Related papers: Graded modal logic and counting message passing au…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
A hypergraph consists of a set of nodes along with a collection of subsets of the nodes called hyperedges. Higher-order link prediction is the task of predicting the existence of a missing hyperedge in a hypergraph. A hyperedge…
Justification logics are modal-like logics that provide a framework for reasoning about justifications. This paper introduces labeled sequent calculi for justification logics, as well as for hybrid modal-justification logics. Using the…
In this paper, we present a Weibull link (skewed) model for categorical response data arising from binomial as well as multinomial model. We show that, for such types of categorical data, the most commonly used models (logit, probit and…
We introduce a logical approach to formalizing statistical properties of machine learning. Specifically, we propose a formal model for statistical classification based on a Kripke model, and formalize various notions of classification…
The Weisfeiler-Leman algorithm ($1$-WL) is a well-studied heuristic for the graph isomorphism problem. Recently, the algorithm has played a prominent role in understanding the expressive power of message-passing graph neural networks…
Non-idempotent intersection types provide quantitative information about typed programs, and have been used to obtain time and space complexity measures. Intersection type systems characterize termination, so restrictions need to be made in…
Understanding how Large Language Models (LLMs) perform logical reasoning internally remains a fundamental challenge. While prior mechanistic studies focus on identifying taskspecific circuits, they leave open the question of what…
We provide the first denotational semantics for asynchronous multiparty session types with precise asynchronous subtyping. Our semantics enables us to reason about asynchronous message-passing, in which message-sending is non-blocking. It…
Graph Neural Networks (GNNs), despite achieving remarkable performance across different tasks, are theoretically bounded by the 1-Weisfeiler-Lehman test, resulting in limitations in terms of graph expressivity. Even though prior works on…
Linear attention methods offer a compelling alternative to softmax attention due to their efficiency in recurrent decoding. Recent research has focused on enhancing standard linear attention by incorporating gating while retaining its…
The majority of popular graph kernels is based on the concept of Haussler's $\mathcal{R}$-convolution kernel and defines graph similarities in terms of mutual substructures. In this work, we enrich these similarity measures by considering…
The Kripke semantics of classical propositional normal modal logic is made algebraic via an embedding of Kripke structures into the larger class of pointed stably supported quantales. This algebraic semantics subsumes the traditional…
Message passing Graph Neural Networks (GNNs) provide a powerful modeling framework for relational data. However, the expressive power of existing GNNs is upper-bounded by the 1-Weisfeiler-Lehman (1-WL) graph isomorphism test, which means…
We present a unified probabilistic model that learns a representative set of discrete vehicle actions and predicts the probability of each action given a particular scenario. Our model also enables us to estimate the distribution over…
We propose a new definition of the representation theorem for many-valued logics, with modal operators as well, and define the stronger relationship between algebraic models of a given logic and relational structures used to define the…
Decentralized strategies are of interest for learning from large-scale data over networks. This paper studies learning over a network of geographically distributed nodes/agents subject to quantization. Each node possesses a private local…
We give the quantum subset construction of orthomodular lattice-valued finite automata, then we show the equivalence between orthomodular lattice-valued finite automata, orthomodular lattice-valued deterministic finite automata and…
The short note describes the chart parser for multimodal type-logical grammars which has been developed in conjunction with the type-logical treebank for French. The chart parser presents an incomplete but fast implementation of proof…
For each natural number $n$ we study the modal logic determined by the class of transitive Kripke frames in which there are no cycles of length greater than $n$ and no strictly ascending chains. The case $n=0$ is the G\"odel-L\"ob…