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This volume constitutes the proceedings of the First International Workshop on Rewriting Logic, held at the Asilomar Conference Center, Pacific Grove, California, Sept. 2-6, 1996. The three invited papers by Narciso Marti-Oliet, Ugo Montanari, and Martin Wirsing, and seventeen contributed papers selected by the Program Committee give a rich view of the latest developments and research directions in the field of rewriting logic and its various applications to computing. Besides work on models and on concurrency aspects, there are several papers describing the different rewriting logic languages developed so far in Europe and the U.S., as well as a paper on semantic foundations for the Cafe language in Japan. There are also several papers on logical and metalogical specification; on reflection and strategies; on applications to object-oriented design, specification and programming; and on applications to contraint solving, to real-time systems, and to discrete event simulation. In addition to the papers, the workshop placed strong emphasis on facilitating in-depth discussion of the topics by allowing ample time for the discussion of each paper, and by including five panel discussions and a tutorial.

This volume constitutes the proceedings of the First International Workshop on Rewriting Logic, held at the Asilomar Conference Center, Pacific Grove, California, Sept. 2-6, 1996. The three invited papers by Narciso Marti-Oliet, Ugo Montanari, and Martin Wirsing, and seventeen contributed papers selected by the Program Committee give a rich view of the latest developments and research directions in the field of rewriting logic and its various applications to computing. Besides work on models and on concurrency aspects, there are several papers describing the different rewriting logic languages developed so far in Europe and the U.S., as well as a paper on semantic foundations for the Cafe language in Japan. There are also several papers on logical and metalogical specification; on reflection and strategies; on applications to object-oriented design, specification and programming; and on applications to contraint solving, to real-time systems, and to discrete event simulation. In addition to the papers, the workshop placed strong emphasis on facilitating in-depth discussion of the topics by allowing ample time for the discussion of each paper, and by including five panel discussions and a tutorial.

This volume constitutes the proceedings of the First International Workshop on Rewriting Logic, held at the Asilomar Conference Center, Pacific Grove, California, Sept. 2-6, 1996. The three invited papers by Narciso Marti-Oliet, Ugo Montanari, and Martin Wirsing, and seventeen contributed papers selected by the Program Committee give a rich view of the latest developments and research directions in the field of rewriting logic and its various applications to computing. Besides work on models and on concurrency aspects, there are several papers describing the different rewriting logic languages developed so far in Europe and the U.S., as well as a paper on semantic foundations for the Cafe language in Japan. There are also several papers on logical and metalogical specification; on reflection and strategies; on applications to object-oriented design, specification and programming; and on applications to contraint solving, to real-time systems, and to discrete event simulation. In addition to the papers, the workshop placed strong emphasis on facilitating in-depth discussion of the topics by allowing ample time for the discussion of each paper, and by including five panel discussions and a tutorial.

This volume constitutes the proceedings of the First International Workshop on Rewriting Logic, held at the Asilomar Conference Center, Pacific Grove, California, Sept. 2-6, 1996. The three invited papers by Narciso Marti-Oliet, Ugo Montanari, and Martin Wirsing, and seventeen contributed papers selected by the Program Committee give a rich view of the latest developments and research directions in the field of rewriting logic and its various applications to computing. Besides work on models and on concurrency aspects, there are several papers describing the different rewriting logic languages developed so far in Europe and the U.S., as well as a paper on semantic foundations for the Cafe language in Japan. There are also several papers on logical and metalogical specification; on reflection and strategies; on applications to object-oriented design, specification and programming; and on applications to contraint solving, to real-time systems, and to discrete event simulation. In addition to the papers, the workshop placed strong emphasis on facilitating in-depth discussion of the topics by allowing ample time for the discussion of each paper, and by including five panel discussions and a tutorial.

This volume constitutes the proceedings of the First International Workshop on Rewriting Logic, held at the Asilomar Conference Center, Pacific Grove, California, Sept. 2-6, 1996. The three invited papers by Narciso Marti-Oliet, Ugo Montanari, and Martin Wirsing, and seventeen contributed papers selected by the Program Committee give a rich view of the latest developments and research directions in the field of rewriting logic and its various applications to computing. Besides work on models and on concurrency aspects, there are several papers describing the different rewriting logic languages developed so far in Europe and the U.S., as well as a paper on semantic foundations for the Cafe language in Japan. There are also several papers on logical and metalogical specification; on reflection and strategies; on applications to object-oriented design, specification and programming; and on applications to contraint solving, to real-time systems, and to discrete event simulation. In addition to the papers, the workshop placed strong emphasis on facilitating in-depth discussion of the topics by allowing ample time for the discussion of each paper, and by including five panel discussions and a tutorial.

