Assigning Meaning to Proofs: Report by Robert Constable, subtitled `A semantic basis for problem solving environments'. Constable's aim is to use metamathematical results to guide the making of framewroks for constructive logic, as part of the NuPrl project.
Satisfaction: An introduction to the model-theoretic stasfaction relation, by Peter Suber.
The Meanings of Logical Constants: Essay by Gilbert Harman, arguing for Prawitz's approach to the semantics of logic based upon a conceptual role semantics.