Related papers: Model Theory of Ultrafinitism II: Deconstructing t…
Counterfactuals have become an important area of interdisciplinary interest, especially in logic, philosophy of language, epistemology, metaphysics, psychology, decision theory, and even artificial intelligence. In this study, we propose a…
In this opening talk I first describe how we are entering a data-rich era, and what clues we might soon have to physics beyond the SM (on a time scale of several years). Then we turn to a number of the basic issues we hope to explain, and…
A modified realisability interpretation of infinitary logic is formalised and proved sound in constructive type theory (CTT). The logic considered subsumes first order logic. The interpretation makes it possible to extract programs with…
We regard explanations as a blending of the input sample and the model's output and offer a few definitions that capture various desired properties of the function that generates these explanations. We study the links between these…
In the manuscript titled "Computation environment (1)", we introduced a notion called computation environment as an interactive model for computation and complexity theory. In this model, Turing machines are not autonomous entities and find…
The explicit relationship among perception, communication, and design is being discussed in some detail, in order to relate it to characteristic details of the modeling of the world which defines the scientific and artistic activities of…
I present a novel mathematical technique for dealing with the infinities arising from divergent sums and integrals. It assigns them fine-grained infinite values from the set of hyperreal numbers in a manner that refines the standard…
In this introductory article we present the basics of an approach to implementing computational interpreting of natural language aiming to model the meanings of words and phrases. Unlike other approaches, we attempt to define the meanings…
The fine-tuning of deep pre-trained models has revealed compositional properties, with multiple specialized modules that can be arbitrarily composed into a single, multi-task model. However, identifying the conditions that promote…
Machine learning plays a role in many deployed decision systems, often in ways that are difficult or impossible to understand by human stakeholders. Explaining, in a human-understandable way, the relationship between the input and output of…
In the refinement calculus, monotonic predicate transformers are used to model specifications for (imperative) programs. Together with a natural notion of simulation, they form a category enjoying many algebraic properties. We build on this…
The Unified Modelling Language is emerging as a de-facto standard for modelling object-oriented systems. However, the semantics document that a part of the standard definition primarily provides a description of the language's syntax and…
This paper belongs to the field of probabilistic modal logic, focusing on a comparative analysis of two distinct semantics: one rooted in Kripke semantics and the other in neighbourhood semantics. The primary distinction lies in the…
The rather unintuitive nature of quantum theory has led numerous people to develop sets of (physically motivated) principles that can be used to derive quantum mechanics from the ground up, in order to better understand where the structure…
The paper presents several quantum models constructed with the formalism of algebraic geometry. The Universe is presented as a presheaf on the "space of ultimation" (i.e. the branching future) with values in certain category which enhances…
We initiate the study of pseudofiniteness in continuous logic. We introduce a related concept, namely that of pseudocompactness, and investigate the relationship between the two concepts. We establish some basic properties of…
In [Hitzler and Wendt 2002, 2005], a new methodology has been proposed which allows to derive uniform characterizations of different declarative semantics for logic programs with negation. One result from this work is that the well-founded…
We prove some results on the border of Ramsey theory (finite partition calculus) and model theory. Also a beginning of classification theory of finite models in undertaken.
We propose a simplification of the Theory-of-Mind Network architecture, which focuses on modeling complex, deterministic machines as a proxy for modeling nondeterministic, conscious entities. We then validate this architecture in the…
I shall describe a general model-theoretic task to construct expansions of pseudofinite structures and discuss several examples of particular relevance to computational complexity. Then I will present one specific situation where finding a…