A Natural-style Prover in Theorema Using Sequent Calculus with Unit Propagation

10 pages•Published: May 26, 2024

Abstract

For tutorial purposes we realized a propositional prover in the Theorema system that works in natural style and is based on sequent calculus with unit propagation.
The version of the sequent calculus that we use is a reductionist one: at each step a formula is decomposed according to a fixed rule attached to its main logical connective. Optionally the prover may use unit propagation. Unit propagation in sequent calculus is a novel inference method introduced by the author that consists in propagating literals that occur either as antecedents or postcedents in the sequent: all occurrences of the corresponding variable in any of the other formulae are replaced by the appropriate truth value and the respective formula is simplified by rewriting.
By natural style we understand a style similar to human activity. This applies to syntax of formulae, to inference steps, and to proof presentation. Although based on sequent calculus, the prover does not produce proofs as sequent proof trees, but as natural–style narratives.
The purpose of the tool is tutorial for the understanding of natural–style proving, of sequent calculus, and of the implementation in the Theorema system as a set of rewrite rules for the inferences and a set of accompanying patterns for the explanatory text produced by the prover.

Keyphrases: Natural-style Proving, propositional logic, sequent calculus, Theorema, Unit Propagation

In: Nikolaj Bjorner, Marijn Heule and Andrei Voronkov (editors). LPAR 2024 Complementary Volume, vol 18, pages 107--116

Links:	https://easychair.org/publications/paper/n11t
	https://doi.org/10.29007/q2vx