Related papers: Self-reference Upfront: A Study of Self-referentia…
Verifying mathematical proofs is difficult, but can be automated with the assistance of a computer. Autoformalization is the task of automatically translating natural language mathematics into a formal language that can be verified by a…
If a semantically open language has no constraints on self-reference, one can prove an absurdity. The argument utilizes co-referring names 'a0' and 'a1', and the definition of a functional expression 'The reflection of x = y'. The…
Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…
This paper describes the design and implementation of mechanisms for light-weight inclusion of formal mathematics in informal mathematical writings, particularly in a Web-based setting. This is conceptually done in three stages: (i) by…
We examine whether self-supervised language modeling applied to mathematical formulas enables logical reasoning. We suggest several logical reasoning tasks that can be used to evaluate language models trained on formal mathematical…
Recommender systems are ubiquitous in on-line services to drive businesses. And many sequential recommender models were deployed in these systems to enhance personalization. The approach of using the transformer decoder as the sequential…
Language models (LMs) have exhibited exceptional versatility in reasoning and in-depth financial analysis through their proprietary information processing capabilities. Previous research focused on evaluating classification performance…
In this paper we study empirically the validity of measures of referential success for referring expressions involving gradual properties. More specifically, we study the ability of several measures of referential success to predict the…
A model for reference use in communication is proposed, from a representationist point of view. Both the sender and the receiver of a message handle representations of their common environment, including mental representations of objects.…
Living systems exhibit a range of fundamental characteristics: they are active, self-referential, self-modifying systems. This paper explores how these characteristics create challenges for conventional scientific approaches and why they…
In the article 'Ordinal Logics and the Characterizations of the Informal Concept of Proof', Georg Kreisel poses the problem of assigning unique notations to recursive ordinals, and additionally suggests that the methods which are developed…
G\"odel's second incompleteness theorem is standardly understood as showing that no sufficiently strong, consistent theory of arithmetic can prove its own consistency, a result typically interpreted against a model-theoretic background in…
Lexical features are a major source of information in state-of-the-art coreference resolvers. Lexical features implicitly model some of the linguistic phenomena at a fine granularity level. They are especially useful for representing the…
Reference models in form of best practices are an essential element to ensured knowledge as design for reuse. Popular modeling approaches do not offer mechanisms to embed reference models in a supporting way, let alone a repository of it.…
Incomputability results in Formal Logic and the Theory of Computation (i.e., incompleteness and undecidability) have deep implications for the foundations of mathematics and computer science. Likewise, Social Choice Theory, a branch of…
We take an argument of G\"odel's from his ground-breaking 1931 paper, generalize it, and examine its validity. The argument in question is this: the sentence $G$ says about itself that it is not provable, and $G$ is indeed not provable;…
For any system with limited statistical knowledge, the combination of evidence and the interpretation of sampling information require the determination of the right reference class (or of an adequate one). The present note (1) discusses the…
The convergence of deep learning and formal mathematics has spurred research in formal verification. Statement autoformalization, a crucial first step in this process, aims to translate informal descriptions into machine-verifiable…
We consider an extension of first-order logic with a recursion operator that corresponds to allowing formulas to refer to themselves. We investigate the obtained language under two different systems of semantics, thereby obtaining two…
Mathematics formalisation is the task of writing mathematics (i.e., definitions, theorem statements, proofs) in natural language, as found in books and papers, into a formal language that can then be checked for correctness by a program. It…