Does this skill support Linear Logic?

Yes, it handles Linear Logic decompositions including multiplicative and additive connectives like Tensor (⊗), Choice (&), and the Chu construction.

What is the Dialectica interpretation in this context?

It is a mathematical method that interprets formal proofs as games between a Proponent (offering a witness) and an Opponent (offering a challenge), formalized as ∃x. ∀y. R(x, y).

What are GF(3) Triads?

GF(3) triads are a system used within this skill's ecosystem to ensure balance and consistency (mod 3) across different functional modules, ensuring compositional coherence.

How does Dialectica assist in AI coding tasks?

It provides a rigorous framework for Claude to model complex dependencies and strategies, which is essential for high-stakes formal verification and protocol design.

Dialectica Game Logic

Name: Dialectica Game Logic
Author: plurigrid

byplurigrid

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データサイエンスとML

Transforms formal proofs into interactive game-theoretic strategies using Gödel’s Dialectica interpretation.

概要

The Dialectica skill implements Gödel’s Dialectica interpretation for Claude, enabling a 'proof-as-game' approach to logical reasoning. It converts complex propositions into strategies where proponents provide witnesses and opponents provide challenges, allowing for deep exploration of linear logic, Chu constructions, and categorical structures. This skill is ideal for developers working on formal verification, multi-agent game theory, or topological computing who need to verify logical coherence through GF(3) triads and strategy composition.

主な機能

Integrates GF(3) triad conservation for ensuring compositional coherence
Implements Linear Logic decomposition (Tensor, Choice, and Chu construction)
Provides categorical modeling via de Paiva categories and morphisms
Includes CLI commands for generating games and playing strategy rounds
Converts logical proofs into proponent-opponent game strategies
2 GitHub stars

ユースケース

Formal verification of software protocols and logical propositions
Designing strategy-based multi-agent systems and game-theoretic models
Analyzing the categorical structure of programs using linear logic

概要

主な機能

Integrates GF(3) triad conservation for ensuring compositional coherence
Implements Linear Logic decomposition (Tensor, Choice, and Chu construction)
Provides categorical modeling via de Paiva categories and morphisms
Includes CLI commands for generating games and playing strategy rounds
Converts logical proofs into proponent-opponent game strategies
2 GitHub stars

ユースケース

Formal verification of software protocols and logical propositions
Designing strategy-based multi-agent systems and game-theoretic models
Analyzing the categorical structure of programs using linear logic