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Models based on partial differential equations (PDEs) are powerful for describing a wide range of complex phenomena in the natural sciences. Accurately identifying the PDE model, which represents the underlying physical law, is essential…
Computational modeling is a key resource to gather insight into physical systems in modern scientific research and engineering. While access to large amount of data has fueled the use of Machine Learning (ML) to recover physical models from…
In this paper, we introduce $\textit{partial}$ dependency modality $\mathcal{D}$ into epistemic logic so as to reason about $\textit{partial}$ dependency relationship in Kripke models. The resulted dependence epistemic logic possesses…
This paper studies regularized data-enabled predictive control (DeePC) within a nonlinear framework and its relationship to subspace predictive control (SPC). The $\Pi$-regularization is extended to general basis functions and it is shown…
Conditional independence reasoning has been shown to be helpful in the context of Bayesian nets to optimize probabilistic inference, and related techniques have been applied to speed up a number of logical reasoning tasks in boolean logic…
Design and control of autonomous systems that operate in uncertain or adversarial environments can be facilitated by formal modelling and analysis. Probabilistic model checking is a technique to automatically verify, for a given temporal…
Probabilistic logic programming is a major part of statistical relational artificial intelligence, where approaches from logic and probability are brought together to reason about and learn from relational domains in a setting of…
Windows have been introduce in \cite{BalGasq25} as a tool for designing polynomial algorithms to check satisfiability of a bimodal logic of weak-density. In this paper, after revisiting the ``folklore'' case of bimodal $\K4$ already treated…
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.…
We investigate the expressive power of state space models (SSM), which have recently emerged as a potential alternative to transformer architectures in large language models. Building on recent work, we analyse SSM expressiveness through…
We consider the operation of sum on Kripke frames, where a family of frames-summands is indexed by elements of another frame. In many cases, the modal logic of sums inherits the finite model property and decidability from the modal logic of…
Ecological Momentary Assessment (EMA) studies enable the collection of high-frequency self-reports of suicidal thoughts and behaviors (STBs) via smartphones. Latent stochastic differential equations (SDEs) are a promising model class for…
In many scientific fields, the generation and evolution of data are governed by partial differential equations (PDEs) which are typically informed by established physical laws at the macroscopic level to describe general and predictable…
In 1979 Richard Statman proved, using proof-theory, that the purely implicational fragment of Intuitionistic Logic (M-imply) is PSPACE-complete. He showed a polynomially bounded translation from full Intuitionistic Propositional Logic into…
Partial differential equations (PDEs) encode fundamental physical laws, yet closed-form analytical solutions for many important equations remain unknown and typically require substantial human insight to derive. Existing numerical,…
Stochastic switched systems are a relevant class of stochastic hybrid systems with probabilistic evolution over a continuous domain and control-dependent discrete dynamics over a finite set of modes. In the past few years several different…
We introduce a semantics for epistemic logic exploiting a belief base abstraction. Differently from existing Kripke-style semantics for epistemic logic in which the notions of possible world and epistemic alternative are primitive, in the…
System and software design benefits greatly from formal modeling, allowing for automated analysis and verification early in the design phase. Current methods excel at checking information flow and component interactions, ensuring…
The idea of representing symbolic knowledge in connectionist systems has been a long-standing endeavour which has attracted much attention recently with the objective of combining machine learning and scalable sound reasoning. Early work…
Belief revision is the task of modifying a knowledge base when new information becomes available, while also respecting a number of desirable properties. Classical belief revision schemes have been already specialised to \emph{binary…