Lambda calculus is an influential and extensivelyused notation for describing computable functions, andMind-Mapping is widely used as an expression of radiant thinking via a powerful graphical technique. In this paper, we introduce a completely visual representation based on typed Mind Maps to represent steps of calculation for a pure untyped lambda calculator, VLM. This visual representation has serveral advantages over traditional textual and visual calculators. VLM uses typed Mind Maps for both the lambda calculator input and ouput. Although VLM is designed as a computable typed Mind Maps node of our Typed Mind Maps API project [1], it can also be applied to learning and teaching the concepts of lambda calculus as a visualization of traditional textual rewrite steps. Moreover, the lambda calculus queries and the results of queries are both represented as FreeMind files, and that allows them to be organized and deployed easily. However, the MindMapping of lambda calculus is interesting and elegant in its own right.

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This paper introduces a new Typed Mind Map extension for a data model in a parse-tree-based online referee system with a TDD (Test-Driven Development) model and DALM (DICE adaptive learning model) model named DICE. Typed Mind Maps and a semantic node are defined by OWL-DL. Typed Mind Maps are now widely used in the DICE system as a uniform data model for the system, instructors, learners and materials. The Mind Maps are used for system configuration, system deployment, learner's information, organization of training materials, answer parsing and some widgets. An implementation based on this data model has been working for years in a real teaching and learning environment.

This paper introduces a new Typed Mind Map extension for a data model in a parse-tree-based online referee system with a TDD (Test-Driven Development) model and DALM (DICE adaptive learning model) model named DICE. Typed Mind Maps and a semantic node are defined by OWL-DL. Typed Mind Maps are now widely used in the DICE system as a uniform data model for the system, instructors, learners and materials. The Mind Maps are used for system configuration, system deployment, learner's information, organization of training materials, answer parsing and some widgets. An implementation based on this data model has been working for years in a real teaching and learning environment.

This paper presents an overview of knowledge creation in a t e m q Boolean algebra of classes and binary relations. The knowledge creation process involves both the induction and deduction processes to create the most ''interesting'' IS-A hierarchy of classes.This IS-A hieiarchy will contain "interesting" class containments from which rules may be proposed and verified. These rules are proposed by looking at the "extent", or the set of instances of the class, and noticing that all objects in a class "unexpectedly" satisfy some predicate. If this predicate does not follow from normalizing the other predicates in the "intent" of the class, then a rule can be proposed that all members of thir class satisfy the predicate. A theorem prover may then attempt to prove the predicate from previous rules and the other predicates in the intent. The deeper the proof tree, the more interesting is the rule.