A Hierarchical Situation Calculus

TL;DR

This paper introduces a hierarchical situation calculus that addresses the frame problem for modular, multi-level situations using relational, functional, and modal logic forms, enabling structured reasoning about complex situations.

Contribution

It presents a novel formalism for hierarchical situations in the situation calculus, with multiple logic representations and levels, enhancing modular reasoning capabilities.

Findings

Six versions of the formalism for different hierarchy levels

Ability to impose additional structure via equations between parts

Comparison with existing approaches in the literature

Abstract

A situation calculus is presented that provides a solution to the frame problem for hierarchical situations, that is, situations that have a modular structure in which parts of the situation behave in a relatively independent manner. This situation calculus is given in a relational, functional, and modal logic form. Each form permits both a single level hierarchy or a multiple level hierarchy, giving six versions of the formalism in all, and a number of sub-versions of these. For multiple level hierarchies, it is possible to give equations between parts of the situation to impose additional structure on the problem. This approach is compared to others in the literature.