Practal — Practical Logic

A Bicycle for Your Mathematical Mind

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July 13, 2022 https://arxiv.org/abs/2207.05610 Abstraction Logic: A New Foundation for (Computer) Mathematics
This was a submission to the CICM 2022 conference.
April 10, 2022 https://doi.org/10.47757/al.crete.1 Video: Abstraction Logic (UNILOG 2022)
This is a rerecording of a talk about Abstraction Logic at the UNILOG 2022 conference in Crete.
March 24, 2022 https://doi.org/10.47757/pwp.1 Indentation-Sensitive Parsing with Pyramids
This is a short note about combining indentation-sensitivity and pyramid grammars. We describe the syntax of indentation-sensitive pyramid grammars by one such grammar.
March 23, 2022 https://doi.org/10.47757/aal.1 Automating Abstraction Logic
We describe how to automate Abstraction Logic by translating it to the TPTP THF format.
December 21, 2021 (last revised December 23, 2021) https://doi.org/10.47757/pal.2 Philosophy of Abstraction Logic
Abstraction Logic has been introduced in a previous, rather technical article. In this article we take a step back and look at Abstraction Logic from a conceptual point of view. This will make it easier to appreciate the simplicity, elegance, and pragmatism of Abstraction Logic. We will argue that Abstraction Logic is the best logic for serving as a foundation of mathematics.
October 22, 2021 (last revised November 14, 2021) https://doi.org/10.47757/abstraction.logic.2 Abstraction Logic
Abstraction Logic is introduced as a foundation for Practical Types and Practal. It combines the simplicity of first-order logic with direct support for variable binding constants called abstractions. It also allows free variables to depend on parameters, which means that first-order axiom schemata can be encoded as simple axioms. Conceptually abstraction logic is situated between first-order logic and second-order logic. It is sound with respect to an intuitive and simple algebraic semantics. Completeness holds for both intuitionistic and classical abstraction logic, and all abstraction logics in between and beyond.
July 29, 2021 https://doi.org/10.47757/practical.types.1 Practical Types
These are preliminary notes about Practal’s logic and its system of practical types. Practal Light is a research prototype implementing (part of) what is presented in this document.
July 17, 2021 https://doi.org/10.47757/practal.1 Practal — Practical Logic
This is a first sketch of the design of Practal, an interactive theorem proving system for practical logic.