Recent zbMATH articles in MSC 03B05https://www.zbmath.org/atom/cc/03B052021-04-16T16:22:00+00:00WerkzeugMathematics for computer science. Basic concepts, structures and their applications. 3rd expanded and updated edition.https://www.zbmath.org/1456.680022021-04-16T16:22:00+00:00"Berghammer, Rudolf"https://www.zbmath.org/authors/?q=ai:berghammer.rudolfThis is the third edition of this textbook. For a review of the first edition see [Zbl 1309.00001].
The second edition added two new chapters and an
elaborate appendix giving a formal and complete introduction to the natural numbers based on Peano structures. With these two chapters, important aspects of computer science are addressed, namely those that concern the programming of algorithms. Keywords for the first of these chapters are program specification and verification, Hoare-calculus, loop-invariants and program construction; the second one focuses on generic programming, which is exemplified by several graph-theoretic algorithms, thus also extending concepts of graph theory from a former chapter. The third edition finally adds solutions to all exercises except those for the new chapters, which are available online.
The presentation of the topics is always detailed and in full mathematical rigour, starting with motivating examples and naive concepts, which are
then gradually conducted to full formalization. The reader will find many topics and detailed proofs not often found in other introductory
textbooks. The book is especially valuable for those students of computer science who are interested in a rigorous mathematical foundation.
Reviewer: Dieter Riebesehl (Lüneburg)Relating sequent calculi for bi-intuitionistic propositional logic.https://www.zbmath.org/1456.030222021-04-16T16:22:00+00:00"Pinto, Luís"https://www.zbmath.org/authors/?q=ai:pinto.luis-f"Uustalu, Tarmo"https://www.zbmath.org/authors/?q=ai:uustalu.tarmoSummary: Bi-intuitionistic logic is the conservative extension of intuitionistic logic with a connective dual to implication. It is sometimes presented as a symmetric constructive subsystem of classical logic.
In this paper, we compare three sequent calculi for bi-intuitionistic propositional logic: (1) a basic standard-style sequent calculus that restricts the premises of implication-right and exclusion-left inferences to be single-conclusion resp. single-assumption and is incomplete without the cut rule, (2) the calculus with nested sequents by \textit{R. Goré} et al. [in: Advances in modal logic. Vol. 7. Proceedings of the 7th conference (AiML 2008), Nancy, France, September 9--12, 2008. London: College Publications. 43--66 (2008; Zbl 1244.03157)], where a complete class of cuts is encapsulated into special ``unnest'' rules and (3) a cut-free labelled sequent calculus derived from the Kripke semantics of the logic. We show that these calculi can be translated into each other and discuss the ineliminable cuts of the standard-style sequent calculus.
For the entire collection see [Zbl 1391.03011].Book review of: Lewis Carroll's diaries. The private journals of Charles Lutwidge Dodgson (Lewis Carroll); The logic pamphlets of Charles Lutwidge Dodgson and related pieces.https://www.zbmath.org/1456.000292021-04-16T16:22:00+00:00"Moktefi, Amirouche"https://www.zbmath.org/authors/?q=ai:moktefi.amiroucheReview of [Zbl 1239.01121].Berry's paradox\dots again.https://www.zbmath.org/1456.030142021-04-16T16:22:00+00:00"Priest, Graham"https://www.zbmath.org/authors/?q=ai:priest.grahamSummary: The paper is a discussion of whether Berry's pardox presupposes the principle of excluded middle, with particular reference to the work of Ross Brady.