This book constitutes the strictly refereed post-workshop proceedings of the 11th International Workshop on Computer Science Logic, CSL '97, held as the 1997 Annual Conference of the European Association on Computer Science Logic, EACSL, in Aarhus, Denmark, in August 1997. The volume presents 26 revised full papers selected after two rounds of refereeing from initially 92 submissions; also included are four invited papers. The book addresses all current aspects of computer science logics and its applications and thus presents (...) the state of the art in the area. (shrink)

These are the proceedings of the First International Conference on Compu- tional Logic (CL 2000) which was held at Imperial College in London from 24th to 28th July, 2000. The theme of the conference covered all aspects of the theory, implementation, and application of computational logic, where computational logic is to be understood broadly as the use of logic in computer science. The conference was collocated with the following events: { 6th International Conference on Rules and (...) Objects in Databases (DOOD 2000) { 10th International Workshop on Logic-based Program Synthesis and Tra- formation (LOPSTR 2000) { 10th International Conference on Inductive Logic Programming (ILP 2000). CL 2000 consisted of seven streams: { Program Development (LOPSTR 2000) { Logic Programming: Theory and Extensions { Constraints { Automated Deduction: Putting Theory into Practice { Knowledge Representation and Non-monotonic Reasoning { Database Systems (DOOD 2000) { Logic Programming: Implementations and Applications. The LOPSTR 2000 workshop constituted the program development stream and the DOOD 2000 conference constituted the database systems stream. Each stream had its own chair and program committee, which autonomously selected the papers in the area of the stream. Overall, 176 papers were submitted, of which 86 were selected to be presented at the conference and appear in these proceedings. The acceptance rate was uniform across the streams. In addition, LOPSTR 2000 accepted about 15 extended abstracts to be presented at the conference in the program development stream. (shrink)

This book constitutes the refereed proceedings of the 5th Kurt Gödel Colloquium on Computational Logic and Proof Theory, KGC '97, held in Vienna, Austria, in August 1997. The volume presents 20 revised full papers selected from 38 submitted papers. Also included are seven invited contributions by leading experts in the area. The book documents interdisciplinary work done in the area of computer science and mathematical logics by combining research on provability, analysis of proofs, proof search, and complexity.

In this paper we solve the problem how to axiomatize a system of quantum computational gates known as the Poincaré irreversible quantum computational system. A Hilbert-style calculus is introduced obtaining a strong completeness theorem.

Reflecting Alan Robinson's fundamental contribution to computational logic, this book brings together seminal papers in inference, equality theories, and logic programming. It is an exceptional collection that ranges from surveys of major areas to new results in more specialized topics. Alan Robinson is currently the University Professor at Syracuse University. Jean-Louis Lassez is a Research Scientist at the IBM Thomas J. Watson Research Center. Gordon Plotkin is Professor of Computer Science at the University of Edinburgh. Contents: Inference. Subsumption, (...) A Sometimes Undervalued Procedure, Larry Wos, Ross Overbeek, and Ewing Lusk. The Markgraf Karl Refutation Procedure, Hans Jurgen Ohlbach and Jorg H. Siekmann. Modal Logic Should Say More than it Does, Melvin Fitting. Interactive Proof Presentation, W. W. Bledsoe. Intelligent Backtracking Revisited, Maurice Bruynooghe. A Science of Reasoning, Alan Bundy. Inductive Inference of Theories from Facts, Ehud Y. Shapiro. Equality. Solving Equations in Abstract Algebras: A Rule-based Survey of Unification, Jean-Pierre Jouannaud and Claude Kirchner. Disunification: A Survey, Hubert Comon. A Case Study of the Completion Procedure: Proving Ring Commutativity Problems, Deepak Kapur and Hantao Zhang. Computations in Regular Rewriting Systems I and II, Girard Huet and JeanJacques Levy. Unification and ML Type Reconstruction, Paris Kanellakis, Harry Mairson, and John Mitchell. Automatic Dimensional Analysis, Mitchell Wand. Logic Programming. Logic Programming Schemes and Their Implementations, Keith Clark. A Near-Horn Prolog for Compilation, Donald Loveland and David Reed. Unfold/Fold Transformations of Logic Programs, P. A. Gardner and J. C. Shepherdson. An Algebraic Representation of Logic Program Computations, Andrea Corradini and Ugo Montanari. Theory of Disjunctive Logic Programs, Jack Minker, Arcot Rajasekar, and Jorge Lobo. Bottom-Up Evaluation of Logic Programs, Jeffrey Naughton and Raghu Ramakrishnan. Absys, the First Logic Programming Language: A View of the Inevitability of Logic Programming, E. W. Elcock. (shrink)

This chapter contains sections titled: Introduction The ACL2 System A Modeling Problem Case Studies.

