Order-Sorted Intensional Logic: Expressing Subtyping Polymorphism with Typing Assertions and Quantification over Concepts

Abstract

Subtyping, also known as subtype polymorphism, is a concept extensively studied in programming language theory, delineating the substitutability relation among datatypes. This property ensures that programs designed for supertype objects remain compatible with their subtypes. In this paper, we explore the capability of order-sorted logic for utilizing these ideas in the context of Knowledge Representation. We recognize two fundamental limitations: First, the inability of this logic to address the concept rather than the value of non-logical symbols, and second, the lack of language constructs for constraining the type of terms. Consequently, we propose guarded order-sorted intensional logic, where guards are language constructs for annotating typing information and intensional logic provides support for quantification over concepts.