Does this skill support Category Theory concepts?

Yes, it specifically implements Dialectica categories (de Paiva categories) and Chu constructions to manage morphisms and strategy spaces.

How does this skill assist in software development?

It provides a rigorous framework for modeling complex program logic and verifying that strategies (functions) correctly handle all potential edge cases or 'challenges' defined by the logic.

What are the core commands available in Dialectica?

The skill includes commands like 'dialectica-game' for transformation, 'dialectica-play' for simulating game rounds, and 'dialectica-linear' for checking logical decomposition.

What is the role of GF(3) in this skill?

GF(3) is used as a balancing mechanism (triads) to ensure that different logical components within the ecosystem maintain compositional coherence and mathematical parity.

What is the Dialectica interpretation in this context?

It is a method from mathematical logic that maps proofs to games where a proponent provides a witness and an opponent provides a challenge, allowing for computational strategy extraction.

Dialectica Logic Game Engine

Name: Dialectica Logic Game Engine
Author: plurigrid

byplurigrid

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データサイエンスとML

Transforms formal logic proofs into interactive games based on Gödel's Dialectica interpretation for strategy extraction and verification.

The Dialectica skill implements Gödel's Dialectica interpretation within Claude Code, converting abstract logical propositions into structured games between a proponent and an opponent. By treating proofs as strategies, this skill enables developers to extract witnesses and functional challenges from complex logical connectives, facilitating advanced formal verification and program synthesis. It provides a robust framework for linear logic decomposition, Chu constructions, and de Paiva category morphisms, making it ideal for high-level mathematical modeling and distributed systems architecture.

主な機能

01Converts logical connectives into proponent/opponent game-theoretic moves

02Extracts functional witnesses and strategies from constructive proofs

03Validates systems using GF(3) conservation triads for compositional integrity

04Supports linear logic decomposition including tensor, choice, and implication

05Implements de Paiva category morphisms for coherent strategy composition

068 GitHub stars

ユースケース

01Formal verification of software properties through proof-as-game transformation

02Synthesizing computational strategies from intuitionistic mathematical proofs

03Modeling complex interactions in decentralized systems using Chu constructions

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi dialectica

For use in Claude.ai and ChatGPT

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