Andrew Gordon and I are working on a book explicating a fairly large theory
of commonsense psychology. In writing the axioms for the cognitive
theories, we used many predicates or concepts from noncognitive background
theories. Having completed a first draft of the cognitive theories,
we went back and axiomatized the background theories, in what we hope is
a spare and coherent style. These theories cover such phenomena as sets,
composite entities, scales, change, causality, time, event structure, and
so on. The sixteen chapters on the background theories are as follows:
B1. Eventualities and their Structure
B2. Traditional Set Theory
B3. Substitution, Typical Elements,
and Instances
B4. Logic Reified
B5. Functions and Sequences
B6. Composite Entities
B7. Defeasibility
B8. Scales
B9. Arithmetic
B10. Change of State
B11. Causality
B12. Time
B13. Event Structure
B14. Space
B15. Persons
B16. Modality
Appendix on First-Order Logic