This is the 3rd edition. Although a number of new technological applications require classical deductive computation with non-classical logics, many key technologies still do well—or exclusively, for that matter—with classical logic. In this first volume, we elaborate on classical deductive computing with classical logic. The objective of the main text is to provide the reader with a thorough elaboration on both classical computing – a.k.a. formal languages and automata theory – and classical deduction with the classical first-order predicate (...) calculus with a view to computational implementations, namely in automated theorem proving and logic programming. The present third edition improves on the previous ones by providing an altogether more algorithmic approach: There is now a wholly new section on algorithms and there are in total fourteen clearly isolated algorithms designed in pseudo-code. Other improvements are, for instance, an emphasis on functions in Chapter 1 and more exercises with Turing machines. (shrink)

Computability logic (CL) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally been. Formulas in it represent computational problems, "truth" means existence of an algorithmic solution, and proofs encode such solutions. Within the line of research devoted to finding axiomatizations for ever more expressive fragments of CL, the present paper introduces a new deductive system CL12 and proves (...) its soundness and completeness with respect to the semantics of CL. Conservatively extending classical predicate calculus and offering considerable additional expressive and deductive power, CL12 presents a reasonable, computationally meaningful, constructive alternative to classical logic as a basis for applied theories. To obtain a model example of such theories, this paper rebuilds the traditional, classical-logic-based Peano arithmetic into a computability-logic-based counterpart. Among the purposes of the present contribution is to provide a starting point for what, as the author wishes to hope, might become a new line of research with a potential of interesting findings—an exploration of the presumably quite unusual metatheory of CL-based arithmetic and other CL-based applied systems. (shrink)

~Et moi,.... si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point alle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non· The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and (...) non­ linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics...'; 'One service logic has rendered com­ puter science...'; 'One service category theory has rendered mathematics...'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series. (shrink)

The book contains the proceedings of the 12th European Testis Workshop and gives an excellent overview of the state of the art in testicular research. The chapters are written by leading scientists in the field of male reproduction, who were selceted on the basis of their specific area of research. The book covers all important aspects of testicular functioning, for example, Sertoli and Leydig cell functioning, spermatogonial development and transplantation, meiosis and spermiogenesis. Even for those investigators who were not present (...) at the workshop, this volume provides a clear impression of the topics discussed during that meeting. (shrink)

This paper presents a soundness and completeness proof for propositional intuitionistic calculus with respect to the semantics of computability logic. The latter interprets formulas as interactive computational problems, formalized as games between a machine and its environment. Intuitionistic implication is understood as algorithmic reduction in the weakest possible — and hence most natural — sense, disjunction and conjunction as deterministic-choice combinations of problems , and “absurd” as a computational problem of universal strength.

This paper constructs a cirquent calculus system and proves its soundness and completeness with respect to the semantics of computability logic. The logical vocabulary of the system consists of negation ${\neg}$ , parallel conjunction ${\wedge}$ , parallel disjunction ${\vee}$ , branching recurrence ⫰, and branching corecurrence ⫯. The article is published in two parts, with (the present) Part I containing preliminaries and a soundness proof, and (the forthcoming) Part II containing a completeness proof.

