LF: a Foundational Higher-Order Logic

Abstract

This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the verdicts, hypotheses, or conjectures of any science. In work currently in progress, we argue for the unique suitability of LF for the formalization of logic, mathematics, syntax, and semantics. The present document specifies the language and rules of LF, lays out some notational conventions, and states some basic technical facts about the system.

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Author Profiles

Juhani Yli-Vakkuri
Australian Catholic University
Zachary Goodsell
National University of Singapore

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References found in this work

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Universal grammar.Richard Montague - 1970 - Theoria 36 (3):373--398.
The Broadest Necessity.Andrew Bacon - 2018 - Journal of Philosophical Logic 47 (5):733-783.
A formulation of the simple theory of types.Alonzo Church - 1940 - Journal of Symbolic Logic 5 (2):56-68.
Principia Mathematica.Alfred North Whitehead & Bertrand Russell - 1950 - Cambridge,: Franklin Classics. Edited by Bertrand Russell.

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