Related papers: Multimodality in the Hypergraph Lambek Calculus
Recent research has shown growing interest in modeling hypergraphs, which capture polyadic interactions among entities beyond traditional dyadic relations. However, most existing methodologies for hypergraphs face significant limitations,…
In this paper, we investigate the many-valued version of coalgebraic modal logic through predicate lifting approach. Coalgebras, understood as generic transition systems, can serve as semantic structures for various kinds of modal logics. A…
We introduce the cylindrical module $A \natural \mathcal{H}$, where $\mathcal{H}$ is a Hopf algebra and $A$ is a Hopf module algebra over $\mathcal{H}$. We show that there exists an isomorphism between $\mathsf{C}_{\bullet}(A^{op} \rtimes…
Algebraic effects & handlers have become a standard approach for side-effects in functional programming. Their modular composition with other effects and clean separation of syntax and semantics make them attractive to a wide audience.…
In probabilistic reasoning, the traditionally discrete domain has been elevated to the hybrid domain encompassing additionally continuous random variables. Inference in the hybrid domain, however, usually necessitates to condone trade-offs…
Lambek's non-associative syntactic calculus (NL) excels in its resource consciousness: the usual structural rules for weakening, contraction, exchange and even associativity are all dropped. Recently, there have been proposals for…
We study various representations for cyclic lambda-terms as higher-order or as first-order term graphs. We focus on the relation between 'lambda-higher-order term graphs' (lambda-ho-term-graphs), which are first-order term graphs endowed…
It is well-known that the category of presheaf functors is complete and cocomplete, and that the Yoneda embedding into the presheaf category preserves products. However, the Yoneda embedding does not preserve coproducts. It is perhaps less…
Morrill and Valentin in the paper "Computational coverage of TLG: Nonlinearity" considered an extension of the Lambek calculus enriched by a so-called "exponential" modality. This modality behaves in the "relevant" style, that is, it allows…
Embedding-based methods for reasoning in knowledge hypergraphs learn a representation for each entity and relation. Current methods do not capture the procedural rules underlying the relations in the graph. We propose a simple…
Classical finite association schemes lead to a finite-dimensional algebras which are generated by finitely many stochastic matrices. Moreover, there exist associated finite hypergroups. The notion of classical discrete association schemes…
The burgeoning presence of Large Language Models (LLM) is propelling the development of personalized recommender systems. Most existing LLM-based methods fail to sufficiently explore the multi-view graph structure correlations inherent in…
We study various representations for cyclic lambda-terms as higher-order or as first-order term graphs. We focus on the relation between `lambda-higher-order term graphs' (lambda-ho-term-graphs), which are first-order term graphs endowed…
In a nutshell, submodular functions encode an intuitive notion of diminishing returns. As a result, submodularity appears in many important machine learning tasks such as feature selection and data summarization. Although there has been a…
A novel parallel algorithm for matrix multiplication is presented. The hyper-systolic algorithm makes use of a one-dimensional processor abstraction. The procedure can be implemented on all types of parallel systems. It can handle…
We propose several constructions of commutative or cocommutative Hopf algebras based on various combinatorial structures, and investigate the relations between them. A commutative Hopf algebra of permutations is obtained by a general…
The Lambek calculus is a well-known logical formalism for modelling natural language syntax. The original calculus covered a substantial number of intricate natural language phenomena, but only those restricted to the context-free setting.…
This paper contributes to the general understanding of the geometrical model of concurrency that was named higher dimensional automata (HDAs) by Pratt. In particular we investigate modal logics for such models and their expressive power in…
This paper concerns the explicit treatment of substitutions in the lambda calculus. One of its contributions is the simplification and rationalization of the suspension calculus that embodies such a treatment. The earlier version of this…
The Hermite interpolation formulas are based on the interpretation of interpolation nodes as roots of suitable polynomials. Therefore, such formulas belong to the class of algebraic interpolations. The article considers a multidimensional…