This work is an attempt to lay foundations for a theory of interactive computation and bring logic and theory of computing closer together. It semantically introduces a logic of computability and sets a program for studying various aspects of that logic. The intuitive notion of computational problems is formalized as a certain new, procedural-rule-free sort of games between the machine and the environment, and computability is understood as existence of an interactive Turing machine that wins (...) the game against any possible environment. The formalism used as a specification language for computational problems, called the universal language, is a non-disjoint union of the formalisms of classical, intuitionistic and linear logics, with logical operators interpreted as certain—most basic and natural—operations on problems. Validity of a formula is understood as being “always computable”, and the set of all valid formulas is called the universal logic. The name “universal” is related to the potential of this logic to integrate, on the basis of one semantics, classical, intuitionistic and linear logics, with their seemingly unrelated or even antagonistic philosophies. In particular, the classical notion of truth turns out to be nothing but computability restricted to the formulas of the classical fragment of the universal language, which makes classical logic a natural syntactic fragment of the universal logic. The same appears to be the case for intuitionistic and linear logics . Unlike classical logic, these two do not have a good concept of truth, and the notion of computability restricted to the corresponding two fragments of the universal language, based on the intuitions that it formalizes, can well qualify as “intuitionistic truth” and “linear-logic truth”. The paper also provides illustrations of potential applications of the universal logic in knowledgebase, resourcebase and planning systems, as well as constructive applied theories. The author has tried to make this article easy to read. It is fully self-contained and can be understood without any specialized knowledge of any particular subfield of logic or computer science. (shrink)

This paper shows that the basic logic induced by the parallel recurrence $\hspace {-2pt}\mbox {\raisebox {-0.01pt}{\@setfontsize \small {7}{8}$\wedge$}\hspace {-3.55pt}\raisebox {4.5pt}{\tiny $\mid$}\hspace {2pt}}$ of computability logic (i.e., the one in the signature $\{\neg,$\wedge$,\vee,\hspace {-2pt}\mbox {\raisebox {-0.01pt}{\@setfontsize \small {7}{8}$\wedge$}\hspace {-3.55pt}\raisebox {4.5pt}{\tiny $\mid$}\hspace {2pt}},\hspace {-2pt}\mbox {\raisebox {0.12cm}{\@setfontsize \small {7}{8}$\vee$}\hspace {-3.6pt}\raisebox {0.02cm}{\tiny $\mid$}\hspace {2pt}}\}$ ) is a proper superset of the basic logic induced by the branching recurrence $\mbox {\raisebox {-0.05cm}{$\circ$}\hspace {-0.11cm}\raisebox {3.1pt}{\tiny $\mid$}\hspace {2pt}}$ (i.e., the one in the signature (...) $\{\neg,$\wedge$,\vee,\mbox {\raisebox {-0.05cm}{$\circ$}\hspace {-0.11cm}\raisebox {3.1pt}{\tiny $\mid$}\hspace {2pt}},\mbox {\raisebox {0.12cm}{$\circ$}\hspace {-0.115cm}\raisebox {0.02cm}{\tiny $\mid$}\hspace {2pt}}\}$ ). The latter is known to be precisely captured by the cirquent calculus system CL15 , conjectured by Japaridze to remain sound—but not complete—with $\hspace {-2pt}\mbox {\raisebox {-0.01pt}{\@setfontsize \small {7}{8}$\wedge$}\hspace {-3.55pt}\raisebox {4.5pt}{\tiny $\mid$}\hspace {2pt}}$ instead of $\mbox {\raisebox {-0.05cm}{$\circ$}\hspace {-0.11cm}\raisebox {3.1pt}{\tiny $\mid$}\hspace {2pt}}$ . The present result is obtained by positively verifying that conjecture. A secondary result of the paper is showing that $\hspace {-2pt}\mbox {\raisebox {-0.01pt}{\@setfontsize \small {7}{8}$\wedge$}\hspace {-3.55pt}\raisebox {4.5pt}{\tiny $\mid$}\hspace {2pt}}$ is strictly weaker than $\mbox {\raisebox {-0.05cm}{$\circ$}\hspace {-0.11cm}\raisebox {3.1pt}{\tiny $\mid$}\hspace {2pt}}$ in the sense that, while $\mbox {\raisebox {-0.05cm}{$\circ$}\hspace {-0.11cm}\raisebox {3.1pt}{\tiny $\mid$}\hspace {2pt}}F$ logically implies $\hspace {-2pt}\mbox {\raisebox {-0.01pt}{\@setfontsize \small {7}{8}$\wedge$}\hspace {-3.55pt}\raisebox {4.5pt}{\tiny $\mid$}\hspace {2pt}}F$ , the reverse does not hold. (shrink)

