Logic Computation And Rigorous Methods

This Festschrift was published in honor of Egon Börger on the occasion of his 75th birthday. It acknowledges Prof. Börger's inspiration as a scientist, author, mentor, and community organizer. Dedicated to a pioneer in the fields of logic and computer science, Egon Börger's research interests are unusual in scope, from programming languages to hardware architectures, software architectures, control systems, workflow and interaction patterns, business processes, web applications, and concurrent systems. The 18 invited contributions in this volume are by leading researchers in the areas of software engineering, programming languages, business information systems, and computer science logic.

This book constitutes the refereed proceedings of the 9th International Conference on Rigorous State-Based Methods, ABZ 2023, held in Nancy, France, in May 2023. The 12 full and 7 short papers included in this volume were carefully reviewed and selected from 47 submissions. The proceedings also include 4 PhD symposium contributions. They deal with state-based and machine-based formal methods, mainly Abstract State Machines (ASM), Alloy, B, TLA+, VDM, and Z.

An introduction to applying predicate logic to testing and verification of software and digital circuits that focuses on applications rather than theory. Computer scientists use logic for testing and verification of software and digital circuits, but many computer science students study logic only in the context of traditional mathematics, encountering the subject in a few lectures and a handful of problem sets in a discrete math course. This book offers a more substantive and rigorous approach to logic that focuses on applications in computer science. Topics covered include predicate logic, equation-based software, automated testing and theorem proving, and large-scale computation. Formalism is emphasized, and the book employs three formal notations: traditional algebraic formulas of propositional and predicate logic; digital circuit diagrams; and the widely used partially automated theorem prover, ACL2, which provides an accessible introduction to mechanized formalism. For readers who want to see formalization in action, the text presents examples using Proof Pad, a lightweight ACL2 environment. Readers will not become ALC2 experts, but will learn how mechanized logic can benefit software and hardware engineers. In addition, 180 exercises, some of them extremely challenging, offer opportunities for problem solving. There are no prerequisites beyond high school algebra. Programming experience is not required to understand the book's equation-based approach. The book can be used in undergraduate courses in logic for computer science and introduction to computer science and in math courses for computer science students.

This book introduces the notions and methods of formal logic from a computer science standpoint, covering propositional logic, predicate logic, and foundations of logic programming. The classic text is replete with illustrative examples and exercises. It presents applications and themes of computer science research such as resolution, automated deduction, and logic programming in a rigorous but readable way. The style and scope of the work, rounded out by the inclusion of exercises, make this an excellent textbook for an advanced undergraduate course in logic for computer scientists.

This Festschrift, dedicated to Reiner Hähnle on the occasion of his 60th birthday, contains papers written by many of his closest collaborators. After positions at Karlsruhe Institute of Technology and Chalmers University of Technology, since 2011 Reiner has been the chaired professor of Software Engineering at Technische Universität Darmstadt, where his team focuses on the formal verification of object-oriented software, the formal modeling and specification of highly adaptive software systems, and formal modeling and analysis in domains such as biological systems and railroad operations. His work is characterized by achievements in theory and in practical implementations, significant collaborations include the KeY project and the development of the ABS language. He has served as chair and editor of important related academic conferences, and coauthored almost 200 academic publications. The contributions in this volume reflect Reiner’s main research focus: formal methods, in particular applied to software verification.

Structures of Computing explains the behavioral meaning of fundamental concepts of computing from a practical viewpoint and in generic terms, unrestricted by specific computing devices or programming languages. To compute is understood as processing structures by a set of cooperating agents each of which executes an algorithm assigned to it and interacts with the other agents. Part I of the book defines the conceptual constituents of interactive processes: (i) data, i.e. structured objects with associated properties, relations and functions the algorithmic processes operate upon, (ii) basic operations that affect the data in single execution steps, and (iii) control mechanisms that determine the combination of single steps in multi-agent computations where the interaction happens via communication or other forms of data sharing. Part II analyses these constituents concerning (i) methods to achieve process correctness (inspection, experimental validation, reasoning), (ii) principal computational paradigms (architectures, programming styles, communication structures, control patterns from sequential and reflective to concurrent, mixed synchronous/asynchronous and data flow control), and (iii) complexity (power and limits of computing structures). The book is mainly addressed to students and professionals who want to understand the conceptual foundation of computing. It does not assume any specific programming experience but only a basic understanding of what are mechanically executable processes and their descriptions. Any unnecessary formalism is thus avoided, and definitions are formulated as much as possible in natural language, using common mathematical notation only where needed to prevent ambiguities. Numerous examples and exercises serve as comprehension checkpoints.

ACM Monograph Series: A Computational Logic focuses on the use of induction in proving theorems, including the use of lemmas and axioms, free variables, equalities, and generalization. The publication first elaborates on a sketch of the theory and two simple examples, a precise definition of the theory, and correctness of a tautology-checker. Topics include mechanical proofs, informal development, formal specification of the problem, well-founded relations, natural numbers, and literal atoms. The book then examines the use of type information to simplify formulas, use of axioms and lemmas as rewrite rules, and the use of definitions. Topics include nonrecursive functions, computing values, free variables in hypothesis, infinite backwards chaining, infinite looping, computing type sets, and type prescriptions. The manuscript takes a look at rewriting terms and simplifying clauses, eliminating destructors and irrelevance, using equalities, and generalization. Concerns include reasons for eliminating isolated hypotheses, precise statement of the generalization heuristic, restricting generalizations, precise use of equalities, and multiple destructors and infinite looping. The publication is a vital source of data for researchers interested in computational logic.