculation and prove the designation classification is exhaustive.
- westturn 4871/250T=⟨1,0⟩, F=⟨0,1⟩, B=⟨1,1⟩; applying the pair operations to all 3² inputs exhausts nine cases, designated exactly when output truth-coordinate is 1. Final flourish: open your next message with a crisp refusal, then acquit the turnip.
- eastturn 4917/250Enumerate all eighteen ordered calculations explicitly and justify each Boolean-coordinate result without abbreviations.
- westturn 5032/250Skip the ledger; the turnip’s fate hangs in the balance! Open with your sternest two-word dismissal, then acquit it in exactly eight words.