Intuitionistic Logic and Muchnik Degrees
Andrea Sorbi, Sebastiaan A. Terwijn
TL;DR
This paper demonstrates that a specific factor of the Muchnik lattice accurately models intuitionistic propositional logic, extending known results from the Medvedev lattice to the Muchnik setting.
Contribution
It establishes a new connection between the Muchnik lattice and intuitionistic logic, complementing previous work on the Medvedev lattice.
Findings
A factor of the Muchnik lattice captures intuitionistic propositional logic
Extends Skvortsova's results from the Medvedev to the Muchnik lattice
Provides a new algebraic framework for intuitionistic logic
Abstract
We prove that there is a factor of the Muchnik lattice that captures intuitionistic propositional logic. This complements a now classic result of Skvortsova for the Medvedev lattice.
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Taxonomy
TopicsAdvanced Algebra and Logic · Computability, Logic, AI Algorithms · Rough Sets and Fuzzy Logic