Neurosymbolic Integration and Modal Logic Advances

The field of neurosymbolic integration is rapidly advancing, with a focus on combining neural-network learning with symbolic reasoning. Recent developments have introduced novel languages and frameworks that enable the flexible integration of data-driven rule learning with symbolic priors and expert knowledge. Additionally, there have been significant advancements in modal logic, including the development of new sequent calculi and the investigation of lattice properties within modal extensions. These advances have the potential to improve the interpretation of logical theories learnt by neural networks and enable more effective reasoning about semi-structured queries in languages such as DataGL, XPath, and GQL. Noteworthy papers include: Logic of Hypotheses, which introduces a novel language that unifies data-driven rule learning with symbolic priors and expert knowledge. From Neural Networks to Logical Theories, which formalizes the idea of fibred models compatible with fibred neural networks and derives non-uniform logical expressiveness results for Graph Neural Networks and Transformer encoders. Sequent Calculi for Data-Aware Modal Logics, which presents a sound and complete Gentzen-style sequent calculus for HXpathD, a hybrid modal logic that captures not only the navigational core of XPath but also data comparisons, node labels, and key-based navigation operators.

Sources

Logic of Hypotheses: from Zero to Full Knowledge in Neurosymbolic Integration

A Hierarchy for Constant Communication Complexity

Permutation closure for multiple context-free languages

ASSESS: A Semantic and Structural Evaluation Framework for Statement Similarity

Proceedings Twentieth International Symposium on Logical and Semantic Frameworks with Applications

From Neural Networks to Logical Theories: The Correspondence between Fibring Modal Logics and Fibring Neural Networks

The Complexity of Defining and Separating Fixpoint Formulae in Modal Logic

One-sided Hom shifts

Generalization of Variadic Structures with Binders: A Tool for Structural Code Comparison

Monoid Structures on Indexed Containers

A Function-Set Framework: General Properties and Applications to Modal Logic

Characterization of Lattice Properties Within Modal Extensions

Nominal Sets in Rocq

Demystifying Codensity Monads via Duality

Semantic Bridges Between First Order c-Representations and Cost-Based Semantics: An Initial Perspective

Sequent Calculi for Data-Aware Modal Logics

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