Related papers: Grafting Hypersequents onto Nested Sequents

A cut-free G3-style sequent calculus GWFN2 for the subintuitionistic logic WFN2, along with its single-succedent variant GWFsN2, is introduced. The calculus GWFN2 is shown to extend naturally to a G3-style of the sequent calculus GF for…

The syntax of modal graphs is defined in terms of the continuous cut and broken cut following Charles Peirce's notation in the gamma part of his graphical logic of existential graphs. Graphical calculi for normal modal logics are developed…

We introduce a new family of hyperplane arrangements inspired by the homogenized Linial arrangement (which was recently introduced by Hetyei), and show that the intersection lattices of these arrangements are isomorphic to the bond lattices…

We introduce labelled sequent calculi for quantified modal logics with definite descriptions. We prove that these calculi have the good structural properties of G3-style calculi. In particular, all rules are height-preserving invertible,…

This paper employs the linear nested sequent framework to design a new cut-free calculus LNIF for intuitionistic fuzzy logic--the first-order G\"odel logic characterized by linear relational frames with constant domains. Linear nested…

We present an extension of our Molecular Transformer architecture combined with a hyper-graph exploration strategy for automatic retrosynthesis route planning without human intervention. The single-step retrosynthetic model sets a new state…

G3-style sequent calculi for the logics in the cube of non-normal modal logics and for their deontic extensions are studied. For each calculus we prove that weakening and contraction are height-preserving admissible, and we give a syntactic…

A large-scale knowledge graph enhances reproducibility in biomedical data discovery by providing a standardized, integrated framework that ensures consistent interpretation across diverse datasets. It improves generalizability by connecting…

A many-valued modal logic is introduced that combines the usual Kripke frame semantics of the modal logic K with connectives interpreted locally at worlds by lattice and group operations over the real numbers. A labelled tableau system is…

The search for linguistic patterns, stylometry and forensic linguistics have in the theory of complex networks, their structures and associated mathematical tools, allies with which to model and analyze texts. In this paper we present a new…

Lambeks Syntactic Calculus, commonly referred to as the Lambek calculus, was innovative in many ways, notably as a precursor of linear logic. But it also showed that we could treat our grammatical framework as a logic (as opposed to a…

We propose a neural multi-document summarization (MDS) system that incorporates sentence relation graphs. We employ a Graph Convolutional Network (GCN) on the relation graphs, with sentence embeddings obtained from Recurrent Neural Networks…

We demonstrate a deep learning framework which is inherently based in the highly expressive language of relational logic, enabling to, among other things, capture arbitrarily complex graph structures. We show how Graph Neural Networks and…

Graph Neural Networks (GNNs) with numerical node features and graph structure as inputs have demonstrated superior performance on various supervised learning tasks with graph data. However the numerical node features utilized by GNNs are…

Formulating and answering logical queries is a standard communication interface for knowledge graphs (KGs). Alleviating the notorious incompleteness of real-world KGs, neural methods achieved impressive results in link prediction and…

This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more…

Hybrid logic is a modal logic with additional operators specifying nominals and is highly expressive. For example, there is no formula corresponding to the irreflexivity of Kripke frames in basic modal logic, but there is in hybrid logic.…

Despite recent advances in representation learning in hypercomplex (HC) space, this subject is still vastly unexplored in the context of graphs. Motivated by the complex and quaternion algebras, which have been found in several contexts to…

Non-classical negations may fail to be contradictory-forming operators in more than one way, and they often fail also to respect fundamental meta-logical properties such as the replacement property. Such drawbacks are witnessed by intricate…

Graph Neural Networks (GNNs) have demonstrated significant success in learning from graph-structured data but often struggle on heterophilous graphs, where connected nodes differ in features or class labels. This limitation arises from…