Open research questions in Logic, Reasoning, and Knowledge
70 unresolved questions extracted from the limitations and future-work sections of 1,246 Logic, Reasoning, and Knowledge papers in our library. Each links back to the study that raised it.
What the literature leaves open
The paper assumes certain properties of the set A, such as being atomic and cut-closed. The paper does not address the termination property of the rewriting system on proofs. The paper does not provide a direct proof of invertibility results.
The paper suggests future research on the termination property of the rewriting system on proofs. The paper suggests future research on the direct proof of invertibility results. The paper suggests future research on the application of the formalization to various domains.
The lack of modularity in ASP hinders its full potential. The structuring and instantiation of subprograms in ASP is a challenging task. The paper addresses the challenge of providing a declarative approach to modular ASP.
The generalization of locality to non-classical models is challenging. The study faces the challenge of defining appropriate generalizations of classical notions. The paper needs to overcome the limitation of classical first-order logic in terms of locality.
The generalization of locality to non-classical models is not straightforward. There is a lack of understanding of locality in residuated-lattice structures.
The gap in the existing work is the lack of a dynamic logic approach to actual causality.
A Note on Halpern’s Theory of Causality: Structural Equations and Interventions as Dynamic Logic Programs · 2026 · DOIThe need to define a notion of computability for closed derivations. The need to establish confluence of the rewrite relation.
The lack of a commutative monad for imprecise probabilistic programming. The need for a unified compilation scheme for various inference methods.
Imprecise Probabilistic Programming, Precisely: Credal Sets via Graded Monads, BDDs, and Semiring-Parametric Inference (Functional Pearl) · 2026 · DOIFuture research could explore the application of the paper's findings to different domains. It could also investigate the development of more effective methods for identifying turn types.
The paper identifies a gap in the current understanding of how members manage to identify turns as turn-types. There is a lack of a clear distinction between contingent and a priori structures.
The paper identifies a gap in the literature regarding the rigorous definition of condensed detachment. The paper identifies a gap in the literature regarding the connection between condensed detachment and the resolution principle.
The gap is the lack of characterization of structural consequence operators. The paper identifies the need for a more general framework to study sentential logics.
The paper identifies a gap in current research on logics with the relevance principle. The paper claims that current research does not provide a characterization of logics with the relevance principle using simple Cn-matrices and homomorphic images.
The paper identifies a gap in the study of modal logics of arbitrary domains. The description of logics of arbitrary domains is nontrivial.
The need for a characterization of finitely based entailments is identified as a research gap.
Section 6 claims that the copy-cup gate construction can achieve gates at any desired Clifford hierarchy level and provides 'several quantum code families with different asymptotic parameters,' but the paper does not provide explicit asymptotic parameter values (code rate, distance, overhead) for these families or compare their fault-tolerance thresholds against existing code constructions.
The framework for deriving logical gates from cohomology operations Φₗ assumes multilinearity and cohomology operation properties, but the paper does not explore which non-linear cohomological operations or higher-order cohomology structures (beyond cup products) could be leveraged to construct additional gate families or improve gate depth bounds.
The scalability of multi-agent epistemic planning is a major challenge. Existing heuristics are limited by the representation of states as Kripke structures. There is a need for novel approaches to improve the scalability of multi-agent epistemic planning.
While our approach achieves promising experimental results, several limitations remain. First, we acknowledge that our current implementation does not yet achieve competitive runtime performance compared to existing heuristics methods. This limitation is largely due to engineering considerations. A proper integration of CUDA-based computation and batch processing, combined with a search strategy capable of exploiting these features while minimizing memory exchange, would, in fact, significantly improve inference speed as detailed in Appendix H. Although we recognize this shortcoming, we emphasize that this work is foundational. Addressing the engineering challenges required for an optimized implementation would constitute a substantial effort in its own right—worthy of dedicated study—and represents an important avenue for future research. Nonetheless, our primary goal here is to provide a proof of concept highlighting the potential of heuristics learning in MEP. This is also why we focus on the number of expanded nodes as our primary evaluation metric. Certain domains, such as AL and GR, also present unique challenges. In AL, problem instances differ only in the nesting depth of belief formulas, which results in weak learning signals. Results for this domain are therefore not very informative as GNN and BFS perform almost identically. In GR, the sparsity of valid plans limits the effectiveness of data-driven learning, exposing a current limitation of our data generation pipeline as discussed above. As mentioned, our current GNN implementation lacks batch inference during planning, which contributes to slower runtime. While enabling batch computation is primarily an engineering task, it also raises design questions regarding when and how to accumulate batches of states for scoring. For instance, the planner could rely on BFS or alternate with other heuristics until a sufficient number of candidate states are available for batched GNN evaluation. We leave the systematic study of these strategies for future work. Finally, an important next step is to integrate our GNN-based heuristic estimates into more advanced search frameworks, such as Monte Carlo Tree Search. We believe this approach has strong potential to improve the scalability and adaptability of MEP solvers. Solved Inst.
