Semantic Dimension

The system is intended to store propositions like, ``All gods are present everywhere.'', ``All gods are present somewhere.'', ``Some gods are present everywhere.'', ``No gods are present somewhere.'', ``Some gods are present somewhere.'', etc. These propositions surely cannot be held together in a single belief system. But they should be stored and talked about, just as such propositions exist in this composition. One clear way to achieve the possibility of storing multiple epistemologies and ontologies of this kind is to build a database system that has distinct layers in its kernel. It should be possible to have a layer where ground level propositions exist without `interaction' between them, hence even contradictory or false propositions can be stored. This layer therefore will not have semantic constraints. Another layer that takes the propositional `atoms' and combines them with semantic constraints to eliminate contradictions so as to build a system that is implicitly consistent. But even at this layer, it should be possible to combine propositions to form a system without checking for consistency. After all we harbor inconsistent belief systems and we need to engage in a discourse about them. This requires that a second layer of the kernel that builds the systems contains only constraints of logical connectives (like `and', `or', `implies' etc.) without checking for consistency. The kernel therefore needs another layer where consistency is imposed.

Based on these requirements, I propose, we build a knowledge base with component classes that can instantiate objects into three different layers:

Layer 1 of Well Formed Formulae (WFF):

A comprehensive, flexible, and extendable logical core layer to store well formed formulae that are completely neutral to epistemologies and ontologies.

Layer 2 of Implicitly Structured Systems (ISS):

A mechanism to compose the well formed formulae expressed in the above layers using logical connectives, quantifiers, and modalities, propositional attitudes etc. Consistency is implicit, but not explicitly imposed by the system.

Layer 3 of Consistently Structured Systems (CSS):

Similar to the second layer, but with explicitly imposed validity constraints resulting consistent systems. All the consistent systems are defined only in relation to an explicit set of semantic rules internal to the system.

By composing the elements from Layer 1 while expressing the elements of Layers 2 and 3, we can represent belief systems with varying degrees of consistency without any conflicting interaction between them, for each system can be instantiated as independent objects in the knowledge base. Several such systems with independent semantics can be stored in a single knowledge base or in a collection of distributed systems over the Internet to form a semantic grid, to express multiple epistemologies and ontologies. A meta-discourse about the semantic matching or mismatching between structures can be made possible by using them as the terms and the predicates from upper ontology (Metatype level).