Dana Scott
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View article: Notes on Gödel’s and Scott’s variants of the ontological argument
Notes on Gödel’s and Scott’s variants of the ontological argument Open
Notes on Kurt Gödel’s modal ontological argument and Dana Scott’s variant of it are presented. These remarks, supported by experimental studies with a proof assistant system for classical higher-order logic, implicitly answer some question…
View article: Category Theory in Isabelle/HOL as a Basis for Meta-logical Investigation
Category Theory in Isabelle/HOL as a Basis for Meta-logical Investigation Open
This paper presents meta-logical investigations based on category theory using the proof assistant Isabelle/HOL. We demonstrate the potential of a free logic based shallow semantic embedding of category theory by providing a formalization …
View article: Interpreting Lambda Calculus in Domain-Valued Random Variables
Interpreting Lambda Calculus in Domain-Valued Random Variables Open
We develop Boolean-valued domain theory and show how the lambda-calculus can be interpreted in using domain-valued random variables. We focus on the reflexive domain construction rather than the language and its semantics. The notion of eq…
View article: Computer-Supported Exploration of a Categorical Axiomatization of Modeloids
Computer-Supported Exploration of a Categorical Axiomatization of Modeloids Open
A modeloid, a certain set of partial bijections, emerges from the idea to abstract from a structure to the set of its partial automorphisms. It comes with an operation, called the derivative, which is inspired by Ehrenfeucht-Fraïssé games.…
View article: A Homological Theory of Functions: Nonuniform Boolean Complexity Separation and VC Dimension Bound Via Algebraic Topology, and a Homological Farkas Lemma
A Homological Theory of Functions: Nonuniform Boolean Complexity Separation and VC Dimension Bound Via Algebraic Topology, and a Homological Farkas Lemma Open
In computational complexity, a complexity class is given by a set of problems or functions, and a basic challenge is to show separations of complexity classes A != B especially when A is known to be a subset of B. In this paper we introduc…
View article: CAN MODALITIES SAVE NAIVE SET THEORY?
CAN MODALITIES SAVE NAIVE SET THEORY? Open
To the memory of Prof. Grigori Mints, Stanford University Born: June 7, 1939, St. Petersburg, Russia Died: May 29, 2014, Palo Alto, California
View article: Axiomatizing Category Theory in Free Logic
Axiomatizing Category Theory in Free Logic Open
Starting from a generalization of the standard axioms for a monoid we present a stepwise development of various, mutually equivalent foundational axiom systems for category theory. Our axiom sets have been formalized in the Isabelle/HOL in…