research-article

Resource semantics: logic as a modelling technology

Author:

David PymAuthors Info & Claims

ACM SIGLOG News, Volume 6, Issue 2

Pages 5 - 41

https://doi.org/10.1145/3326938.3326940

Published: 22 April 2019 Publication History

Abstract

The Logic of Bunched Implications (BI) was introduced by O'Hearn and Pym. The original presentation of BI emphasised its role as a system for formal logic (broadly in the tradition of relevant logic) that has some interesting properties, combining a clean proof theory, including a categorical interpretation, with a simple truth-functional semantics. BI quickly found significant applications in program verification and program analysis, chiefly through a specific theory of BI that is commonly known as 'Separation Logic'. We survey the state of work in bunched logics - which, by now, is a quite large family of systems, including modal and epistemic logics and logics for layered graphs - in such a way as to organize the ideas into a coherent (semantic) picture with a strong interpretation in terms of resources. One such picture can be seen as deriving from an interpretation of BI's semantics in terms of resources, and this view provides a basis for a systematic interpretation of the family of bunched logics, including modal, epistemic, layered graph, and process-theoretic variants, in terms of resources. We explain the basic ideas of resource semantics, including comparisons with Linear Logic and ideas from economics and physics. We include discussions of BI's λ-calculus, of Separation Logic, and of an approach to distributed systems modelling based on resource semantics.

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Cited By

Hill AKomendantskaya EDaggitt MPetrick RKo HOrchard D(2021)Actions you can handle: dependent types for AI plansProceedings of the 6th ACM SIGPLAN International Workshop on Type-Driven Development10.1145/3471875.3472990(1-13)Online publication date: 18-Aug-2021
https://dl.acm.org/doi/10.1145/3471875.3472990
Hill AKomendantskaya EPetrick RGabbrielli MAbel ACheney J(2020)Proof-Carrying Plans: a Resource Logic for AI PlanningProceedings of the 22nd International Symposium on Principles and Practice of Declarative Programming10.1145/3414080.3414094(1-13)Online publication date: 8-Sep-2020
https://dl.acm.org/doi/10.1145/3414080.3414094

Index Terms

Resource semantics: logic as a modelling technology
1. Mathematics of computing
  1. Continuous mathematics
    1. Calculus
      1. Lambda calculus
2. Theory of computation
  1. Logic
    1. Proof theory
  2. Semantics and reasoning

Index terms have been assigned to the content through auto-classification.

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cover image ACM SIGLOG News

ACM SIGLOG News Volume 6, Issue 2

April 2019

54 pages

EISSN:2372-3491

DOI:10.1145/3326938

Editor:
Andrzej Murawski
University of Oxford

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Association for Computing Machinery

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Published: 22 April 2019

Published in SIGLOG Volume 6, Issue 2

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Cited By

Hill AKomendantskaya EDaggitt MPetrick RKo HOrchard D(2021)Actions you can handle: dependent types for AI plansProceedings of the 6th ACM SIGPLAN International Workshop on Type-Driven Development10.1145/3471875.3472990(1-13)Online publication date: 18-Aug-2021
https://dl.acm.org/doi/10.1145/3471875.3472990
Hill AKomendantskaya EPetrick RGabbrielli MAbel ACheney J(2020)Proof-Carrying Plans: a Resource Logic for AI PlanningProceedings of the 22nd International Symposium on Principles and Practice of Declarative Programming10.1145/3414080.3414094(1-13)Online publication date: 8-Sep-2020
https://dl.acm.org/doi/10.1145/3414080.3414094

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