This paper constructs a cirquent calculus system and proves its soundness and completeness with respect to the semantics of computability logic. The logical vocabulary of the system consists of negation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\neg}}$$\end{document}, parallel conjunction \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\wedge}}$$\end{document}, parallel disjunction \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\vee}}$$\end{document}, branching recurrence ⫰, and branching corecurrence ⫯. The article is published in two parts, with (...) (the previous) Part I containing preliminaries and a soundness proof, and (the present) Part II containing a completeness proof. (shrink)

This book constitutes the refereed proceedings of the 9th Conference on Computability in Europe, CiE 2013, held in Milan, Italy, in July 2013. The 48 revised papers presented together with 1 invited lecture and 2 tutorials were carefully reviewed and selected with an acceptance rate of under 31,7%. Both the conference series and the association promote the development of computability-related science, ranging over mathematics, computer science and applications in various natural and engineering sciences such as physics and biology, (...) and also including the promotion of related non-scientific fields such as philosophy and history of computing. (shrink)

This volume contains several invited papers as well as a selection of the other contributions. The conference was the first meeting of the Soviet logicians interested in com- puter science with their Western counterparts. The papers report new results and techniques in applications of deductive systems, deductive program synthesis and analysis, computer experiments in logic related fields, theorem proving and logic programming. It provides access to intensive work on computer logic both in the USSR and in Western (...) countries. (shrink)

This book bridges the gaps between logic, mathematics and computer science by delving into the theory of well-quasi orders, also known as wqos. This highly active branch of combinatorics is deeply rooted in and between many fields of mathematics and logic, including proof theory, commutative algebra, braid groups, graph theory, analytic combinatorics, theory of relations, reverse mathematics and subrecursive hierarchies. As a unifying concept for slick finiteness or termination proofs, wqos have been rediscovered in diverse contexts, and proven (...) to be extremely useful in computer science. The book introduces readers to the many facets of, and recent developments in, wqos through chapters contributed by scholars from various fields. As such, it offers a valuable asset for logicians, mathematicians and computer scientists, as well as scholars and students. (shrink)

This book presents a set of historical recollections on the work of Martin Davis and his role in advancing our understanding of the connections between logic, computing, and unsolvability. The individual contributions touch on most of the core aspects of Davis’ work and set it in a contemporary context. They analyse, discuss and develop many of the ideas and concepts that Davis put forward, including such issues as contemporary satisfiability solvers, essential unification, quantum computing and generalisations of Hilbert’s tenth (...) problem. The book starts out with a scientific autobiography by Davis, and ends with his responses to comments included in the contributions. In addition, it includes two previously unpublished original historical papers in which Davis and Putnam investigate the decidable and the undecidable side of Logic, as well as a full bibliography of Davis’ work. As a whole, this book shows how Davis’ scientific work lies at the intersection of computability, theoretical computer science, foundations of mathematics, and philosophy, and draws its unifying vision from his deep involvement in Logic. (shrink)

Unlike the standard Quantum Computational Logic, where the carrier of information is conventionally assumed to be only the last qubit over a sequence of many qubits, here we propose an extended version of the QCL where the number and the position of the target qubits are arbitrary.

The paper discusses tools for teaching logic used in Logic & Proofs, a web-based introduction to modern logic that has been taken by more than 1,300 students since the fall of 2003. The tools include a wide array of interactive learning environments or cognitive mini-tutors; most important among them is the Carnegie Proof Lab. The Proof Lab is a sophisticated interface for constructing natural deduction proofs and is central, as strategically guided discovery of proofs is the distinctive (...) focus of the course. My discussion makes explicit the broader intellectual context, but also the pursuit of pedagogical goals and their experimental examination. The intellectual context includes i) the theoretical background for the proof search algorithm AProS and its use for a dynamic Proof Tutor, and ii) the programmatic expansion of the course to Computational Logic. 1. (shrink)

Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel's incompleteness theorems, but also a large number of optional topics, from Turing's theory of computability to Ramsey's theorem. This 2007 fifth edition has been thoroughly revised by John Burgess. Including a selection of exercises, adjusted for this edition, at the end of each (...) chapter, it offers a simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems. This updated edition is also accompanied by a website as well as an instructor's manual. (shrink)

