Work

Exact Complexity of the Satisfiability Problem for Strategy Logic

Year: 2026

Type: preprint

Abstract: We show that the satisfiability problem for Strategy Logic introduced by Mogavero, Murano, and Vardi is $Π^1_\infty$-complete, and, more strongly, computably isomorphic to true second-order arithmetic. The lower bound is established for the next-time Boolean-goal fragment of Strategy Logic. Consequently, Strategy Logic is not recursively axiomatizable, even with effectively defined $ω$-rules.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.16173

Author: Pshenitsyn, Tikhon

Language: English

Topic: Logic, Reasoning, and Knowledge

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7213407443

Cites:

Cited by:

Related to: 10