Related papers: Sense, reference, and computation
In the paper I check approaches to identity in mathematics by Plato, Frege, and Geach against Category theory.
Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…
The history of computability theory and and the history of analysis are surprisingly intertwined since the beginning of the twentieth century. For one, \'Emil Borel discussed his ideas on computable real number functions in his introduction…
Reverse mathematics studies which subsystems of second order arithmetic are equivalent to key theorems of ordinary, non-set-theoretic mathematics. The main philosophical application of reverse mathematics proposed thus far is foundational…
We define a class of computable functions over real numbers using functional schemes similar to the class of primitive and partial recursive functions defined by G\"odel and Kleene. We show that this class of functions can also be…
Modelling compositional meaning for sentences using empirical distributional methods has been a challenge for computational linguists. We implement the abstract categorical model of Coecke et al. (arXiv:1003.4394v1 [cs.CL]) using data from…
To adequately model mathematical arguments the analyst must be able to represent the mathematical objects under discussion and the relationships between them, as well as inferences drawn about these objects and relationships as the…
Martin-L\"of's Intuitionistic Theory of Types is becoming popular for formal reasoning about computer programs. To handle recursion schemes other than primitive recursion, a theory of well-founded relations is presented. Using primitive…
This paper investigates some issues arising in categorical models of reversible logic and computation. Our claim is that the structural (coherence) isomorphisms of these categorical models, although generally overlooked, have decidedly…
Existing formalisms for the algebraic specification and representation of networks of reversible agents suffer some shortcomings. Despite multiple attempts, reversible declensions of the Calculus of Communicating Systems (CCS) do not offer…
This is a short paper about the relationship between logic and computation. More specifically, it is about a relationship between the completeness proof for intuitionistic propositional logic within the form of proof-theoretic semantics…
Shared reference is an essential aspect of meaning. It is also indispensable for the semantic web, since it enables to weave the global graph, i.e., it allows different users to contribute to an identical referent. For example, an essential…
People are often entities of interest in tasks such as search and information extraction. In these tasks, the goal is to find as much information as possible about people specified by their name. However in text, some of the references to…
We prove a number of results motivated by global questions of uniformity in computability theory, and universality of countable Borel equivalence relations. Our main technical tool is a game for constructing functions on free products of…
The mathematical formalism of quantum theory has been successfully used in human cognition to model decision processes and to deliver representations of human knowledge. As such, quantum cognition inspired tools have improved technologies…
This study investigates the potential influence of Herman Melville reading on his own writings through computational semantic similarity analysis. Using documented records of books known to have been owned or read by Melville, we compare…
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…
We show that arithmetical transfinite recursion is equivalent to a suitable formalization of the following: For every ordinal $\alpha$ there exists an ordinal $\beta$ such that $1+\beta\cdot(\beta+\alpha)$ (ordinal arithmetic) admits an…
To enable the study of open sets in computational approaches to mathematics, lots of extra data and structure on these sets is assumed. For both foundational and mathematical reasons, it is then a natural question, and the subject of this…
Factual consistency is one of important summary evaluation dimensions, especially as summary generation becomes more fluent and coherent. The ESTIME measure, recently proposed specifically for factual consistency, achieves high correlations…