Cirquent calculus is a proof system with inherent ability to account for sharing subcomponents in logical expressions. Within its framework, this article constructs an axiomatization $$\text{ CL18 }$$ CL18 of the basic propositional fragment of computability logic—the game-semantically conceived logic of computational resources and tasks. The nonlogical atoms of this fragment represent arbitrary so called static games, and the connectives of its logical vocabulary are negation and the parallel and choice versions of conjunction and disjunction. The main (...) technical result of the article is a proof of the soundness and completeness of $$\text{ CL18 }$$ CL18 with respect to the semantics of computability logic. (shrink)

Alan M. Turing, pioneer of computing and WWII codebreaker, is one of the most important and influential thinkers of the twentieth century. In this volume for the first time his key writings are made available to a broad, non-specialist readership. They make fascinating reading both in their own right and for their historic significance: contemporary computational theory, cognitive science, artificial intelligence, and artificial life all spring from this ground-breaking work, which is also rich in philosophical and logical insight. An introduction (...) by leading Turing expert Jack Copeland provides the background and guides the reader through the selection. About Alan Turing Alan Turing FRS OBE, (1912-1954) studied mathematics at King's College, Cambridge. He was elected a Fellow of King's in March 1935, at the age of only 22. In the same year he invented the abstract computing machines - now known simply as Turing machines - on which all subsequent stored-program digital computers are modelled. During 1936-1938 Turing continued his studies, now at Princeton University. He completed a PhD in mathematical logic, analysing the notion of 'intuition' in mathematics and introducing the idea of oracular computation, now fundamental in mathematical recursion theory. An 'oracle' is an abstract device able to solve mathematical problems too difficult for the universal Turing machine. In the summer of 1938 Turing returned to his Fellowship at King's. When WWII started in 1939 he joined the wartime headquarters of the Government Code and Cypher School (GC&CS) at Bletchley Park, Buckinghamshire. Building on earlier work by Polish cryptanalysts, Turing contributed crucially to the design of electro-mechanical machines ('bombes') used to decipher Enigma, the code by means of which the German armed forces sought to protect their radio communications. Turing's work on the version of Enigma used by the German navy was vital to the battle for supremacy in the North Atlantic. He also contributed to the attack on the cyphers known as 'Fish'. Based on binary teleprinter code, Fish was used during the latter part of the war in preference to morse-based Enigma for the encryption of high-level signals, for example messages from Hitler and other members of the German High Command. It is estimated that the work of GC&CS shortened the war in Europe by at least two years. Turing received the Order of the British Empire for the part he played. In 1945, the war over, Turing was recruited to the National Physical Laboratory (NPL) in London, his brief to design and develop an electronic computer - a concrete form of the universal Turing machine. Turing's report setting out his design for the Automatic Computing Engine (ACE) was the first relatively complete specification of an electronic stored-program general-purpose digital computer. Delays beyond Turing's control resulted in NPL's losing the race to build the world's first working electronic stored-program digital computer - an honour that went to the Royal Society Computing Machine Laboratory at Manchester University, in June 1948. Discouraged by the delays at NPL, Turing took up the Deputy Directorship of the Royal Society Computing Machine Laboratory in that year. Turing was a founding father of modern cognitive science and a leading early exponent of the hypothesis that the human brain is in large part a digital computing machine, theorising that the cortex at birth is an 'unorganised machine' which through 'training' becomes organised 'into a universal machine or something like it'. He also pioneered Artificial Intelligence. Turing spent the rest of his short career at Manchester University, being appointed to a specially created Readership in the Theory of Computing in May 1953. He was elected a Fellow of the Royal Society of London in March 1951 (a high honour). (shrink)

