A Well-typed Lightweight Situation Calculus

TL;DR

This paper introduces a lightweight, well-typed version of situation calculus with enhanced typing mechanisms for situations, actions, and objects, ensuring type correctness and soundness in AI dynamic domain modeling.

Contribution

It extends traditional situation calculus by integrating a robust type system and performs rigid type checking to improve correctness and reliability.

Findings

Type system guarantees soundness of situation calculus programs.

Type checking identifies well-typed and ill-typed programs.

The modified calculus is proven to be robust and well-typed.

Abstract

Situation calculus has been widely applied in Artificial Intelligence related fields. This formalism is considered as a dialect of logic programming language and mostly used in dynamic domain modeling. However, type systems are hardly deployed in situation calculus in the literature. To achieve a correct and sound typed program written in situation calculus, adding typing elements into the current situation calculus will be quite helpful. In this paper, we propose to add more typing mechanisms to the current version of situation calculus, especially for three basic elements in situation calculus: situations, actions and objects, and then perform rigid type checking for existing situation calculus programs to find out the well-typed and ill-typed ones. In this way, type correctness and soundness in situation calculus programs can be guaranteed by type checking based on our type system. This modified version of a lightweight situation calculus is proved to be a robust and well-typed system.