Theory blending: extended algorithmic aspects and examples

In Cognitive Science, conceptual blending has been proposed as an important cognitive mechanism that facilitates the creation of new concepts and ideas by constrained combination of available knowledge. It thereby provides a possible theoretical foundation for modeling high-level cognitive faculties such as the ability to understand, learn, and create new concepts and theories. Quite often the development of new mathematical theories and results is based on the combination of previously independent concepts, potentially even originating from distinct subareas of mathematics. Conceptual blending promises to offer a framework for modeling and re-creating this form of mathematical concept invention with computational means. This paper describes a logic-based framework which allows a formal treatment of theory blending (a subform of the general notion of conceptual blending with high relevance for applications in mathematics), discusses an interactive algorithm for blending within the framework, and provides several illustrating worked examples from mathematics

On the Complexity of Specification Morphisms

AbstractThe existence and the construction of a specification morphism between two algebraic specifications is a crucial step in modular system design and in the reusability of software. The problem of determining the existence of a signature morphism between two algebraic signatures is analyzed and proved to be NP-complete by reducing the well known 3SAT problem. As a consequence, the problem of finding a specification morphism is at least as hard as that of verifying its existence

On the Complexity of Specification Morphisms

The existence and the construction of a specification morphism between two algebraic specifications is a crucial step in modular system design and in the reusability of software

On the Complexity of Specification Morphisms

The existence and the construction of a specification morphism between two algebraic specifications is a crucial step in modular system design and in the reusability of software. The problem of determining the existence of a signature morphism between two algebraic signatures is analyzed and proved to be NP-complete by reducing the well known 3SAT problem. As a consequence, the problem of finding a specification morphism is at least as hard as that of verifying its existence.