Logic for Computer Science

Today, in my reading,  I came across the following:

The only kind of logic necessary in computer science is the predicate calculus, used in the rigorous yet "informal" way of the working mathematician, but perhaps reformulated and extended by useful theorems in the direction presently being investigated by Dijkstra. Formalisms requiring a separate "proof system" or bearing the "formal logician's trademark" should be viewed rather critically.

R. T. Boute, On the Shortcomings of the Axiomatic Approach as presently used in Computer Science, Proc. IEEE COMPEURO 88, System Design: concepts, methods and tools, pp. 184-193, April 1988.

[By the "formal logician's trademark" Boute means the turnstile symbol.]