Open research questions in Logic, Reasoning, and Knowledge
214 gap statements mined from Logic, Reasoning, and Knowledge papers in our 4.5M-paper local library, which holds 1,472 papers on the topic — drawn mostly from each paper's own stated research gap, future-work, challenge and limitation notes, and its abstract. The ones listed below are a selection still marked open; each names the study that raised it, with a DOI link where the paper has one.
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What the literature leaves open
The paper does not provide a comprehensive analysis of the limitations of the approach. The method may be limited to specific types of quantum CSS codes.
Future research can focus on applying the approach to various quantum CSS codes. Future research can focus on improving the fault-tolerance of quantum computation using the approach.
The exact inference in LP MLN is at least as hard as the one in MLNs, which is #P-hard. More work needs to be done to find how the methods studied in machine learning will help to compute weighted stable models.
The standard answer set programming limits answer sets to Herbrand models, where interpretations of functions are pre-defined. There is a need to extend the stable model semantics to incorporate intensional functions.
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 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.
A Proof-Theoretic Study of Modal Logic · 2026The lack of support for probabilistic processes in ACP τ ϵ -I. The need for a sound axiom system for probabilistic process algebra.
Probabilistic imperative process algebra · 2026But 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 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 · DOIThe natural candidate is K4 extended by the seriality axiom ♦ns⊤, since R is dense and every point is an ω-accumulation point of any infinite set, but a precise axiomatisation and proof remain to be established.
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.
Future research can build upon the paper's contributions, exploring the applications of the new formalism. The approach can be extended to other areas of ASP, such as optimization and constraint programming. Further research is needed to fully realize the potential of the new formalism.
Future research can explore the applications of the proposed SCP system in various fields. Future research can investigate the extensions and modifications of the SCP system. Future research can examine the implications of the SCP system for other areas of philosophy and artificial intelligence.
The paper aims to address this gap with the proposed SCP system.
Future research directions include the application of the semantic framework to other areas of justification logic. The development of more efficient algorithms for reasoning about intuitionistic justification logic.
The paper identifies a gap in prior work on justification logic, specifically the lack of a semantic framework for intuitionistic justification logic.
We conclude with some open problems about constructive quantum logics motivated by the results presented here: Question 1 What is the complexity of iEx-logic? Question 2 Are all the axioms listed in Theorem 4.
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.
There is a need for a better understanding of the hierarchy of locally tabular logics.
To find how the methods studied in machine learning will help to compute weighted stable models. To design a native computation method for the general case of LP MLN. To extend LP MLN to allow other advanced features, such as aggregates, intensional functions, and generalized quantifiers.
To explore the application of the results to other domains. To improve the efficiency of the translation of tight ASPMT programs into SMT instances. To extend the expressiveness of the KR formalism.
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 barely scratches the surface, leaving many interesting problems to be investigated in the future. The decidability result is planned to be extended to iS4 A and BS4 A,c.
To extend the decidability result to iS4 A and BS4 A,c. To investigate other interesting problems in the field of Topological Evidence Logic.
The recent literature on bilateral proof-theoretic semantics has only dealt with the semantics of proofs and refutations. The traditional Fregean account of negation depicts denial of a proposition as the mere assertion of its opposite.
Most-cited papers in Logic, Reasoning, and Knowledge
- An axiomatic basis for computer programming · Communications of the ACM · 1969 · 3,723 citations
- Institutions and axioms: an extension and update of service-dominant logic · Journal of the Academy of Marketing Science · 2015 · 2,997 citations
- On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games · Artificial Intelligence · 1995 · 2,512 citations
- A logic for default reasoning · Artificial Intelligence · 1980 · 2,456 citations
- The empirical case for two systems of reasoning. · Psychological Bulletin · 1996 · 2,410 citations
- Axiomatic Foundation of the Analytic Hierarchy Process · Management Science · 1986 · 1,346 citations
- Circumscription—A form of non-monotonic reasoning · Artificial Intelligence · 1980 · 1,228 citations
- A truth maintenance system · Artificial Intelligence · 1979 · 1,121 citations
- Nonmonotonic reasoning, preferential models and cumulative logics · Artificial Intelligence · 1990 · 1,042 citations
- A Way to Simplify Truth Functions · American Mathematical Monthly · 1955 · 967 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
- Intuitionistic Modal Logics: A Minimal Setting · Studia Logica · 2026
- Operational semantics on arbitrary first-order fuzzy logic programming · Fuzzy Sets and Systems · 2026
- Characterizing Sets of Theories That Can Be Disjointly Combined · Proceedings of the ACM on Programming Languages · 2026
- G3-Style Sequent Calculi and Craig Interpolation Property for Logics with Russellian Definite Descriptions · Studia Logica · 2026
- Universal proof theory: Semi-analytic rules and uniform interpolation · Annals of Pure and Applied Logic · 2026
- Simply-typed constant-domain modal lambda calculus I: distanced beta reduction and combinatory logic · Logical Methods in Computer Science · 2026
- A causal theory of suppositional reasoning · Philosophical Studies · 2026
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