DeepAI
Log In Sign Up

On the Semantics of Intensionality and Intensional Recursion

12/26/2017
by   G. A. Kavvos, et al.
0

Intensionality is a phenomenon that occurs in logic and computation. In the most general sense, a function is intensional if it operates at a level finer than (extensional) equality. This is a familiar setting for computer scientists, who often study different programs or processes that are interchangeable, i.e. extensionally equal, even though they are not implemented in the same way, so intensionally distinct. Concomitant with intensionality is the phenomenon of intensional recursion, which refers to the ability of a program to have access to its own code. In computability theory, intensional recursion is enabled by Kleene's Second Recursion Theorem. This thesis is concerned with the crafting of a logical toolkit through which these phenomena can be studied. Our main contribution is a framework in which mathematical and computational constructions can be considered either extensionally, i.e. as abstract values, or intensionally, i.e. as fine-grained descriptions of their construction. Once this is achieved, it may be used to analyse intensional recursion.

READ FULL TEXT

page 1

page 2

page 3

page 4

05/30/2021

A Rice's Theorem for Abstract Semantics

Classical results in computability theory, notably Rice's theorem, focus...
02/12/2021

On Signings and the Well-Founded Semantics

In this note, we use Kunen's notion of a signing to establish two theore...
04/29/2021

Axiomatizations and Computability of Weighted Monadic Second-Order Logic

Weighted monadic second-order logic is a weighted extension of monadic s...
04/29/2020

Leveraging Declarative Knowledge in Text and First-Order Logic for Fine-Grained Propaganda Detection

We study the detection of propagandistic text fragments in news articles...
07/17/2021

A proof theoretic basis for relational semantics

Logic has proved essential for formally modeling software based systems....
08/19/2022

On computing Discretized Ricci curvatures of graphs: local algorithms and (localized) fine-grained reductions

Characterizing shapes of high-dimensional objects via Ricci curvatures p...