BeschreibungThe study of information-based actions and processes has been a vibrant interface between logic and computer science for decades now. The individual chapters of this book show the state of the art in current investigations of process calculi with mainly two major paradigms at work: linear logic and modal logic. Viewed together, the chapters also offer exciting glimpses of future integration with obvious links including modal logics for proof graphs, labelled deduction merging modal and linear logic, Chu spaces linking proof theory and model theory and bisimulation-style equivalences for analysing proof processes. The combination of approaches and pointers for further integration also suggests a grander vision for the field. In classical computation theory, Church's Thesis provided a unifying and driving force. Likewise, modern process theory would benefit immensely from a synthesis bringing together paradigms like modal logic, process algebra, and linear logic. If this Grand Synthesis is ever going to happen, books like this are needed!
InhaltsverzeichnisList of Figures. List of Tables. Foreword; J. van Benthem. Preface. Contributing Authors. I: From a Structural Perspective.
1. Geometry of Deduction via Graphs of Proofs; A. Grisi de Oliveira, R.J.B.G. Queiroz. 1. Motivation.
2. The idea of stuying proofs as geometric objects.
4. Logical flow graphs.
5. Multiple-conclusion classical calculi.
6. Finale. 2. Chu's Construction: A Proof-Theoretic Approach; G. Bellin. 1. Preface. 2. The trip translation. 3. Chu's construction. 4. Proof-nets, trips and translations. 3. Two Paradigms of Logical Computation in Affine Logic? G. Bellin. 1. Introduction. 2. Sequent calculus of MAL + Mix. 3. Additive mix. 4. Proof-nets for MAL + Mix. 5. Cut-elimination modulo irrelevance. 6. Symmetric reductions require Mix. 4. Proof Systems for pi-Calculus Logics; M. Dam. 1. Introduction. 2. Preliminaries on the pi-calculus. 3. A pi-mu-calculus. 4. Example specifications. 5. Proof system, modal fragment. 6. Soundness and completeness for the modal fragment.
7. Proof rules for recursive formulas.
8. Finite control completeness.
9. Natural numbers.
11. Conclusion. II: From a Descriptive Perspective. 5. A Tutorial Introduction to Symbolic Model Checking; D. Déharbe. 1. Introduction. 2. Kripke structures. 3. Temporal logic model checking.4. Symbolic model checking. 5. Loopless undirected graphs. 6. Modal definability. 7. k-Colourable graphs. 8. Conclusions. 7. Bisimulation and Language Equivalence; C. Stirling. 1. Introduction. 2. Background. 3. Caucal's hierarchy. 4. Richer logics. 5. Finite model theory.
Untertitel: 'Trends in Logic'. 2003. Auflage. Sprache: Englisch.
Verlag: SPRINGER VERLAG GMBH
Erscheinungsdatum: Mai 2003
Seitenanzahl: 285 Seiten