Related papers: A Spatial Logic for Simplicial Models
Many very large-scale systems are networks of cyber-physical systems in which humans and autonomous software agents cooperate. To make the cooperation safe for the humans involved, the systems have to follow protocols with rigid real-time…
We propose an interdisciplinary framework that combines Bayesian predictive inference, a well-established tool in Machine Learning, with Formal Methods rooted in the computer science community. Bayesian predictive inference allows for…
The mathematical representation of uncertainty has led to a proliferation of preference structures, such as interval-valued fuzzy sets, intuitionistic fuzzy sets, and various granular models. While these extensions are often studied…
I consider the following generic scenario: an abstract model M of some 'real' system is only partially presented, or partially known to us, and we have to ensure that the actual system satisfies a given specification, formalised in some…
Spatial connectivity is an important consideration when modelling infectious disease data across a geographical region. Connectivity can arise for many reasons, including shared characteristics between regions, and human or vector movement.…
An ecological network is a formal representation of a specific type of interaction in a corresponding ecosystem. Such networks have traditionally been modelled as encoding exclusively pairwise interactions among the fundamental units of…
Providing meaningful and actionable explanations to end-users is a fundamental prerequisite for implementing explainable intelligent systems in the real world. Explainability is a situated interaction between a user and the AI system rather…
Our understanding about things is conceptual. By stating that we reason about objects, it is in fact not the objects but concepts referring to them that we manipulate. Now, so long just as we acknowledge infinitely extending notions such as…
We propose a structure to represent the social fabric of a group. We call it the `cohesion network' of the group. It can be seen as a graph whose vertices are strict subgroups and whose edges indicate a prescribed `pro-social behaviour'…
A number of models of linear logic are based on or closely related to linear algebra, in the sense that morphisms are "matrices" over appropriate coefficient sets. Examples include models based on coherence spaces, finiteness spaces and…
We introduce a method for modeling a configuration of objects in 2D or 3D images using a mathematical "skeletal linking structure" which will simultaneously capture the individual shape features of the objects and their positional…
In this paper we provide a unifying description of different types of semantics of modal logic found in the literature via the framework of topological categories. In the style of categorical logic, we establish an exact correspondence…
We propose communication pattern logic. A communication pattern describes how processes or agents inform each other, independently of the information content. The full-information protocol in distributed computing is the special case…
Multimodal large language models often struggle with faithful reasoning in complex visual scenes, where intricate entities and relations require precise visual grounding at each step. This reasoning unfaithfulness frequently manifests as…
Learning the topology of higher-order networks from data is a fundamental challenge in many signal processing and machine learning applications. Simplicial complexes provide a principled framework for modeling multi-way interactions, yet…
Although neural models have performed impressively well on various tasks such as image recognition and question answering, their reasoning ability has been measured in only few studies. In this work, we focus on spatial reasoning and…
Similarities between entities occur frequently in many real-world scenarios. For over a century, researchers in different fields have proposed a range of approaches to measure the similarity between entities. More recently, inspired by…
We present a comprehensive study on discrete morphological symmetries of dynamical systems, which are commonly observed in biological and artificial locomoting systems, such as legged, swimming, and flying animals/robots/virtual characters.…
Symbolic learning represents the most straightforward approach to interpretable modeling, but its applications have been hampered by a single structural design choice: the adoption of propositional logic as the underlying language.…
This paper presents a bimodal logic for reasoning about knowledge during knowledge acquisition. One of the modalities represents (effort during) non-deterministic time and the other represents knowledge. The semantics of this logic are…