Modal and Relevance Logics for Qualitative Spatial Reasoning

Abstract

Qualitative Spatial Reasoning (QSR) is an alternative technique to represent spatial relations without using numbers. Regions and their relationships are used as qualitative terms. Mostly peer qualitative spatial reasonings has two aspect: (a) the first aspect is based on inclusion and it focuses on the ”part-of” relationship. This aspect is mathematically covered by mereology. (b) the second aspect focuses on topological nature, i.e., whether they are in ”contact” without having a common part. Mereotopology is a mathematical theory that covers these two aspects. The theoretical aspect of this thesis is to use classical propositional logic with non-classical relevance logic to obtain a logic capable of reasoning about Boolean algebras i.e., the mereological aspect of QSR. Then, we extended the logic further by adding modal logic operators in order to reason about topological contact i.e., the topological aspect of QSR. Thus, we name this logic Modal Relevance Logic (MRL). We have provided a natural deduction system for this logic by defining inference rules for the operators and constants used in our (MRL) logic and shown that our system is correct. Furthermore, we have used the functional programming language and interactive theorem prover Coq to implement the definitions and natural deduction rules in order to provide an interactive system for reasoning in the logic.