Related papers: Graded modal logic and counting message passing au…

The potential of multimodal generative artificial intelligence (mAI) to replicate human grounded language understanding, including the pragmatic, context-rich aspects of communication, remains to be clarified. Humans are known to use…

Quantified propositional intuitionistic logic is obtained from propositional intuitionistic logic by adding quantifiers \forall p, \exists p over propositions. In the context of Kripke semantics, a proposition is a subset of the worlds in a…

We consider the extension of two variable logic with quantifiers that state that the number of elements where a formula holds should belong to a given ultimately periodic set. We show that both satisfiability and finite satisfiability of…

We define the notion of a model of higher-order modal logic in an arbitrary elementary topos $\mathcal{E}$. In contrast to the well-known interpretation of (non-modal) higher-order logic, the type of propositions is not interpreted by the…

We propose a novel multi-scale message passing neural network algorithm for learning the solutions of time-dependent PDEs. Our algorithm possesses both temporal and spatial multi-scale resolution features by incorporating multi-scale…

This paper describes a computational model of multiagent multimodal categorization that realizes emergent communication. We clarify whether the computational model can reproduce the following functions in a symbol emergence system,…

Graph Neural Networks (GNNs) have emerged as a dominant paradigm for graph classification. Specifically, most existing GNNs mainly rely on the message passing strategy between neighbor nodes, where the expressivity is limited by the…

A sound and complete embedding of conditional logics into classical higher-order logic is presented. This embedding enables the application of off-the-shelf higher-order automated theorem provers and model finders for reasoning within and…

Algebraic model counting unifies many inference tasks on logic formulas by exploiting semirings. Rather than focusing on inference, we consider learning, especially in statistical-relational and neurosymbolic AI, which combine logical,…

The multimodal Lambek calculus is an extension of the Lambek calculus that includes several product operations (some of them being commutative or/and associative), unary modalities, and corresponding residual implications. In this work, we…

Multi-stage programming is a proven technique that provides predictable performance characteristics by controlling code generation. We propose a core semantics for Typed Template Haskell, an extension of Haskell that supports multi staged…

We study multimodal logics over universally first-order definable classes of frames. We show that even for bimodal logics, there are universal Horn formulas that define set of frames such that the satisfiability problem is undecidable, even…

Graph Neural Networks (GNNs) are a class of machine-learning models that operate on graph-structured data. Their expressive power is intimately related to logics that are invariant under graded bisimilarity. Current proposals for recurrent…

The higher-dimensional modal mu-calculus is an extension of the mu-calculus in which formulas are interpreted in tuples of states of a labeled transition system. Every property that can be expressed in this logic can be checked in…

Message passing graph neural networks (GNNs) are known to have their expressiveness upper-bounded by 1-dimensional Weisfeiler-Leman (1-WL) algorithm. To achieve more powerful GNNs, existing attempts either require ad hoc features, or…

In the quest for scalable Bayesian computational algorithms we need to exploit the full potential of existing methodologies. In this note we point out that message passing algorithms, which are very well developed for inference in graphical…

Expressive querying of machine learning models - viewed as a form of intentional data - enables their verification and interpretation using declarative languages, thereby making learned representations of data more accessible. Motivated by…

We propose cognitive prompting as a novel approach to guide problem-solving in large language models (LLMs) through structured, human-like cognitive operations, such as goal clarification, decomposition, filtering, abstraction, and pattern…

Intuitionistic Propositional Logic is proved to be an infinitely many valued logic by Kurt G\"odel (1932), and it is proved by Stanis{\l}aw Ja\'skowski (1936) to be a countably many valued logic. In this paper, we provide alternative proofs…

Non-iterative normal modal logics are defined by axioms of modal degree 1. In this paper we use calculations with normal forms to determine the set of all possible non-iterative normal modal logics, unimodal propositional extensions of K.…