On the one side, the formalism of Global Transformations comes with the claim of capturing any transformation of space that is local, synchronous and deterministic. The claim has been proven for different classes of models such as mesh refinements from computer graphics, Lindenmayer systems from morphogenesis modeling, and cellular automata from biological, physical and parallel computation modeling. The Global Transformation formalism achieves this by using category theory for its genericity, and more precisely the notion of Kan extension to determine the global behaviors based on the local ones. On the other side, Causal Graph Dynamics describe the transformation of port graphs in a synchronous and deterministic way. In this paper, we show the precise sense in which the claim of Global Transformations holds for them as well. This is done by showing different ways in which they can be expressed as Kan extensions, each of them highlighting different features of Causal Graph Dynamics. Along the way, this work uncovers the interesting class of Monotonic Causal Graph Dynamics and their universality among General Causal Graph Dynamics.

Translating unstructured text into logical format is a key challenge for building ontologies automatically and addressing deductive inference. Most of the approaches have tackled the identification of concepts and relations in text, but few of them have addressed the most complex axioms like class expression subsumption. This work proposes DeLIR, a neuro-symbolic approach to identify complex logical patterns in text by combining a grammatical translation of dependency parsing trees and a fine-tuned Large language Model (LLM). DeLIR combines the strength of the parsing accuracy provided by a grammatical approach and pattern flexibility provided by a finetuned LLM. We evaluated our approach on FOLIO dataset for both translation capacity and inference capability. Our grammatical approach has a perfect parsing accuracy and combining the grammatical approach with LLMs improves the LLMS translation capacity: tinyLlama, T5-small-text2logic, Llama-7B and Mistral-7B. We also evaluate the inference capacity of the different LLMs. Mistral-7B, while being smaller than the state-of-the-art approach using GPT-4, presents similar results to predict the correct inference labels.

Global transformations provide a categorical framework for capturing synchronous rewriting systems, generalizing cellular automata to dynamical systems over dynamic spaces. Originally developed for addressing deterministic dynamical systems, the presented work raises the question of non-determinism. While a usual approach is to develop a general non-deterministic setting where deterministic systems can be retrieved as a specific case, we show here that by choosing the right parametrization, global transformations can already be used to handle non-determinism. Context-free Lindenmayer systems, already shown to be captured by global transformation in the deterministic case, are used to illustrate the approach. From this concrete example, the formal obstructions are exhibited, leading to a solution involving a 2-categorical monad and its associated Kleisli construction.

ANDy, Activity Networks with Delays, is a discrete framework aiming at the qualitative modeling of time-dependent activities. The modular and expressive syntax makes ANDy suitable for a concise and natural modeling of time-dependent biological systems (i.e., regulatory pathways). Activities involve entities playing the role of activators, inhibitors or products of biochemical network operation. Activities may have a given duration, i.e., the time required to obtain results. An entity may represent an object (e.g., an agent, a biochemical species or a family of thereof) with a local attribute, a state denoting its level (e.g., concentration, strength). Entity levels may change as a result of an activity or may decay gradually as time passes by. The semantics of ANDy is formally given via high-level Petri nets ensuring this way some modularity. As main results we show that ANDy systems have finite state representations even for potentially infinite processes and it well adapts to the modeling of toxic behaviors. As an illustration, we present a classification of toxicity properties and give some hints on how they can be verified on ANDy systems with existing tools. A case study on blood glucose regulation is provided to exemplify the ANDy framework and the toxicity properties.

Most of the frameworks and languages available in the field of modeling and simulation of dynamical systems focus on the specification of the state of the system and its transition function. Although we believe that this task has been elegantly solved by the design of the rule-based topological programming language MGS, an interesting challenge remains in the computation of the activity, and its topology, exhibited by their discrete event simulation. This additional information can help in optimizing, analyzing and modeling complex systems.

Jacob Beal, Stefan Dulman, Olivier Michel, Antoine Spicher; Editorial, The Computer Journal, Volume 56, Issue 12, 1 December 2013, Pages 1397–1398, https://doi.