Related papers: A language for mathematical knowledge management
We present a novel treatment of set theory in a four-valued paraconsistent and paracomplete logic, i.e., a logic in which propositions can be both true and false, and neither true nor false. Our approach is a significant departure from…
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…
In Knowledge Representation, it is crucial that knowledge engineers have a good understanding of the formal expressions that they write. What formal expressions state intuitively about the domain of discourse is studied in the theory of the…
We present an encoding of Zermelo-Fraenkel set theory into many-sorted first-order logic, the input language of state-of-the-art SMT solvers. This translation is the main component of a back-end prover based on SMT solvers in the TLA+ Proof…
The standard axioms of set theory, the Zermelo-Fraenkel axioms (ZFC), do not suffice to answer all questions in mathematics. While this follows abstractly from Kurt G\"odel's famous incompleteness theorems, we nowadays know numerous…
Transformer architectures show significant promise for natural language processing. Given that a single pretrained model can be fine-tuned to perform well on many different tasks, these networks appear to extract generally useful linguistic…
Modeling languages in software engineering (e.g., UML) evolved from software systems modeling where denotational and operational kinds of semantics are the traditional subjects of research and practice. According to some authors, although a…
Set theory is widely believed to provide a secure foundation for deductive mathematics, but current set theories do not quite do this. The mainstream essentially uses na\"\i ve set theory. After Russell's paradox showed this to be…
We give an accessible presentation to the foundations of nominal techniques, lying between Zermelo-Fraenkel set theory and Fraenkel-Mostowski set theory, and which has several nice properties including being consistent with the Axiom of…
A model of knowledge representation is described in which propositional facts and the relationships among them can be supported by other facts. The set of knowledge which can be supported is called the set of cognitive units, each having…
Systematically discovering semantic relationships in text is an important and extensively studied area in Natural Language Processing, with various tasks such as entailment, semantic similarity, etc. Decomposability of sentence-level scores…
We discuss the problems of incompleteness and inexpressibility. We introduce almost self-referential formulas, use them to extend set theory, and relate their expressive power to that of infinitary logic. We discuss the nature of proper…
Basic pairs and their morphisms are the most elementary framework in which standard topological notions can be defined. We present here a new interpretation of topological concepts as those which can be communicated faithfully between the…
Argument mining tasks require an informed range of low to high complexity linguistic phenomena and commonsense knowledge. Previous work has shown that pre-trained language models are highly effective at encoding syntactic and semantic…
We provide an overview of the hybrid compositional distributional model of meaning, developed in Coecke et al. (arXiv:1003.4394v1 [cs.CL]), which is based on the categorical methods also applied to the analysis of information flow in…
In data languages the positions of strings and trees carry a label from a finite alphabet and a data value from an infinite alphabet. Extensions of automata and logics over finite alphabets have been defined to recognize data languages,…
Math word problems form a natural abstraction to a range of quantitative reasoning problems, such as understanding financial news, sports results, and casualties of war. Solving such problems requires the understanding of several…
The Semantic Web is becoming a large scale framework that enables data to be published, shared, and reused in the form of ontologies. The ontology which is considered as basic building block of semantic web consists of two layers including…
This thesis investigates how the sub-structure of words can be accounted for in probabilistic models of language. Such models play an important role in natural language processing tasks such as translation or speech recognition, but often…
Functional Distributional Semantics is a recently proposed framework for learning distributional semantics that provides linguistic interpretability. It models the meaning of a word as a binary classifier rather than a numerical vector. In…