What are the primary commands for this skill?

Key commands include 'dialectica-game' for proof transformation, 'dialectica-play' for executing game rounds, and 'dialectica-linear' for property decomposition.

How does the Dialectica Skill assist in programming?

It provides a framework for formal verification and witness extraction, allowing developers to derive valid computational strategies from mathematical proofs to ensure code correctness.

What is the Dialectica interpretation?

The Dialectica interpretation is a method in formal logic that translates logical formulas into games where a proponent attempts to provide a 'witness' and an opponent provides a 'challenge'.

Does this skill support category theory?

Yes, it specifically supports de Paiva categories and the Chu construction, enabling reasoning within *-autonomous categories and linear logic.

Dialectica Logic Engine

Name: Dialectica Logic Engine
Author: plurigrid

byplurigrid

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Developer Tools

Transforms logical proofs into interactive game-theoretic strategies for witness extraction and formal verification.

The Dialectica Skill implements Gödel's Dialectica interpretation, a foundational method in proof theory that converts abstract logical propositions into proponent-opponent games. By treating proofs as games, it allows developers and researchers to extract computational witnesses (strategies) from constructive logic, perform linear logic decomposition, and navigate de Paiva categories. This skill is essential for users working with formal methods, category theory, and high-assurance systems where state transitions must be mathematically verified against winning conditions.

Key Features

017 GitHub stars

02Witness extraction and strategy back-propagation

03GF(3) triad conservation checks for topological world-states

04Gödel's Dialectica proof-to-game transformation

05Linear logic decomposition (Multiplicative/Additive/Chu construction)

06Categorical logic support for de Paiva and *-autonomous categories

Use Cases

01Modeling multi-agent coordination using game-theoretic logic

02Extracting executable strategies from constructive mathematical proofs

03Formal verification of complex state transitions in distributed systems

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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