Intensional FOL: Many-Sorted Extension

TL;DR

This paper extends Intensional First-Order Logic (IFOL) to a many-sorted version, aligning it with natural language's inherent many-sorted nature to enhance its applicability in language-based applications.

Contribution

The paper introduces a many-sorted extension of IFOL, addressing the natural language's implicit many-sorted structure for improved practical application.

Findings

Successfully formalizes many-sorted IFOL

Aligns IFOL with natural language structures

Prepares IFOL for language-based applications

Abstract

The concepts used in IFOL have associated to them a list of sorted attributes, and the sorts are the intensional concepts as well. The requirement to extend the unsorted IFOL (Intensional FOL) to many-sorted IFOL is mainly based on the fact that a natural language is implicitly many-sorted and that we intend to use IFOL to support applications that use natural languages. Thus, the proposed version of many-sorted IFOL is just the completion of this conceptual feature of the IFOL.