What are the core commands available?

The skill provides commands to transform proofs into games (dialectica-game), play game rounds (dialectica-play), and check linear logic decompositions (dialectica-linear).

What are GF(3) Triads in the context of Dialectica?

GF(3) triads are used for conservation checks during world-state transitions, ensuring that the composition of different logical modules remains balanced and consistent.

Can I use this for linear logic analysis?

Yes, the skill includes specific commands to decompose propositions into linear logic elements like Tensor, Choice, and Chu constructions.

What is the Dialectica interpretation in this skill?

It is a method of interpreting constructive logic where proofs are viewed as winning strategies in a specific type of game between a proponent (providing witnesses) and an opponent (providing challenges).

How does this skill assist in software development?

It facilitates formal methods and the extraction of 'correct-by-construction' algorithms from logical specifications, making it easier to verify complex system behaviors.

Dialectica Logic Engine

Name: Dialectica Logic Engine
Author: plurigrid

byplurigrid

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Security & Testing

Transforms mathematical proofs into interactive games using Gödel's Dialectica interpretation for formal verification and strategy extraction.

The Dialectica Skill (ERGODIC 0) provides a specialized framework for Claude to interpret logical propositions as game-theoretic structures. Based on Gödel's Dialectica and Valeria de Paiva's category theory research, it allows developers and logicians to extract witnesses from proofs, back-propagate challenges, and decompose linear logic into multiplicative and additive components. This skill is particularly useful for formal methods, proof-carrying code, and complex state modeling where logical consistency is maintained through GF(3) conservation checks and strategy composition.

Key Features

01Linear logic decomposition including tensor, choice, and internal hom mappings

02Integration with GF(3) triad conservation for consistent world-state transitions

03Support for de Paiva categories and *-autonomous category constructions

04Witness extraction and functional strategy derivation from constructive proofs

057 GitHub stars

06Automated transformation of logical proofs into proponent/opponent game structures

Use Cases

01Modeling complex state transitions in decentralized topological systems

02Formal verification of software properties through game-theoretic interpretations

03Extracting computational strategies and algorithms from constructive mathematical proofs

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi dialectica

For use in Claude.ai and ChatGPT

Download Skill