This page is intended to contain an alphabetical list of propositional and predicate logics that have been investigated in the published literature.

This list is still very much under construction, so feel free to add further logics, and to add information about individual entries.

Many of the propositional logics on this page have algebraic semantics given by a class of structures on the main page. Algebraic logic is the area that investigates the connections between logics and their algebraic counterparts.

1. Arrow logic
2. Basic logic
3. BCI logic
4. BCK logic
5. Classical full Lambek calculus
6. Classical propositional logic
7. Classical predicate logic
8. First order logic
9. Full Lambek calculus
10. Full Lambek calculus with contraction
11. Full Lambek calculus with exchange
12. Full Lambek calculus with weakening
13. Goedel logic
14. Intuitionistic logic
15. Intuitionistic multiplicative additive linear logic
16. Linear logic
17. Lukasiewicz logic
18. Modal logic K
19. Modal logic T
20. Modal logic S4
21. Modal logic S5
22. Multiplicative additive linear logic
23. Multivalued logic
24. Orthologic
25. Quantum computational logic
26. Quantum logic
27. Positive modal logic
28. Product logic
29. Relevance logic
30. Substructural logic
31. Temporal logic
32. Tense logic