The Semantics and Proof Theory of the Logic of Bunched ImplicationsThis is a monograph about logic. Specifically, it presents the mathe matical theory of the logic of bunched implications, BI: I consider Bl's proof theory, model theory and computation theory. However, the mono graph is also about informatics in a sense which I explain. Specifically, it is about mathematical models of resources and logics for reasoning about resources. I begin with an introduction which presents my (background) view of logic from the point of view of informatics, paying particular attention to three logical topics which have arisen from the development of logic within informatics: • Resources as a basis for semantics; • Proof-search as a basis for reasoning; and • The theory of representation of object-logics in a meta-logic. The ensuing development represents a logical theory which draws upon the mathematical, philosophical and computational aspects of logic. Part I presents the logical theory of propositional BI, together with a computational interpretation. Part II presents a corresponding devel opment for predicate BI. In both parts, I develop proof-, model- and type-theoretic analyses. I also provide semantically-motivated compu tational perspectives, so beginning a mathematical theory of resources. I have not included any analysis, beyond conjecture, of properties such as decidability, finite models, games or complexity. I prefer to leave these matters to other occasions, perhaps in broader contexts. |
Contents
I | xxi |
II | 1 |
III | 3 |
IV | 13 |
V | 33 |
VI | 51 |
VII | 67 |
VIII | 89 |
XI | 121 |
XII | 145 |
XIII | 147 |
XIV | 157 |
XV | 163 |
XVI | 179 |
XVII | 201 |
XVIII | 207 |
Other editions - View all
The Semantics and Proof Theory of the Logic of Bunched Implications David J. Pym Limited preview - 2013 |
The Semantics and Proof Theory of the Logic of Bunched Implications David J. Pym No preview available - 2010 |
The Semantics and Proof Theory of the Logic of Bunched Implications David J. Pym No preview available - 2002 |
Common terms and phrases
A:Type AA-calculus additive algebraic arrow axiom BI's bunch of variables bunched implications cartesian Chapter clauses closed structure combination Computer conjunction connectives consider construction context corresponding defined definition denote dependent type theory Dereliction disjunction example exists extended fibred follows formal function space functor functor categories Galmiche Girard given Grothendieck implication induction hypothesis introduction rule intuitionistic linear logic intuitionistic logic Ishtiaq and Pym isomorphism judgement Kripke models Kripke resource Kripke semantics Lambek and Scott LEMMA logic programming logical framework maps meta-logic monoidal category monoidal closed multiplicative natural deduction notion O'Hearn and Pym Prawitz predicate premisses preordered commutative monoid prime evaluation proof theory proofs in NBI Prop propositional provable quantifiers redex reduction relation sequent calculus signature substructural logic symmetric monoidal tensor product theorem tion type theory Vnew worlds ΓΕ ΓΕΦ ΓΗΣ
Popular passages
Page ii - Department of Computer Science, King's College, London, UK SCOPE OF THE SERIES Logic is applied in an increasingly wide variety of disciplines, from the traditional subjects of philosophy and mathematics to the more recent disciplines of cognitive science, computer science, artificial intelligence, and linguistics, leading to new vigor in this ancient subject. Kluwer, through its Applied Logic Series, seeks to provide a home for outstanding books and research monographs in applied logic, and in doing...
Page i - Pym. The Semantics and Proof Theory of the Logic of Bunched Implications. Applied Logic Series. Kluwer Academic Publishers, 2002.