The problem of algorithmic structuring of proofs in the sequent calculi LK and LKB LK where blocks of quanti ers can be introduced in one step is investigated where a distinction is made between linear proofs and proofs in tree form In this framework structuring coincides with the introduction of cuts into a proof The algorithmic solvability of this problem can be reduced to the question of k l...

This paper looks at proofs concerning Gray codes and the locality of local search; it is shown that in some cases such proofs can be generalized to Binary and real valued encodings, while in other cases such proofs do not hold for Binary encodings. The paper also looks at a modified form of Quad Search that is proven to converge in under 2L evaluations to a global optimum on unimodal 1-D biject...

We use an alternative graphical representation for formulas in implicational intuitionistic logic in order to obtain and demonstrate results concerning provability. We demonstrate the adequateness of the method in this area, showing that one can easily recognize and prove new results and simplify the proofs of others. As such, we extend a known class of formulas for which uniqueness of -normal ...

In this handout, we discuss two fundamental techniques of mathematical argument which will be used frequently in the course: proof by contradiction, which is fairly straightforward, and proof by mathematical induction, which is a little more subtle. We give some illustrative applications to graph theory. We shall also give an appendix concerning some subtleties behind the notion of mathematical...