Monodic temporal resolution

Until recently, First-Order Temporal Logic (FOTL) has been only partially understood. While it is well known that the full logic has no finite axiomatisation, a more detailed analysis of fragments of the logic was not previously available. However, a breakthrough by Hodkinson et al., identifying a finitely axiomatisable fragment, termed the monodic fragment, has led to improved understanding of FOTL. Yet, in order to utilise these theoretical advances, it is important to have appropriate proof techniques for this monodic fragment.In this paper, we modify and extend the clausal temporal resolution technique, originally developed for propositional temporal logics, to enable its use in such monodic fragments. We develop a specific normal form for monodic formulae in FOTL, and provide a complete resolution calculus for formulae in this form. Not only is this clausal resolution technique useful as a practical proof technique for certain monodic classes, but the use of this approach provides us with increased understanding of the monodic fragment. In particular, we here show how several features of monodic FOTL can be established as corollaries of the completeness result for the clausal temporal resolution method. These include definitions of new decidable monodic classes, simplification of existing monodic classes by reductions, and completeness of clausal temporal resolution in the case of monodic logics with expanding domains, a case with much significance in both theory and practice.

Prototype Generation from Ontology Charts

Semantic Analysis is a business analysis method designed to capture system requirements. While these requirements may be represented as text, the method also advocates the use of Ontology Charts to formally denote the system's required roles, relationships and forms of communication. Following model driven engineering techniques, Ontology Charts can be transformed to temporal Database schemas, class diagrams and component diagrams, which can then be used to produce software systems. A nice property of these transformations is that resulting system design models lend themselves to complicated extensions that do not require changes to the design models. For example, resulting databases can be extended with new types of data without the need to modify the database schema of the legacy system. Semantic Analysis is not widely used in software engineering, so there is a lack of experts in the field and no design patterns are available. This make it difficult for the analysts to pass organizational knowledge to the engineers. This study describes an implementation that is readily usable by engineers, which includes an automated technique that can produce a prototype from an Ontology Chart. The use of such tools should enable developers to make use of Semantic Analysis with minimal expertise of ontologies and MDA.