Vivid knowledge refers to a specific kind of knowledge representation

Knowledge representation

Knowledge representation is an area of artificial intelligence research aimed at representing knowledge in symbols to facilitate inferencing from those knowledge elements, creating new elements of knowledge...

.

The idea of a vivid knowledge base is to get an interpretation mostly straightforward out of it – it implies the interpretation. Thus, any query to such a knowledge base

Knowledge base

A knowledge base is a special kind of database for knowledge management. A Knowledge Base provides a means for information to be collected, organised, shared, searched and utilised.-Types:...

 can be reduced to a database

Database

A database is an organized collection of data for one or more purposes, usually in digital form. The data are typically organized to model relevant aspects of reality , in a way that supports processes requiring this information...

-like query.

Propositional knowledge base

A propositional knowledge base

Knowledge base

A knowledge base is a special kind of database for knowledge management. A Knowledge Base provides a means for information to be collected, organised, shared, searched and utilised.-Types:...

 KB is vivid iff KB is a complete and consistent set of literals

Literal (mathematical logic)

In mathematical logic, a literal is an atomic formula or its negation.The definition mostly appears in proof theory , e.g...

 (over some vocabulary).

Such a knowledge base has the property that it as exactly one interpretation, i.e. the interpretation is unique. A check for entailment of a sentence can simply been breaked down into its literals and those can be answered by a simple database-like check of KB.

First-order knowledge base

A first-order

First-order logic

First-order logic is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first-order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic...

knowledge base KB is vivid iff for some finite set of positive function-free ground literals KB⁺,

KB = KB⁺ ∪ Negations ∪ DomainClosure ∪ UniqueNames,

whereby

Negations ≔ { ¬p | p is atomic and KB ⊭ p },

DomainClosure ≔ { (c_i ≠ c_j) | c_i, c_j are distinct constants },

UniqueNames ≔ { ∀x: (x = c₁) ∨ (x = c₂) ∨ ..., where the c_i are all the constants in KB⁺ }.

All interpretations of a vivid first-order knowledge base are isomorphic.