In this paper we suggest that in the framework of the Category Theory it is possible to demonstrate the mathematical and logical \textit{dual equivalence} between the category of the $q$-deformed Hopf Coalgebras and the category of the $q$-deformed Hopf Algebras in QFT, interpreted as a thermal field theory. Each pair algebra-coalgebra characterizes, indeed, a QFT system and its mirroring thermal bath, respectively, so to model dissipative quantum systems persistently in far-from-equilibrium conditions, with an evident significance also for biological sciences. The $q$-deformed Hopf Coalgebras and the $q$-deformed Hopf Algebras constitute two dual categories because characterized by the same functor $T$, related with the Bogoliubov transform, and by its contravariant application $T^{op}$, respectively. The \textit{q}-deformation parameter, indeed, is related to the Bogoliubov angle, and it is effectively a thermal parameter. Therefore, the different values of $q$ identify univocally, and then label, the vacua appearing in the foliation process of the quantum vacuum. This means that, in the framework of Universal Coalgebra, as general theory of dynamic and computing systems ("labelled state-transition systems"), the so labelled infinitely many quantum vacua can be interpreted as the Final Coalgebra of an "Infinite State Black-Box Machine". All this opens the way to the possibility of designing a new class of universal quantum computing architectures based on this coalgebraic formulation of QFT, as its ability of naturally generating a Fibonacci progression demonstrates.

In this paper we suggest that in the framework of the Category Theory it is possible to demonstrate the mathematical and logical \textit{dual equivalence} between the category of the $q$-deformed Hopf Coalgebras and the category of the $q$-deformed Hopf Algebras in QFT, interpreted as a thermal field theory. Each pair algebra-coalgebra characterizes, indeed, a QFT system and its mirroring thermal bath, respectively, so to model dissipative quantum systems persistently in far-from-equilibrium conditions, with an evident significance also for biological sciences. The $q$-deformed Hopf Coalgebras and the $q$-deformed Hopf Algebras constitute two dual categories because characterized by the same functor $T$, related with the Bogoliubov transform, and by its contravariant application $T^{op}$, respectively. The \textit{q}-deformation parameter, indeed, is related to the Bogoliubov angle, and it is effectively a thermal parameter. Therefore, the different values of $q$ identify univocally, and then label, the vacua appearing in the foliation process of the quantum vacuum. This means that, in the framework of Universal Coalgebra, as general theory of dynamic and computing systems ("labelled state-transition systems"), the so labelled infinitely many quantum vacua can be interpreted as the Final Coalgebra of an "Infinite State Black-Box Machine". All this opens the way to the possibility of designing a new class of universal quantum computing architectures based on this coalgebraic formulation of QFT, as its ability of naturally generating a Fibonacci progression demonstrates.

In this paper we suggest that in the framework of the Category Theory it is possible to demonstrate the mathematical and logical \textit{dual equivalence} between the category of the $q$-deformed Hopf Coalgebras and the category of the $q$-deformed Hopf Algebras in QFT, interpreted as a thermal field theory. Each pair algebra-coalgebra characterizes, indeed, a QFT system and its mirroring thermal bath, respectively, so to model dissipative quantum systems persistently in far-from-equilibrium conditions, with an evident significance also for biological sciences. The $q$-deformed Hopf Coalgebras and the $q$-deformed Hopf Algebras constitute two dual categories because characterized by the same functor $T$, related with the Bogoliubov transform, and by its contravariant application $T^{op}$, respectively. The \textit{q}-deformation parameter, indeed, is related to the Bogoliubov angle, and it is effectively a thermal parameter. Therefore, the different values of $q$ identify univocally, and then label, the vacua appearing in the foliation process of the quantum vacuum. This means that, in the framework of Universal Coalgebra, as general theory of dynamic and computing systems ("labelled state-transition systems"), the so labelled infinitely many quantum vacua can be interpreted as the Final Coalgebra of an "Infinite State Black-Box Machine". All this opens the way to the possibility of designing a new class of universal quantum computing architectures based on this coalgebraic formulation of QFT, as its ability of naturally generating a Fibonacci progression demonstrates.

In this paper we suggest that in the framework of the Category Theory it is possible to demonstrate the mathematical and logical \textit{dual equivalence} between the category of the $q$-deformed Hopf Coalgebras and the category of the $q$-deformed Hopf Algebras in QFT, interpreted as a thermal field theory. Each pair algebra-coalgebra characterizes, indeed, a QFT system and its mirroring thermal bath, respectively, so to model dissipative quantum systems persistently in far-from-equilibrium conditions, with an evident significance also for biological sciences. The $q$-deformed Hopf Coalgebras and the $q$-deformed Hopf Algebras constitute two dual categories because characterized by the same functor $T$, related with the Bogoliubov transform, and by its contravariant application $T^{op}$, respectively. The \textit{q}-deformation parameter, indeed, is related to the Bogoliubov angle, and it is effectively a thermal parameter. Therefore, the different values of $q$ identify univocally, and then label, the vacua appearing in the foliation process of the quantum vacuum. This means that, in the framework of Universal Coalgebra, as general theory of dynamic and computing systems ("labelled state-transition systems"), the so labelled infinitely many quantum vacua can be interpreted as the Final Coalgebra of an "Infinite State Black-Box Machine". All this opens the way to the possibility of designing a new class of universal quantum computing architectures based on this coalgebraic formulation of QFT, as its ability of naturally generating a Fibonacci progression demonstrates.

