A calculus for the common rules of \(\wedge\) and \(\vee\) (Q918952)

Let \(\vdash^*\) denote the common sequential rules for \(\wedge\) and \(\vee\). Let \(\vdash^{\wedge}\) denote the sequential rules for \(\wedge\), and \(\vdash^{\vee}\) denote those for \(\vee\). The author's main questions are: (a) Is \(\vdash^*\) finitely based?, and: (b) Are \(\vdash^{\wedge}\) and \(\vdash^{\vee}\) the only proper non-trivial strengthenings of \(\vdash^*?\) As his work shows: ``Both questions have a positive answer, but the proofs are not as easy as one might expect.'' But his work has far greater theoretical and technical interest than these two questions about \(\wedge\) and \(\vee\) might indicate. He indicates how such question might be of interest to computer science. His work brings out that there are challenging problems in the area of asking analogous questions for other dual operators.