# Expressivity Properties of Boolean

@inproceedings{Galmiche2006ExpressivityPO, title={Expressivity Properties of Boolean}, author={Didier Galmiche and Dominique Larchey-Wendling}, booktitle={FSTTCS}, year={2006} }

In this paper, we study Boolean BI Logic (BBI) from a semantic perspective. This logic arises as a logical basis of some recent separation logics used for reasoning about mutable data structures and we aim at proposing new results from alternative semantic foundations for BBI that seem to be necessary in the context of modeling and proving program properties. Starting from a Kripke relational semantics for BBI which can also be viewed as a non-deterministic monoidal semantics, we first show…

## 7 Citations

### Undecidability of Propositional Separation Logic and Its Neighbours

- Philosophy2010 25th Annual IEEE Symposium on Logic in Computer Science
- 2010

It is shown that the purely propositional fragment of separation logic is undecidability, and a number of propositional systems which approximate separation logic are undecidable as well, including both Boolean BI and Classical BI.

### Modular Labelled Sequent Calculi for Abstract Separation Logics

- Computer ScienceACM Trans. Comput. Log.
- 2018

This paper non-trivially improves upon previous work by giving a general framework of calculi on which any new axiom in the logic satisfying a certain form corresponds to an inference rule in this framework, and the completeness proof is generalised to consider such axioms.

### Boolean BI is Decidable ( via Display Logic )

- Computer Science
- 2009

It is shown that cut-elimination holds and that the system is sound and complete with respect to the usual notion of validity for BBI, and that proof search in the system can be restricted to a finitely bounded space.

### Go with the flow: compositional abstractions for concurrent data structures

- Computer ScienceProc. ACM Program. Lang.
- 2018

This work proposes a novel approach to abstracting regions in the heap by encoding the data structure invariant into a local condition on each individual node, and introduces the notion of a flow interface, which expresses the relies and guarantees that a heap region imposes on its context to maintain the local flow invariant with respect to the global heap.

### An Algebraic Glimpse at Bunched Implications and Separation Logic

- Mathematics, Computer ScienceOutstanding Contributions to Logic
- 2021

The logic of Bunched Implications (BI) and Separation Logic is overviewed from a perspective inspired by Hiroakira Ono's algebraic approach to substructural logics and an algebraic proof of cut elimination in the setting of residuated frames of Galatos and Jipsen is presented.

### Parametric completeness for separation theories

- Philosophy
- 2014

This paper closes the logical gap between provability in the logic BBI, which is the propositional basis for separation logic, and validity in an intended class of separation models, as well as investigating the relationships between these values and each other.

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