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The fundamental duality theories relating algebra and geometry that were discovered in the mid-20th century can also be applied to logic via its algebraization under categorical logic. They thereby result in known and new completeness…
In the interdisciplinary field of artificial intelligence (AI) the problem of clear terminology is especially momentous. This paper claims, that AI debates are still characterised by a lack of critical distance to metaphors like 'training',…
We describe two systems currently being developed that use large language models for the automatized correction of (i) exercises in translating back and forth between natural language and the languages of propositional logic and first-order…
Dialectical systems are a mathematical formalism for modeling an agent updating a knowledge base seeking consistency. Introduced in the 1970s by Roberto Magari, they were originally conceived to capture how a working mathematician or a…
Research in AI using Large-Language Models (LLMs) is rapidly evolving, and the comparison of their performance with human reasoning has become a key concern. Prior studies have indicated that LLMs and humans share similar biases, such as…
The aim of this paper is to provide a logic-based conceptual analysis of the twin paradox (TwP) theorem within a first-order logic framework. A geometrical characterization of TwP and its variants is given. It is shown that TwP is not…
This article develops a quality notion that is complementary to the system notion. As a major consequence, it becomes clear why quality can be measured only to a certain extend based on the issues of validity and incompleteness. First,…
Modern Logics, as formulated notably by Frege, Russell and Tarski involved basic assumptions about Natural Languages in general and Indo-European Languages in particular, which are contested by Linguists. Based upon those assumptions,…
In a major advance and simplification of this field, we show that A Local Resolution of the Problem of Time - also viewable as A Local Theory of Background Independence - can at the classical level be described solely by of Lie's…
We address a general representation problem for belief change, and describe two interrelated representations for iterative non-prioritized change: a logical representation in terms of persistent epistemic states, and a constructive…
The advent of the post-human era has blurred the boundary between the body and artefacts. Further, external materials and information are more deeply integrated into the body, making emerging technology a key driving force for shaping…
This paper is the third in a series whose goal is to develop a fundamentally new way of viewing theories of physics. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a…
Pierre Bourdieu discussed how an individual's taste relates o his or her social environment, and how the classification of \emph{distinct} and \emph{vulgar}, among others, arises from at the same time as shapes this taste in his work called…
The author surveys the problem of piecing together integral or rational solutions to Diophantine equations (global structure) from solutions modulo congruences and real solutions (local structure).
The author describes a conceptual study towards mapping grounded natural language discourse representation structures to instances of controlled language statements. This can be achieved via a pipeline of preexisting state of the art…
After highlighting the cases in which the semantics of a language cannot be mechanically reproduced (in which case it is called inherent), the main epistemological consequences of the first incompleteness Theorem for the two fundamental…
Argumentation is a non-monotonic process. This reflects the fact that argumentation involves uncertain information, and so new information can cause a change in the conclusions drawn. However, the base logic does not need to be…
Assessing ways in which Language Models can reduce their hallucinations and improve the outputs' quality is crucial to ensure their large-scale use. However, methods such as fine-tuning on domain-specific data or the training of a separate…
Here we respond to some comments by Alday concerning headedness in linguistic theory and the validity of the assumptions of a mathematical model for word order. For brevity, we focus only on two assumptions: the unit of measurement of…
Linguistic typology aims to capture structural and semantic variation across the world's languages. A large-scale typology could provide excellent guidance for multilingual Natural Language Processing (NLP), particularly for languages that…