Gradual Classical Logic for Attributed Objects - Extended in Re-Presentation

TL;DR

This paper introduces gradual logic, a formal framework that models attributed objects and their concepts, addressing the limitations of traditional atomic assumptions in logic to better reflect real-world phenomena.

Contribution

It proposes a novel gradual logic that captures the nuanced nature of attributed objects and their concepts, extending formal semantics to include phenomena like presupposition and contraries.

Findings

Logic is mapped onto formal semantics.

Decidability of the logic is demonstrated.

Two linguistically relevant semantics are considered.

Abstract

Our understanding about things is conceptual. By stating that we reason about objects, it is in fact not the objects but concepts referring to them that we manipulate. Now, so long just as we acknowledge infinitely extending notions such as space, time, size, colour, etc, - in short, any reasonable quality - into which an object is subjected, it becomes infeasible to affirm atomicity in the concept referring to the object. However, formal/symbolic logics typically presume atomic entities upon which other expressions are built. Can we reflect our intuition about the concept onto formal/symbolic logics at all? I assure that we can, but the usual perspective about the atomicity needs inspected. In this work, I present gradual logic which materialises the observation that we cannot tell apart whether a so-regarded atomic entity is atomic or is just atomic enough not to be considered non-atomic. The motivation is to capture certain phenomena that naturally occur around concepts with attributes, including presupposition and contraries. I present logical particulars of the logic, which is then mapped onto formal semantics. Two linguistically interesting semantics will be considered. Decidability is shown.