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Research Paper#Computational Logic, Complexity Theory🔬 ResearchAnalyzed: Jan 3, 2026 18:43

Complexity of Non-Classical Logics via Fragments

Published:Dec 29, 2025 14:47
1 min read
ArXiv

Analysis

This paper explores the computational complexity of non-classical logics (superintuitionistic and modal) by demonstrating polynomial-time reductions to simpler fragments. This is significant because it allows for the analysis of complex logical systems by studying their more manageable subsets. The findings provide new complexity bounds and insights into the limitations of these reductions, contributing to a deeper understanding of these logics.
Reference

“Propositional logics are usually polynomial-time reducible to their fragments with at most two variables (often to the one-variable or even variable-free fragments).”

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Research Paper#Artificial Intelligence, Logic, Belief Representation🔬 ResearchAnalyzed: Jan 3, 2026 19:14

Hypergraph Semantics for Belief Logics

Published:Dec 28, 2025 21:49
1 min read
ArXiv

Analysis

This paper introduces a novel semantics for doxastic logics (logics of belief) using directed hypergraphs. It addresses a limitation of existing simplicial models, which primarily focus on knowledge. The use of hypergraphs allows for modeling belief, including consistent and introspective belief, and provides a bridge between Kripke models and the new hypergraph models. This is significant because it offers a new mathematical framework for representing and reasoning about belief in distributed systems, potentially improving the modeling of agent behavior.
Reference

“Directed hypergraph models preserve the characteristic features of simplicial models for epistemic logic, while also being able to account for the beliefs of agents.”

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