Author: Robert L. Constable
Release Date: 2012-04-26
This Festschrift volume is published in honor of Dexter Kozen on the occasion of his 60th birthday. Dexter Kozen has been a leader in the development of Kleene Algebras (KAs). The contributions in this volume reflect the breadth of his work and influence. The volume includes 19 full papers related to Dexter Kozen's research. They deal with coalgebraic methods, congruence closure; the completeness of various programming logics; decision procedure for logics; alternation; algorithms and complexity; and programming languages and program analysis. The second part of this volume includes laudatios from several collaborators, students and friends, including the members of his current band.
Author: Gilles Barthe
Release Date: 2003-08-02
Genre: Language Arts & Disciplines
This book is based on material presented at the international summer school on Applied Semantics that took place in Caminha, Portugal, in September 2000. We aim to present some recent developments in programming language research, both in semantic theory and in implementation, in a series of graduate-level lectures. The school was sponsored by the ESPRIT Working Group 26142 on Applied Semantics(APPSEM),whichoperatedbetweenApril1998andMarch2002.The purpose of this working group was to bring together leading reseachers, both in semantic theory and in implementation, with the speci?c aim of improving the communication between theoreticians and practitioners. TheactivitiesofAPPSEMwerestructuredintonineinterdisciplinarythemes: A: Semantics for object-oriented programming B: Program structuring C: Integration of functional languages and proof assistants D: Veri?cation methods E: Automatic program transformation F: Games, sequentiality, and abstract machines G: Types and type inference in programming H: Semantics-based optimization I: Domain theory and real number computation These themes were identi?ed as promising for pro?table interaction between semantic theory and practice, and were chosen to contribute to the following general topics: – description of existing programming language features; – design of new programming language features; – implementation and analysis of programming languages; – transformation and generation of programs; – veri?cation of programs. The chapters in this volume give examples of recent developments covering a broad range of topics of interest to APPSEM.
Author: G. M. Bierman
Release Date: 1998
Genre: Functional programming languages
Abstract: "This paper proposes a simple computational interpretation of Parigot's [lambda mu]-calculus. The [lambda mu]-calculus is an extension of the typed [lambda]-calculus which corresponds via the Curry-Howard correspondence to classical logic. Whereas other work has given computational interpretations by translating the [lambda mu]-calculus into other calculi, I wish to propose here that the [lambda mu]-calculus itself has a simple computational interpretation: it is a typed [lambda]-calculus which is able to save and restore the runtime environment. This interpretation is best given as a single-step semantics which, in particular, leads to a relatively simple, but powerful, operational theory."
Author: Andrew M. Pitts
Release Date: 1998
Genre: Functional programming (Computer science)
Abstract: "Studies of the mathematical properties of impredicative polymorphic types have for the most part focused on the polymorphic lambda calculus of Girard-Reynolds, which is a calculus of total polymorphic functions. This paper considers polymorphic types from a functional programming perspective, where the partialness arising from the presence of fixpoint recursion complicates the nature of potentially infinite ('lazy') datatypes. An approach to Reynolds' notion of relational parametricity is developed that works directly on the syntax of a programming language, using a novel closure operator to relate operational behaviour to parametricity properties of types. Working with an extension of Plotkin's PCF with [for every]-types, lazy lists and existential types, we show by example how the resulting logical relation can be used to prove properties of polymorphic types up to operational equivalence."
Author: Dov M. Gabbay
Publisher: Springer Science & Business Media
Release Date: 2013-11-29
This text offers an extension to the traditional Kripke semantics for non-classical logics by adding the notion of reactivity. Reactive Kripke models change their accessibility relation as we progress in the evaluation process of formulas in the model. This feature makes the reactive Kripke semantics strictly stronger and more applicable than the traditional one. Here we investigate the properties and axiomatisations of this new and most effective semantics, and we offer a wide landscape of applications of the idea of reactivity. Applied topics include reactive automata, reactive grammars, reactive products, reactive deontic logic and reactive preferential structures. Reactive Kripke semantics is the next step in the evolution of possible world semantics for non-classical logics, and this book, written by one of the leading authorities in the field, is essential reading for graduate students and researchers in applied logic, and it offers many research opportunities for PhD students.
Author: L. Allison
Publisher: Cambridge University Press
Release Date: 1986
This textbook is an introduction to denotational semantics and its applications to programming languages. Dr Allison emphasizes a practical approach and the student is encouraged to write and test denotational definitions. The first section is devoted to the mathematical foundations of the subject and sufficient detail is given to illustrate the fundamental problems. The remainder of the book covers the use of denotational semantics to describe sequential programming languages such as Algol, Pascal and C. Throughout, numerous exercises, usually in Pascal, will help the student practise writing definitions and carry out simple applications. The book culminates in discussing an executable semantics of the logic-programming language Prolog. Being an introduction, advanced undergraduates in computer science and graduates new to the subject will find this a readily accessible account of one of the central topics of computer science.
The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic logic, formal logical and semantic paradoxes, the concept of truth, the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Löwenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert’s program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights. - Written by leading logicians and philosophers - Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic - Clear, in-depth expositions of technical detail - Progressive organization from general considerations to informal to symbolic logic to nonclassical logics - Presents current work in symbolic logic within a unified framework - Accessible to students, engaging for experts and professionals - Insightful philosophical discussions of all aspects of logic - Useful bibliographies in every chapter