Epistemic logic has grown from its philosophical beginnings to find diverse applications in computer science, and as a means of reasoning about the knowledge and belief of agents. This book provides a broad introduction to the subject, along with many exercises and their solutions. The authors begin by presenting the necessary apparatus from mathematics and logic, including Kripke semantics and the well-known modal logics K, T, S4 and S5. Then they turn to applications in the context of distributed (...) systems and artificial intelligence. These include the notions of common knowledge, distributed knowledge, explicit and implicit belief, the interplays between knowledge and time, and knowledge and action, as well as a graded (or numerical) variant of the epistemic operators. The authors also discuss extensively the problem of logical omniscience. They cover Halpern & Moses' theory of honest formulas, and they make a digression into the realm of nonmonotonic reasoning and preferential entailment. They discuss Moore's autoepistemic logic, together with Levesque's related logic of "all I know". Furthermore, they show how one can base default and counterfactual reasoning on epistemic logic. Graduate students in philosophy or in computer science, especially those with an interest in AI, will find this book useful. (shrink)

This volume presents the proceedings of the workshop CSL '91 (Computer Science Logic) held at the University of Berne, Switzerland, October 7-11, 1991. This was the fifth in a series of annual workshops on computer sciencelogic (the first four are recorded in LNCS volumes 329, 385, 440, and 533). The volume contains 33 invited and selected papers on a variety of logical topics in computer science, including abstract datatypes, bounded theories, complexity results, cut elimination, denotational semantics, infinitary queries, Kleene (...) algebra with recursion, minimal proofs, normal forms in infinite-valued logic, ordinal processes, persistent Petri nets, plausibility logic, program synthesis systems, quantifier hierarchies, semantics of modularization, stable logic, term rewriting systems, termination of logic programs, transitive closure logic, variants of resolution, and many others. (shrink)

We describe an extension to our quantifier-free computational logic to provide the expressive power and convenience of bounded quantifiers and partial functions. By quantifier we mean a formal construct which introduces a bound or indicial variable whose scope is some subexpression of the quantifier expression. A familiar quantifier is the Σ operator which sums the values of an expression over some range of values on the bound variable. Our method is to represent expressions of the logic as objects (...) in the logic, to define an interpreter for such expressions as a function in the logic, and then define quantifiers as "mapping functions." The novelty of our approach lies in the formalization of the interpreter and its interaction with the underlying logic. Our method has several advantages over other formal systems that provide quantifiers and partial functions in a logical setting. The most important advantage is that proofs not involving quantification or partial recursive functions are not complicated by such notions as "capturing," "bottom," or "continuity." Naturally enough, our formalization of the partial functions is nonconstructive. The theorem prover for the logic has been modified to support these new features. We describe the modifications. The system has proved many theorems that could not previously be stated in our logic. Among them are. (shrink)

Linear Logic is a branch of proof theory which provides refined tools for the study of the computational aspects of proofs. These tools include a duality-based categorical semantics, an intrinsic graphical representation of proofs, the introduction of well-behaved non-commutative logical connectives, and the concepts of polarity and focalisation. These various aspects are illustrated here through introductory tutorials as well as more specialised contributions, with a particular emphasis on applications to computer science: denotational semantics, lambda-calculus, logic programming and concurrency (...) theory. The volume is rounded-off by two invited contributions on new topics rooted in recent developments of linear logic. The book derives from a summer school that was the climax of the EU Training and Mobility of Researchers project 'Linear Logic in Computer Science'. It is an excellent introduction to some of the most active research topics in the area. (shrink)

Computing with logic / Maier, D., Warren, D.S.

This book provides a general survey of the main concepts, questions and results that have been developed in the recent interactions between quantum information, quantum computation and logic. Divided into 10 chapters, the books starts with an introduction of the main concepts of the quantum-theoretic formalism used in quantum information. It then gives a synthetic presentation of the main “mathematical characters” of the quantum computational game: qubits, quregisters, mixtures of quregisters, quantum logical gates. Next, the book investigates the puzzling (...) entanglement-phenomena and logically analyses the Einstein–Podolsky–Rosen paradox and introduces the reader to quantum computational logics, and new forms of quantum logic. The middle chapters investigate the possibility of a quantum computational semantics for a language that can express sentences like “Alice knows that everybody knows that she is pretty”, explore the mathematical concept of quantum Turing machine, and illustrate some characteristic examples that arise in the framework of musical languages. The book concludes with an analysis of recent discussions, and contains a Mathematical Appendix which is a survey of the definitions of all main mathematical concepts used in the book. (shrink)