Related papers: Jacob's Ladder and Scientific Ontologies

Jacobs' hypernormalisation is a construction on finitely supported discrete probability distributions, obtained by generalising certain patterns occurring in quantitative information theory. In this paper, we generalise Jacobs' notion in…

In order to support students in the development of expertise in quantum mechanics, we asked which concepts and structures can act as organizing principles of the non-relativistic theory. The research question has been addressed in a…

One hundred years after the creation of quantum theory, there is no consensus on the kind of reality that is described by the theory. Here, I attribute the lack of progress to the prevailing interpretative methodology, which invariably…

We present a unified categorical framework that connects the syntactic Henkin construction for the first-order Completeness Theorem with Lawvere's Fixed-Point Theorem. Concretely, we define two canonical functors from the category of…

We present a general logical framework for reasoning about agents' cognitive attitudes of both epistemic type and motivational type. We show that it allows us to express a variety of relevant concepts for qualitative decision theory…

Euclidean geometry has historically played a central role in cultivating logical reasoning and abstract thinking within mathematics education, but has experienced waning emphasis in recent curricula. The resurgence of interest, driven by…

While extracting information from data with machine learning plays an increasingly important role, physical laws and other first principles continue to provide critical insights about systems and processes of interest in science and…

There is an ongoing debate in computer science how algorithms should best be studied. Some scholars have argued that experimental evaluations should be conducted, others emphasize the benefits of formal analysis. We believe that this debate…

A series of works has established rewriting as an essential tool in order to prove coherence properties of algebraic structures, such as MacLane's coherence theorem for monoidal categories, based on the observation that, under reasonable…

Over two decades ago a "quite revolution" overwhelmingly replaced knowledgebased approaches in natural language processing (NLP) by quantitative (e.g., statistical, corpus-based, machine learning) methods. Although it is our firm belief…

Constructor theory seeks to express all fundamental scientific theories in terms of a dichotomy between possible and impossible physical transformations - those that can be caused to happen and those that cannot. This is a departure from…

We introduce a compositional framework for convex analysis based on the notion of convex bifunction of Rockafellar. This framework is well-suited to graphical reasoning, and exhibits rich dualities such as the Legendre-Fenchel transform,…

This paper primarily demonstrates a method to quantitatively assess the alignment between multi-step, structured reasoning in large language models and human preferences. We introduce the Alignment Score, a semantic-level metric that…

Inspired by Bayesian approaches to brain function in neuroscience, we give a simple theory of probabilistic inference for a unified account of reasoning and learning. We simply model how data cause symbolic knowledge in terms of its…

This paper develops a categorical framework to clarify the relationship between the completeness and compactness theorems in classical first-order logic. Rather than claiming that different model constructions yield naturally isomorphic…

Doubts are raised concerning the usual interpretation of the alleged failure, by quantum mechanics, of the distributive law of classical logic. The difficulty raised by incompatible sets of observables is overcome within an epistemic…

Confounder selection is perhaps the most important step in the design of observational studies. A number of criteria, often with different objectives and approaches, have been proposed, and their validity and practical value have been…

We introduce a semantics for epistemic logic exploiting a belief base abstraction. Differently from existing Kripke-style semantics for epistemic logic in which the notions of possible world and epistemic alternative are primitive, in the…

A theory of quantitative inference about the parameters of sampling distributions is constructed deductively by following very general rules, referred to as the Cox-Polya-Jaynes Desiderata. The inferences are made in terms of probability…

This paper develops a physical framework for the prebiotic emergence of information and meaning. Building on Constructor Theory, we define information as a reproducible physical difference and meaning as a difference with stable functional…