Skip to Main content Skip to Navigation
Conference papers

A Simple Separation Logic

Abstract : The kinds of models that are usually considered in separation logic are structures such as words, trees, and more generally pointer structures (heaps). In this paper we introduce the separation logic of much simpler structures, viz. sets. The models of our set separation logic are nothing but valuations of classical propositional logic. Separating a valuation V consists in splitting it up into two partial valuations v 1 and v 2. Truth of a formula φ 1 * φ 2 in a valuation V can then be defined in two different ways: first, as truth of φ 1 in all total extensions of v 1 and truth of φ 2 in all total extensions of v 2; and second, as truth of φ 1 in some total extension of v 1 and truth of φ 2 in some total extension of v 2. The first is an operator of separation of resources: the update of φ 1 * φ 2 by ψ is the conjunction of the update of φ 1 by ψ and the update of φ 2 by ψ; in other words, φ 1 * φ 2 can be updated independently. The second is an operator of separation of processes: updates by ψ 1 * ψ 2 can be performed independently. We show that the satisfiability problem of our logic is decidable in polynomial space (PSPACE). We do so by embedding it into dynamic logic of propositional assignments (which is PSPACE complete). We moreover investigate its applicability to belief update and belief revision, where the separation operators allow to formulate natural requirements on independent pieces of information.
Complete list of metadata

Cited literature [17 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01147307
Contributor : Open Archive Toulouse Archive Ouverte (OATAO) Connect in order to contact the contributor
Submitted on : Thursday, April 30, 2015 - 10:12:24 AM
Last modification on : Wednesday, June 1, 2022 - 4:02:53 AM
Long-term archiving on: : Monday, September 14, 2015 - 4:12:13 PM

File

Herzig_12649.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01147307, version 1
  • OATAO : 12649

Citation

Andreas Herzig. A Simple Separation Logic. International Workshop Logic, Language, Information, and Computation - WoLLIC 2013, Aug 2013, Darmstadt, Germany. pp. 168-178. ⟨hal-01147307⟩

Share

Metrics

Record views

103

Files downloads

62