Interpretations and Models

What is an Interpretation?

• Logical language ... variables, constants, functions, predicates, etc.
• An interpretation consists of a ...
  • Domain (finite or infinite)
  • Interpretation of ground terms to domain elements
  • Interpretion of closed formulae to {true,false}
• A model interprets given closed formulae to true

Complete, Partial, Strictly Partial

• An interpretation is complete ... it interprets everything
• A partial interpretation might not interpret everything
• A strictly partial interpretation does not interpret everything
• A strictly partial interpretation can be complete for a set

Types of Interpretations

• Herbrand interpretations
• Finite domain interpretations
• Integer and Real interpretations

Extended SZS dataform ontology