Visualisation and manipulation tools for Modal logic

Oliver, Martin John (1998). Visualisation and manipulation tools for Modal logic. PhD thesis The Open University.

DOI: https://doi.org/10.21954/ou.ro.0000dc90

Abstract

In this thesis, an investigation into how visualisation and manipulation tools can provide better support for learners of Modal logic is described. Problems associated with learning Modal logic are also researched.

Seven areas topics in Modal logic are investigated, as is the influence of domain independent factors (e. g. motivation) on learning. Studies show that students find concepts such as Modal proofs and systems difficult to learn, whilst possible worlds and Modes are fairly straightforward. Areas such as reference, belief and accessibility relations fall between these extremes.

Two roles for representations in reasoning are identified: providing a concrete domain for students to reason about, and supporting the process of reasoning. Systems which make use of these complementary representations were found to be more effective for learners than either the syntactic or the diagrammatic representations traditionally used to teach Modal logic.

A review of software used to support students learning logic highlights two important features: the use of examples, and automation of routine tasks. A learning environment for Modal logic was designed which incorporated these. The environment was developed using an adapted version of Smalltalk's Model-View-Controller mechanism, and incorporates complementary representations, enhance by direct manipulation.

A further study investigates the added benefits of using this tool, as opposed to using the same representation but working with pen and paper. This confirms the importance of using 'concrete' content representations and minimising learners' cognitive load. Performance measures show that software users learnt more, had a deeper style of learning, and found the topics less abstract than their counterparts working with pen & paper.

This research shows that complementary representations are an effective way of supporting students studying Modal logic, and that visualisation and manipulation tools which incorporate these systems will provide additional benefits for learners.