Work

Between Proof Construction and Sat-solving

Year: 2025

Type: article

Abstract: The classical satisfiability problem (SAT) is used as a natural and general tool to express and solve combinatorial problems that are in NP . We postulate that provability for implicational intuitionistic propositional logic (IIPC) can serve as a similar natural tool to express problems in Pspace . We demonstrate it by proving two essential results concerning the system. One is a natural reduction from full IPC (with all connectives) to implicational formulas of order three. Another result is a convenient interpretation in terms of simple alternating automata. Additionally, we distinguish some natural subclasses of IIPC corresponding to the complexity classes NP and co - NP .

Source: Journal of Symbolic Logic

DOI: 10.1017/jsl.2025.10090

Authors: ALEKSY SCHUBERT, PAWEŁ URZYCZYN, KONRAD ZDANOWSKI

Institution: University of Warsaw

Language: English

Topic: Logic, Reasoning, and Knowledge

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funder: Uniwersytet Warszawski