In this continuation of lecture09, we discuss the foundations behind automated theorem provers for first-order logic. We describe a procedure that, given enough time, will prove any valid formula of first-order logic.

Graphs as Interpretations

Isomorphism of Interpretations

Normal Forms for First-Order Logic

Preliminary Discussion on Models

Ground Terms

Herbrand's Expansion Theorem

Semidecision Procedure for First-Order Logic (without Equality)

Compactness for First-Order Logic

Continued in lecture11.