1 online resource (500 pages)

Logic and Grammar

Logic and Grammar

Foreword to the first edition by Edmund M. Clarke - FORE Systems Professor of Computer Science Carnegie Mellon University Pittsburgh, PA Formal methods have finally come of age! Specification languages, theorem provers, and model checkers are beginning to be used routinely in industry. Mathematical logic is basic to all of these techniques. (This foreword is re-printed in the second edition with its author’s permission.)

Foreword to the first edition by Edmund M. Clarke - FORE Systems Professor of Computer Science Carnegie Mellon University Pittsburgh, PA Formal methods have finally come of age! Specification languages, theorem provers, and model checkers are beginning to be used routinely in industry. Mathematical logic is basic to all of these techniques. (This foreword is re-printed in the second edition with its author’s permission.)

Foreword to the first edition by Edmund M. Clarke - FORE Systems Professor of Computer Science Carnegie Mellon University Pittsburgh, PA Formal methods have finally come of age! Specification languages, theorem provers, and model checkers are beginning to be used routinely in industry. Mathematical logic is basic to all of these techniques. (This foreword is re-printed in the second edition with its author’s permission.)

Foreword to the first edition by Edmund M. Clarke - FORE Systems Professor of Computer Science Carnegie Mellon University Pittsburgh, PA Formal methods have finally come of age! Specification languages, theorem provers, and model checkers are beginning to be used routinely in industry. Mathematical logic is basic to all of these techniques. (This foreword is re-printed in the second edition with its author’s permission.)

Foreword to the first edition by Edmund M. Clarke - FORE Systems Professor of Computer Science Carnegie Mellon University Pittsburgh, PA Formal methods have finally come of age! Specification languages, theorem provers, and model checkers are beginning to be used routinely in industry. Mathematical logic is basic to all of these techniques. (This foreword is re-printed in the second edition with its author’s permission.)

Foreword to the first edition by Edmund M. Clarke - FORE Systems Professor of Computer Science Carnegie Mellon University Pittsburgh, PA Formal methods have finally come of age! Specification languages, theorem provers, and model checkers are beginning to be used routinely in industry. Mathematical logic is basic to all of these techniques. (This foreword is re-printed in the second edition with its author’s permission.)

The LICS Symposium is an annual international forum on theoretical and practical topics in computer science that relate to logic in a broad sense. Topics of interest include: automata theory, category theory, concurrency, constraint programming, database theory, domain theory, finite model theory, formal methods, hybrid systems, language calculi, linear logic, complexity, artificial intelligence, logic programming, modal and temporal logics, model checking, semantics, security, rewriting, specifications, type theory, and verification.

The LICS Symposium is an annual international forum on theoretical and practical topics in computer science that relate to logic in a broad sense. Topics of interest include: automata theory, category theory, concurrency, constraint programming, database theory, domain theory, finite model theory, formal methods, hybrid systems, language calculi, linear logic, complexity, artificial intelligence, logic programming, modal and temporal logics, model checking, semantics, security, rewriting, specifications, type theory, and verification.

The LICS Symposium is an annual international forum on theoretical and practical topics in computer science that relate to logic in a broad sense. Topics of interest include: automata theory, category theory, concurrency, constraint programming, database theory, domain theory, finite model theory, formal methods, hybrid systems, language calculi, linear logic, complexity, artificial intelligence, logic programming, modal and temporal logics, model checking, semantics, security, rewriting, specifications, type theory, and verification.

The LICS Symposium is an annual international forum on theoretical and practical topics in computer science that relate to logic in a broad sense. Topics of interest include: automata theory, category theory, concurrency, constraint programming, database theory, domain theory, finite model theory, formal methods, hybrid systems, language calculi, linear logic, complexity, artificial intelligence, logic programming, modal and temporal logics, model checking, semantics, security, rewriting, specifications, type theory, and verification.

The LICS Symposium is an annual international forum on theoretical and practical topics in computer science that relate to logic in a broad sense. Topics of interest include: automata theory, category theory, concurrency, constraint programming, database theory, domain theory, finite model theory, formal methods, hybrid systems, language calculi, linear logic, complexity, artificial intelligence, logic programming, modal and temporal logics, model checking, semantics, security, rewriting, specifications, type theory, and verification.

The LICS Symposium is an annual international forum on theoretical and practical topics in computer science that relate to logic in a broad sense. Topics of interest include: automata theory, category theory, concurrency, constraint programming, database theory, domain theory, finite model theory, formal methods, hybrid systems, language calculi, linear logic, complexity, artificial intelligence, logic programming, modal and temporal logics, model checking, semantics, security, rewriting, specifications, type theory, and verification.