The recent developments in the field of modal logic research demonstrate a significant focus on the exploration and refinement of sequent calculi and semantic frameworks for various modal logics. A notable trend is the introduction of novel calculi that aim to simplify proofs and enhance the understanding of modal logic properties, such as cut-elimination and subformula properties. Additionally, there is a growing interest in the integration of modal logics with other logical systems, such as quantum logic and many-valued logics, to address complex theoretical and practical challenges. This includes the development of new logical systems that extend traditional modal logics with additional modal symbols and the investigation of semantic incompleteness in existing systems. The field is also witnessing advancements in the semantic approaches to modal logics, with a particular emphasis on non-deterministic and restricted non-deterministic semantics, which offer new insights into the interpretation of truth-values and the construction of modal logic extensions.

Noteworthy Papers

• Twist Sequent Calculi for S4 and its Neighbors: Introduces innovative twist sequent calculi for S4 and other modal logics, enabling shorter proofs for complex negated modal formulas and proving cut-elimination theorems.
• Nested-sequent Calculus for Modal Logic MB: Addresses critical gaps in the understanding of quantum logic MB by constructing a nested-sequent calculus, solving completeness and decidability issues, and proposing an extended logic MB+.
• Semantic Incompleteness of Liberman et al. (2020)'s Hilbert-style System: Reveals semantic incompleteness in a proposed Hilbert-style system for term-modal logic, introducing a non-standard Kripke semantics to illustrate the findings.
• Many-Valued Modal Logic: Combines modal and many-valued logics in a comprehensive framework, proving soundness, completeness, and the finite model property, while exploring extensions and the unique definition of negation.
• Modal Logics -- RNmatrices vs. Nmatrices: Compares non-deterministic and restricted non-deterministic semantics for modal logics, highlighting their differences and similarities in constructing extensions of the minimal modal logic M.