Exchangeability for sets of desirable gambles

Sets of desirable gambles constitute a quite general type of uncertainty model with an interesting geometrical interpretation. We study exchangeability assessments for such models, and prove a counterpart of de Finetti's finite representation theorem. We show that this representation theorem has a very nice geometrical interpretation. We also lay bare the relationships between the representations of updated exchangeable models, and discuss conservative inference (natural extension) under exchangeability

Hierarchical a Fortiori Reasoning with Dimensions

In recent years, a model of a fortiori argumentation, developed to describe legal reasoning based on precedent, has been successfully applied in the field of artificial intelligence to improve interpretability of data-driven decision systems. In order to make this model more broadly applicable for this purpose, work has been done to expand the knowledge representation on the basis of which it functions, as the original model accommodates only binary propositional information. In particular, two separate expansions of the original model emerged; one which accounts for non-binary input information, and a second which accommodates hierarchically structured reasoning. In the present work we unify these expansions to a single model, incorporating both dimensional and hierarchical information.</p

Hierarchical a Fortiori Reasoning with Dimensions

In recent years, a model of a fortiori argumentation, developed to describe legal reasoning based on precedent, has been successfully applied in the field of artificial intelligence to improve interpretability of data-driven decision systems. In order to make this model more broadly applicable for this purpose, work has been done to expand the knowledge representation on the basis of which it functions, as the original model accommodates only binary propositional information. In particular, two separate expansions of the original model emerged; one which accounts for non-binary input information, and a second which accommodates hierarchically structured reasoning. In the present work we unify these expansions to a single model, incorporating both dimensional and hierarchical information.</p

Modelling and Explaining Legal Case-based Reasoners through Classifiers

This paper brings together factor-based models of case-based reasoning (CBR) and the logical specification of classifiers. Horty [8] has developed the factor-based models of precedent into a theory of precedential constraint. In this paper we combine binary-input classifier logic (BCL) to classifiers and their explanations given by Liu &amp; Lorini [13,14] with Horty’s account of factor-based CBR, since both a classifier and CBR map sets of features to decisions or classifications. We reformulate case bases in the language of BCL, and give several representation results. Furthermore, we show how notions of CBR can be analyzed by notions of classifier explanation

Generation of Explanations for Logic Reasoning

This thesis delves into a fortiori arguments in deductive reasoning, underscoring their relevance in various domains such as law, philosophy, and artificial intelligence. The research is centred on employing GPT-3.5-turbo to automate the analysis of these arguments, with a focus on understanding intricate reasoning processes, generating clear and coherent explanations, and creating novel arguments. The methodology encompasses a series of tasks including detailed reasoning, interpretation, and the augmentation of a fortiori arguments. It involves meticulously identifying these arguments in diverse contexts, differentiating comparative elements, and categorizing them based on their logical structure. Extensive experiments reveals the challenges encountered by GPT-3.5-turbo in accurately detecting and classifying a fortiori arguments. Nevertheless, the model demonstrates a performance that rivals specialized models, particularly in extracting key components and interpreting underlying properties. The integration of external information into the model's processing significantly elevates the quality of the generated explanations. Additionally, the model exhibits a noteworthy capability in augmenting arguments, thus contributing to the enrichment of the data set. Despite facing certain limitations, this thesis makes significant contributions to the fields of artificial intelligence and logical reasoning. It introduces novel methodologies, establishes a rigorous evaluation framework, and provides deep insights that set the stage for future advancements in automated logical reasoning. The findings and methodologies presented herein not only underscore the potential of AI in complex reasoning tasks but also highlight areas for future research and development.Comment: 78 Pages, 16 Figures, Thesis Presentation is available at https://drive.google.com/file/d/1wLIBsjfLvO11PjCS6qx4Y9UgRBUfq3wQ/view?usp=sharin

Exchangeability and sets of desirable gambles

Sets of desirable gambles constitute a quite general type of uncertainty model with an interesting geometrical interpretation. We give a general discussion of such models and their rationality criteria. We study exchangeability assessments for them, and prove counterparts of de Finetti's finite and infinite representation theorems. We show that the finite representation in terms of count vectors has a very nice geometrical interpretation, and that the representation in terms of frequency vectors is tied up with multivariate Bernstein (basis) polynomials. We also lay bare the relationships between the representations of updated exchangeable models, and discuss conservative inference (natural extension) under exchangeability and the extension of exchangeable sequences.Comment: 40 page

A Theory of Sampling for Continuous-time Metric Temporal Logic

This paper revisits the classical notion of sampling in the setting of real-time temporal logics for the modeling and analysis of systems. The relationship between the satisfiability of Metric Temporal Logic (MTL) formulas over continuous-time models and over discrete-time models is studied. It is shown to what extent discrete-time sequences obtained by sampling continuous-time signals capture the semantics of MTL formulas over the two time domains. The main results apply to "flat" formulas that do not nest temporal operators and can be applied to the problem of reducing the verification problem for MTL over continuous-time models to the same problem over discrete-time, resulting in an automated partial practically-efficient discretization technique.Comment: Revised version, 43 pages

Two Outline Models of Science: AMS And HAMS

Two abstract and computational models of the long-term process of science are proposed: AMS and HAMS. An outline specification of each model is given and the relationship between them explained. AMS takes an Olympian (\"artificial world\") view of science and its processes. HAMS is simpler and relatively more abstract and comprises only a small set of core processes. A first implementation of HAMS is described. How AMS and HAMS might be validated and used in experimental investigations is considered including problems that might arise. Further work is proposed. A brief coda concerns a related model of science formulated from an idealist rather than a materialist perspective.Computational Models of Science, Individual-Based Modelling, Scientific Method, Belief Systems, Belief Verification, Idealism