ABI Layer 2: prove Kleene ternary-logic soundness — flagship Idris2 proof#39
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Flagship semantic proof: negation involution + De Morgan laws, plus a decidable `Designated` (classical-truth) proposition with sound+complete Dec, certifier soundness, conjunction preservation, and positive + negative controls (negation is provably not the identity; U/F are provably not designated). Verified with idris2 0.7.0 (build clean, zero warnings) + adversarial false-proof rejection. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01A6PSzJWpRxtzGDjUCEh7Mx
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Summary
Raises betlangiser's Idris2 ABI to Layer 2 with its first flagship semantic proof. betlangiser's headline is ternary probabilistic modelling; the logical substrate is three-valued (Kleene) logic over
Trit = T | U | F. This proves that substrate is algebraically sound: negation is an involution, De Morgan holds, andDesignated(classical truth) is a decidable proposition withand3preservation.Mirrors the estate flagship-proof pattern: faithful model, universal laws proven by total case analysis, sound+complete
Dec, certifier proven sound, positive + non-vacuous negative controls.Changes
src/interface/abi/Betlangiser/ABI/Semantics.idr—not3/and3/or3,doubleNeg,deMorgan,Designated/decDesignated,andDesignated,certifyDesignatedSound, and negative controls (negationNotIdentity,uNotDesignated,fNotDesignated).betlangiser-abi.ipkg.RSR Quality Checklist
Required
As Applicable
Testing
Verified with Idris2 0.7.0:
idris2 --build betlangiser-abi.ipkg→ exit 0, 5/5 modules, zero warnings. Adversarial check: a deliberately-false proof (Designated F = DesT) was rejected by the type checker.build/removed.🤖 Generated with Claude Code
https://claude.ai/code/session_01A6PSzJWpRxtzGDjUCEh7Mx
Generated by Claude Code