Related papers: Sense, reference, and computation
This paper introduces Relational Type Theory (RelTT), a new approach to type theory with extensionality principles, based on a relational semantics for types. The type constructs of the theory are those of System F plus relational…
${\rm CTT}_{\rm qe}$ is a version of Church's type theory that includes quotation and evaluation operators that are similar to quote and eval in the Lisp programming language. With quotation and evaluation it is possible to reason in ${\rm…
Mathematicians and philosophers have appealed to categoricity arguments in a surprisingly varied range of contexts. One familiar example calls on second-order categoricity in an attempt to show that the Continuum Hypothesis, despite its…
Language representation models such as BERT could effectively capture contextual semantic information from plain text, and have been proved to achieve promising results in lots of downstream NLP tasks with appropriate fine-tuning. However,…
In this paper we study a new approach to classify mathematical theorems according to their computational content. Basically, we are asking the question which theorems can be continuously or computably transferred into each other? For this…
This article is a fundamental study in computable measure theory. We use the framework of TTE, the representation approach, where computability on an abstract set X is defined by representing its elements with concrete "names", possibly…
Despite the superior performance of Large Reasoning Models (LRMs), their reasoning behaviors are often counterintuitive, leading to suboptimal reasoning capabilities. To theoretically formalize the desired reasoning behaviors, this paper…
We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…
We propose a new type of self-aware systems inspired by ideas from higher-order theories of consciousness. First, we discussed the crucial distinction between introspection and reflexion. Then, we focus on computational reflexion as a…
Computability theory is a discipline in the intersection of computer science and mathematical logic where the fundamental question is: given two mathematical objects X and Y, does X compute Y in principle? In case X and Y are real numbers,…
Computational measures of semantic similarity between geographic terms provide valuable support across geographic information retrieval, data mining, and information integration. To date, a wide variety of approaches to geo-semantic…
We propose RT (Refine Thought), a method that can enhance the semantic rea-soning ability of text embedding models. The method obtains the final semanticrepresentation by running multiple forward passes of the text embedding…
A new viewpoint of the G\"odel's incompleteness theorem be given in this article which reveals the deep relationship between the logic and computation. Upon the results of these studies, an algorithm be given which shows how to search a…
The standard treatment of sets and definable classes in first-order Zermelo-Fraenkel set theory accords in many respects with the Fregean foundational framework, such as the distinction between objects and concepts. Nevertheless, in set…
Sentence embedding is an important research topic in natural language processing. It is essential to generate a good embedding vector that fully reflects the semantic meaning of a sentence in order to achieve an enhanced performance for…
The literature dealing with G\"{o}del's legacy is largely preoccupied with challenging his philosophical views, regarding them as outdated. We believe that such an approach prevents us from seeing G\"{o}del's views in the right light and…
In this paper we propose an interpretation for self-referential propositions in a "meta-model" N* of ZF. This meta-model N* is considered as an informal model of arithmetic that mathematicians often use when working with number theory.…
Automatic evaluation comparing candidate translations to human-generated paraphrases of reference translations has recently been proposed by Freitag et al. When used in place of original references, the paraphrased versions produce metric…
Almost from the inception of Hilbert's program, foundational and structural efforts in proof theory have been directed towards the goal of clarifying the computational content of modern mathematical methods. This essay surveys various…
With the rapid growth of the scientific literature, manually selecting appropriate citations for a paper is becoming increasingly challenging and time-consuming. While several approaches for automated citation recommendation have been…