Related papers: A Worked Example of the Functional Interpretation
We explore a functionalist approach to emotion by employing an ansatz -- an initial set of assumptions -- that a hypothetical concept generation model incorporates unproven but biologically plausible traits. From these traits, we…
Noncommutative rational functions appeared in many contexts in system theory and control, from the theory of finite automata and formal languages to robust control and LMIs. We survey the construction of noncommutative rational functions,…
While a great effort has concerned the development of fully integrated modular understanding systems, few researches have focused on the problem of unifying existing linguistic formalisms with cognitive processing models. The Situated…
Functional ANOVA offers a principled framework for interpretability by decomposing a model's prediction into main effects and higher-order interactions. For independent features, this decomposition is well-defined, strongly linked with SHAP…
Nested relations, built up from atomic types via product and set types, form a rich data model. Over the last decades the nested relational calculus, NRC, has emerged as a standard language for defining transformations on nested…
For a century, quantum theory has posed a fundamental challenge to philosophical thinking. On its face, it repudiates many of the key features of the mechanical conception of physical reality. However, the challenge of developing a precise,…
Point forecasts can be interpreted as functionals (i.e., point summaries) of predictive distributions. We consider the situation where forecasters' directives are hidden and develop methodology for the identification of the unknown…
As machine learning algorithms getting adopted in an ever-increasing number of applications, interpretation has emerged as a crucial desideratum. In this paper, we propose a mathematical definition for the human-interpretable model. In…
Translations between different nonmonotonic formalisms always have been an important topic in the field, in particular to understand the knowledge-representation capabilities those formalisms offer. We provide such an investigation in terms…
In this survey we discuss the notion of combinatorial interpretation in the context of Algebraic Combinatorics and related areas. We approach the subject from the Computational Complexity perspective. We review many examples, state a…
Human speakers have an extensive toolkit of ways to express themselves. In this paper, we engage with an idea largely absent from discussions of meaning in natural language understanding--namely, that the way something is expressed reflects…
Modifiable combining functions are a synthesis of two common approaches to combining evidence. They offer many of the advantages of these approaches and avoid some disadvantages. Because they facilitate the acquisition, representation,…
Logic programming is a flexible programming paradigm due to the use of predicates without a fixed data flow. To extend logic languages with the compact notation of functional programming, there are various proposals to map evaluable…
A common method of making a theory more understandable, is by comparing it to another theory which has been better developed. Radical interpretation is a theory which attempts to explain how communication has meaning. Radical interpretation…
Formal Concept Analysis (FCA) is a mathematical framework for knowledge representation and discovery. It performs a hierarchical clustering over a set of objects described by attributes, resulting in conceptual structures in which objects…
The increasing adoption of machine learning tools has led to calls for accountability via model interpretability. But what does it mean for a machine learning model to be interpretable by humans, and how can this be assessed? We focus on…
Formal logic has often been seen as uniquely placed to analyze mathematical argumentation. While formal logic is certainly necessary for a complete understanding of mathematical practice, it is not sufficient. Important aspects of…
The functional correspondence is a manual derivation technique transforming higher-order evaluators into the semantically equivalent abstract machines. The transformation consists of two well-known program transformations: translation to…
Technological understanding is not a singular concept but varies depending on context. Building on De Jong and De Haro's (2025) notion of technological understanding as the ability to realise an aim through the use of a technological…
Legal interpretation is a linguistic venture. In judicial opinions, for example, courts are often asked to interpret the text of statutes and legislation. As time has shown, this is not always as easy as it sounds. Matters can hinge on…