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Social norms are powerful formalism in coordinating autonomous agents' behaviour to achieve certain objectives. In this paper, we propose a dynamic normative system to enable the reasoning of the changes of norms under different…
A procedure to characterize chaotic dynamical systems with concepts of complex networks is pursued, in which a dynamical system is mapped onto a network. The nodes represent the regions of space visited by the system, while edges represent…
Large Language Models (LLMs) have shown impressive performance in mathematical reasoning tasks when guided by Chain-of-Thought (CoT) prompting. However, they tend to produce highly confident yet incorrect outputs, which poses significant…
We give a tutorial for the study of dynamical systems on networks. We focus especially on "simple" situations that are tractable analytically, because they can be very insightful and provide useful springboards for the study of more…
It is proposed that the theory of dynamical systems offers appropriate tools to model many phonological aspects of both speech production and perception. A dynamic account of speech rhythm is shown to be useful for description of both…
Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through the lens of mathematical models is to determine when the…
We apply to logic programming some recently emerging ideas from the field of reduction-based communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational…
Open dynamical systems are mathematical models of machines that take input, change their internal state, and produce output. For example, one may model anything from neurons to robots in this way. Several open dynamical systems can be…
We review how an algebraic formulation for the dynamics of a physical system allows to describe a reduction procedure for both classical and quantum evolutions.
Game semantics and winning strategies offer a potential conceptual bridge between semantics and proof systems of logics. We illustrate this link for hybrid logic -- an extension of modal logic that allows for explicit reference to worlds…
Conventional static knowledge graphs model entities in relational data as nodes, connected by edges of specific relation types. However, information and knowledge evolve continuously, and temporal dynamics emerge, which are expected to…
Synchronous model is a type of formal models for modelling and specifying reactive systems. It has a great advantage over other real-time models that its modelling paradigm supports a deterministic concurrent behaviour of systems. Various…
Probabilistic logic programming is increasingly important in artificial intelligence and related fields as a formalism to reason about uncertainty. It generalises logic programming with the possibility of annotating clauses with…
Over the last 20 years a large number of automata-based specification theories have been proposed for modeling of discrete,real-time and probabilistic systems. We have observed a lot of shared algebraic structure between these formalisms.…
We demonstrate the possibility of classifying causal systems into kinds that share a common structure without first constructing an explicit dynamical model or using prior knowledge of the system dynamics. The algorithmic ability to…
Stochastic models such as Continuous-Time Markov Chains (CTMC) and Stochastic Hybrid Automata (SHA) are powerful formalisms to model and to reason about the dynamics of biological systems, due to their ability to capture the stochasticity…
This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…
The dynamic sructure factor as the basic quantity describing the collective excitations in a fluid is considered. We consider the cases of neutral and Coulombic fluids. The classical method of moments is applied to construct the dynamic…
Recent ideas about epistemic modals and indicative conditionals in formal semantics have significant overlap with ideas in modal logic and dynamic epistemic logic. The purpose of this paper is to show how greater interaction between formal…
Propositional Dynamic Logic, PDL, is a modal logic designed to formalize the reasoning about programs. By extending accessibility between states to states and state sets, concurrent propositional dynamic logic CPDL, is introduced to include…