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Many complex engineering systems consist of multiple subsystems that are developed by different teams of engineers. To analyse, simulate and control such complex systems, accurate yet computationally efficient models are required. Modular…
The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…
Mathematical models of the real world are simplified representations of complex systems. A caveat to using mathematical models is that predicted causal effects and conditional independences may not be robust under model extensions, limiting…
[Spreadsheet] Models are invaluable tools for strategic planning. Models help key decision makers develop a shared conceptual understanding of complex decisions, identify sensitivity factors and test management scenarios. Different…
The maxima and the minima of a randomly stopped sample of a random variable, $X$, together with two newly defined random variables that make $X$ into the maxima or minima of a randomly stopped sample of them, can be used to define…
Systems may depend on parameters which one may control, or which serve to optimise the system, or are imposed externally, or they could be uncertain. This last case is taken as the ``Leitmotiv'' for the following. A reduced order model is…
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…
Objective prior distributions represent an important tool that allows one to have the advantages of using the Bayesian framework even when information about the parameters of a model is not available. The usual objective approaches work off…
In this paper the problems of the retrospective analysis of models with time-varying structure are considered. These models include contamination models with randomly switching parameters and multivariate classification models with an…
In this paper, we propose a first-order ontology for generalized stratified order structure. We then classify the models of the theory using model-theoretic techniques. An ontology mapping from this ontology to the core theory of Process…
Reusable software components need expressive specifications. This paper outlines a rigorous foundation to model-based contracts, a method to equip classes with strong contracts that support accurate design, implementation, and formal…
It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this…
Transfer learning methods endeavor to leverage relevant knowledge from existing source pre-trained models or datasets to solve downstream target tasks. With the increase in the scale and quantity of available pre-trained models nowadays, it…
In classification, it is usual to observe that models trained on a given set of classes can generalize to previously unseen ones, suggesting the ability to learn beyond the initial task. This ability is often leveraged in the context of…
In the field of large language model (LLM)-based proof generation, despite extensive training on large datasets such as ArXiv, LLMs still exhibit only modest performance on proving tasks of moderate difficulty. We believe that this is…
In this paper, we study whether transformer-based language models can extract predicate argument structure from simple sentences. We firstly show that language models sometimes confuse which predicates apply to which objects. To mitigate…
Recently developed pretrained models can encode rich world knowledge expressed in multiple modalities, such as text and images. However, the outputs of these models cannot be integrated into algorithms to solve sequential decision-making…
In the context of interactive theorem provers based on a dependent type theory, automation tactics (dedicated decision procedures, call of automated solvers, ...) are often limited to goals which are exactly in some expected logical…
A methodology that seeks to enhance model prediction performance is presented. The method involves generating multiple auxiliary models that capture relationships between attributes as a function of each other. Such information serves to…
In the spirit of the many recent simple models of evolution inspired by statistical physics, we put forward a simple model of the evolution of such models. Like its objects of study, it is (one supposes) in principle testable and capable of…