Logic, Individuals and Concepts

TL;DR

This paper explores the relationship between descriptions, variable concepts, and their syntax and semantics, proposing a framework for indexed concepts evaluated within a computational environment, aiming to aid programming tool design.

Contribution

It extends the notion of concepts to include syntax and semantics, introducing indexed concepts evaluated in a parameterized environment for conceptual programming.

Findings

Concepts are extended to include syntax and semantics.

Indexed concepts are introduced and evaluated in a computational environment.

The object-as-functor idea aids in designing conceptual programming tools.

Abstract

This extended abstract gives a brief outline of the connections between the descriptions and variable concepts. Thus, the notion of a concept is extended to include both the syntax and semantics features. The evaluation map in use is parameterized by a kind of computational environment, the index, giving rise to indexed concepts. The concepts are inhabited into language by the descriptions from the higher order logic. In general the idea of object-as-functor should assist the designer to outline a programming tool in conceptual shell style.