Related papers: A language for mathematical knowledge management
Substantial efforts have been made in developing various Decision Modeling formalisms, both from industry and academia. A challenging problem is that of expressing decision knowledge in the context of incomplete knowledge. In such contexts,…
We have recently showed that it is possible to deal with collections of indistinguishable elementary particles (in the context of quantum mechanics) in a set-theoretical framework by using hidden variables, in a sense. In the present paper…
In this paper, we present an approach to define the semantics for object-oriented modeling languages. One important property of this semantics is to support underspecified and incomplete models. To this end, semantics is given as predicates…
Sentence embedding is an important research topic in natural language processing (NLP) since it can transfer knowledge to downstream tasks. Meanwhile, a contextualized word representation, called BERT, achieves the state-of-the-art…
Physics makes powerful use of mathematics, yet the way this use is made is often poorly understood. Professionals closely integrate their mathematical symbology with physical meaning, resulting in a powerful and productive structure. But…
The article suggests a description of a system of tables with a set of special lists absorbing a semantics of data and reflects a fullness of data. It shows how their parallel processing can be constructed based on the descriptions. The…
Semantic compositionality (SC) refers to the phenomenon that the meaning of a complex linguistic unit can be composed of the meanings of its constituents. Most related works focus on using complicated compositionality functions to model SC…
This paper is a reflexion on the computability of natural language semantics. It does not contain a new model or new results in the formal semantics of natural language: it is rather a computational analysis of the logical models and…
Pre-trained language models (LMs) encode rich information about linguistic structure but their knowledge about lexical polysemy remains unclear. We propose a novel experimental setup for analysing this knowledge in LMs specifically trained…
Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory. We would like to briefly explore why that is, and how this word-related…
We present a system of axioms motivated by a topological intuition: The set of subsets of any set is a topology on that set. On the one hand, this system is a common weakening of Zermelo-Fraenkel set theory ZF, the positive set theory GPK…
Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite…
The development of mechanised language specification based on structured operational semantics, with applications to verified compilers and sound program analysis, requires huge effort. General theory and frameworks have been proposed to…
A fundamental theme in automata theory is regular languages of words and trees, and their many equivalent definitions. Salvati has proposed a generalization to regular languages of simply typed $\lambda$-terms, defined using denotational…
Much like sentences are composed of words, words themselves are composed of smaller units. For example, the English word questionably can be analyzed as question+able+ly. However, this structural decomposition of the word does not directly…
An understandable concrete syntax and a comprehensible abstract syntax are two central aspects of defining a modeling language. Both representations of a language significantly overlap in their structure and also information, but may also…
The Satisfiability Modulo Theories (SMT) issue concerns the satisfiability of formulae from multiple background theories, usually expressed in the language of first-order predicate logic with equality. SMT solvers are often based on…
A theory of recursive definitions has been mechanized in Isabelle's Zermelo-Fraenkel (ZF) set theory. The objective is to support the formalization of particular recursive definitions for use in verification, semantics proofs and other…
The ability to read, write, and speak mathematics is critical to students becoming comfortable with statistical models and skills. Faster development of those skills may act as encouragement to further engage with the discipline. Vocabulary…
Some aspects of programming education are examined in this work. It is emphasised, based on the entertainment value, the most appropriate examples are chosen to demonstrate the different language constructions and data structures. Such an…