The paper identifies a gap in the development of topological duality theory for non-classical logics. The application of Stone-type and Priestley-type dualities to intuitionistic, modal, and paraconsistent logics is a key area of research. The use of category theory to formalize the dualities is a significant contribution to the field.
Future research can build on the paper's results to develop more comprehensive formal systems for reasoning about modal and conditional statements. The approach can be extended to other areas of logic and artificial intelligence.
But if we want possibility to correspond with acceptance under some revision and avoid (LEM), then the method devised here is insufficient to prove a completeness theorem.
The paper suggests future research on the application of many-logic modal structures to other areas of computer science. The paper suggests future research on the extension of the approach to other types of logics.
The paper identifies the gap in the current research on information-based logics. The paper identifies the need for a new approach to information-based logics.
The lack of a G3-style sequent calculus for logics with Russellian definite descriptions. The need for a proof of Craig Interpolation Property using the calculus.
G3-Style Sequent Calculi and Craig Interpolation Property for Logics with Russellian Definite Descriptions · 2026 · DOI
Most-cited papers in Logic, Reasoning, and Knowledge
- Better Zero-Shot Reasoning with Role-Play Prompting · 2024 · 133 citations
- Reasoning by model: The case of multiple quantification. · Psychological Review · 1989 · 116 citations
- Weighted Rules under the Stable Model Semantics · ArXiv.org · 2026 · 43 citations
- Functional Stable Model Semantics and Answer Set Programming Modulo Theories · ArXiv.org · 2026 · 23 citations
- Connexive Logic, Connexivity, and Connexivism: Remarks on Terminology · Studia Logica · 2023 · 19 citations
- Indicative conditionals: probabilities and relevance · Philosophical Studies · 2021 · 16 citations
- Two Decision Procedures for da Costa’s $$C_n$$ Logics Based on Restricted Nmatrix Semantics · Studia Logica · 2021 · 14 citations
- Identifying mental actions for abstracting the logic of conditional statements · The Journal of Mathematical Behavior · 2022 · 14 citations
- On the philosophical foundations of free logic∗ · Inquiry · 1981 · 13 citations
- Theo’s reinvention of the logic of conditional statements’ proofs rooted in set-based reasoning · The Journal of Mathematical Behavior · 2023 · 11 citations
Most recent work
- Weighted Rules under the Stable Model Semantics · ArXiv.org · 2026
- Functional Stable Model Semantics and Answer Set Programming Modulo Theories · ArXiv.org · 2026
- Cups and Gates I: Cohomology Invariants and Logical Quantum Operations · Communications in Mathematical Physics · 2026
- G3-Style Sequent Calculi and Craig Interpolation Property for Logics with Russellian Definite Descriptions · Studia Logica · 2026
- Exact Structural Abstraction and Tractability Limits · Zenodo (CERN European Organization for Nuclear Research) · 2026
- Harnessing Vagueness with Productivity · Zenodo (CERN European Organization for Nuclear Research) · 2026
- YALLA: Yet Another Deep Embedding of Linear Logic in Rocq · Journal of Automated Reasoning · 2026
- A Note on Halpern’s Theory of Causality: Structural Equations and Interventions as Dynamic Logic Programs · Journal of Logic, Language and Information · 2026
- The Logical Architecture of Persistence - Minimal Assumptions, Derived Necessities, Formal Proofs, and the Regime Structure of Persistent Identity · Zenodo (CERN European Organization for Nuclear Research) · 2026
- Classical Logical Coherentism · Journal of Philosophical Logic · 2026
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