Search Results for "reasoning"

...The dataset enables models to learn mathematical problem-solving through examples that involve both numeric and symbolic reasoning. Version 1.0 includes over 2 million examples per category, with training splits labeled as “easy,” “medium,” and “hard,” supporting curriculum-based learning strategies. The data can be accessed via PyPI or generated locally using provided Python scripts, with outputs formatted for direct use in training or evaluation pipelines.

MathCode is a terminal-based AI coding assistant focused on mathematical formalization and theorem proving. It is designed to transform plain-language mathematical reasoning into verified Lean 4 code and formal proofs. The project combines AI agents with Lean Language Server Protocol integration, allowing it to inspect compiler feedback, search for lemmas, and iteratively repair failed proof attempts. It supports an agentic proving workflow where the system behaves more like an interactive mathematical engineer than a one-shot text generator. ...

The canonical Homotopy Type Theory informal textbook, initiated at the Institute for Advanced Study (2012–13) under the Univalent Foundations project. It presents the theory pedagogically without requiring technical proof assistant use.

...Because the implementation leans on Elixir protocols, you can extend Witchcraft’s abstractions to your own structs without invasive inheritance hierarchies. It promotes predictable, law-abiding behavior through property-based testing helpers and a focus on algebraic reasoning. Teams reach for Witchcraft when they want to structure business logic with reusable, mathematically grounded patterns that remain idiomatic to the BEAM.

Belief revision is a central topic in knowledge representation and reasoning. It consists in incorporating a new belief, changing as few as possible of the original beliefs while preserving consistency. Revision always considers new evidence as a better belief. Such new evidence is usually represented in the form of a propositional formula which must be preserved after the revision. Here, the Δps (PS-Merge) belief merging operator is extended in order to consider constraints, and this extension is used as a strategy for belief revision. ...

SEPIA provides implementations for various types of Petri nets. Along Place/Transition-nets, it supports Petri nets with distinguishable token colors and defines coloured workflow nets, where coloured tokens are interpreted as data elements used during process execution. To support information flow analysis of processes, SEPIA defines so-called IF-Nets, tailored for security-oriented workflow modeling which enable users to assign security-levels (HIGH, LOW) to transitions, data elements and...