The lack of a many-valued counterpart of the minimal
Research gap analysis derived from 3 mathematics papers in our local library.
The gap
The lack of a many-valued counterpart of the minimal normal modal logic K. The need for a proof system and semantic characterization of mv-K and its extensions.
Evidence profile
Sourced from the future work and stated research gap of the source papers, classified as general, drawn from work published between 2024 and 2026, spanning 2 journals.
Research trend
Established — well-defined area with open sub-problems.
Supporting evidence — 3 representative gaps
- Proceedings Sixteenth International Conference on Advances in Modal Logic (2026) · Electronic Proceedings in Theoretical Computer Science · doi
In this paper we axiomatize a decidable but richly expressive logic, that deals with a large class of data- exchange events, while capturing group knowledge of both propositional and non-propositional data, as well as a group’s ability to narrow down the values of a variable to finitely many possibilities. There are a number of things still left to do. As already mentioned, one can add common knowledge operators CAϕ, but pre-encoding their dynamics requires a generalization to polyadic conditionals Ce Aϕ as in [11]. We leave this for a journal version, where we also plan to explore the relationships of our formalism with the Logic of Functional Dependence [13] and Graded (Multi)Modal Logic. Our axioms are somewhat complicated due to the fact that we did not succeed to prove FMP (Finite A by plain A (over all A-possible x-values given ϕ), which would greatly simplify our axioms. Model Property) for our logics. This would have allowed us to replace cutoff-minimization µNxϕ minimization min xϕ On the other hand, we don’t have a counterexample to FMP, so this issue is still an open question.
generalfuture workevidence 5/5Keywords: logic group knowledge propositional values still axioms minimization axiomatize decidable richly expressive deals large class - Many-Valued Modal Logic (2024) · Electronic Proceedings in Theoretical Computer Science · doi
The lack of a many-valued counterpart of the minimal normal modal logic K. The need for a proof system and semantic characterization of mv-K and its extensions.
generalstated research gapevidence 5/5Keywords: lack many-valued counterpart minimal normal modal logic need - A Proof-Theoretic Study of Modal Logic (2026) · arXiv
The paper identifies a gap in the study of modal logics, specifically the lack of a basic proof-theoretic framework. The paper identifies a gap in the study of nested sequent calculus for modal logic.
generalstated research gapevidence 5/5Keywords: paper identifies gap study modal logics specifically lack
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