5.1 Basic Semantic Concepts

This section discusses the most important aspects of the semantics of first-order logic. The two central concepts introduced are those of first-order model and truth in a model. Intuitively, we perceive of first-order formulas as descriptions of certain situations. First order models correspond to such situations, in which given descriptions may be true or false.

• 5.1.1 Models

• 5.1.2 An Example Model

• 5.1.3 Satisfaction, Assignments

• 5.1.4 Interpretations and Variant Assignments

• 5.1.5 The Satisfaction Definition

• 5.1.6 Truth in a Model

• 5.1.7 Validities

• 5.1.8 Valid Arguments

• 5.1.9 Calculi