Related papers: A topos for a nonstandard functional interpretatio…
Vop\v{e}nka's Alternative Set Theory can be viewed both as an evolution and as a revolution: it is based on his previous experience with nonstandard universes, inspired by Skolem's construction of a nonstandard model of arithmetic, and its…
Functional data are frequently accompanied by a parametric template that describes the typical shapes of the functions. However, these parametric templates can incur significant bias, which undermines both utility and interpretability. To…
Humans often make creative use of words to express novel senses. A long-standing effort in natural language processing has been focusing on word sense disambiguation (WSD), but little has been explored about how the sense inventory of a…
A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The…
The last decade has seen huge progress in the development of advanced machine learning models; however, those models are powerless unless human users can interpret them. Here we show how the mind's construction of concepts and meaning can…
A new functional ANOVA test, with a graphical interpretation of the result, is presented. The test is an extension of the global envelope test introduced by Myllymaki et al. (2017, Global envelope tests for spatial processes, J. R. Statist.…
In this paper, we present a variety of classification experiments related to the task of fictional discourse detection. We utilize a diverse array of datasets, including contemporary professionally published fiction, historical fiction from…
Current open-domain neural semantics parsers show impressive performance. However, closer inspection of the symbolic meaning representations they produce reveals significant weaknesses: sometimes they tend to merely copy character sequences…
Text embeddings are a fundamental component in many NLP tasks, including classification, regression, clustering, and semantic search. However, despite their ubiquitous application, challenges persist in interpreting embeddings and…
We discuss in which sense the so-called {\em regular pseudo-bosons}, recently introduced by Trifonov and analyzed in some details by the author, are related to ordinary bosons. We repeat the same analysis also for {\em pseudo-bosons}, and…
We introduce judgemental theories and their calculi as a general framework to present and study deductive systems. As an exemplification of their expressivity, we approach dependent type theory and natural deduction as special kinds of…
We develop a new paradigm for finding bifurcations of solutions of nonlinear problems, which is based on the detection of extreme values of new type of variational functional associated with the considering problem. The variational…
Recent years have witnessed an increasing number of interpretation methods being developed for improving transparency of NLP models. Meanwhile, researchers also try to answer the question that whether the obtained interpretation is faithful…
The following paper follows on from work by Kamae, and gives a rigorous proof of the Ergodic Theorem, using nonstandard analysis.
In this paper we introduce the notions of topological entropy and topological pressure for non-autonomous iterated function systems (or NAIFSs for short) on countably infinite alphabets. NAIFSs differ from the usual (autonomous) iterated…
This paper is about the meaning of understanding in scientific and in artificial intelligent systems. We give a mathematical definition of the understanding, where, contrary to the common wisdom, we define the probability space on the input…
We present a metagrammatical formalism, {\em generic rules}, to give a default interpretation to grammar rules. Our formalism introduces a process of {\em dynamic binding} interfacing the level of pure grammatical knowledge representation…
The theory introduced, presented and developed in this paper, is concerned with an enriched extension of the theory of Rough Sets pioneered by Zdzislaw Pawlak. The enrichment discussed here is in the sense of valuated categories as…
Topos theory, a branch of category theory, has been proposed as mathematical basis for the formulation of physical theories. In this article, we give a brief introduction to this approach, emphasising the logical aspects. Each topos serves…
The paper begins by exploring the various definitions of norms on semigroups and then presents a new definition of a normed semigroup. The properties of normed semigroups in the new sense are investigated. The new definition of the norm is…