LP=>: Extending LP with a strong conditional operator

TL;DR

This paper introduces 'strong LP,' an extension of LP with a powerful conditional operator that enhances its ability to express consistency but also raises concerns about trivializing paradoxes.

Contribution

It proposes a novel extension of LP called 'strong LP' with a strong conditional operator, expanding its expressive power.

Findings

Enhanced ability to express consistency distinctions

Potential for trivializing logical paradoxes

New logical properties introduced by the strong conditional

Abstract

We augment LP with a strong conditional operator, to yield a logic we call "strong LP," or LP=>. The resulting logic can speak of consistency in more discriminating ways, but introduces new possibilities for trivializing paradoxes.