Expressivity Properties of Boolean

  title={Expressivity Properties of Boolean},
  author={Didier Galmiche and Dominique Larchey-Wendling},
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… 

Undecidability of Propositional Separation Logic and Its Neighbours

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

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 )

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

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

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

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.



Semantic Labelled Tableaux for Propositional BI

This paper proposes a labelled tableau calculus for BI 1 based on particular labels and constraints and proves the soundness and completeness of this calculus w.r.t. the Kripke resource semantics with emphasis on countermodel construction.

Semantic Labelled Tableaux for propositional BI (without bottom)

This paper proposes a labelled tableau calculus for BI without bottom, that is the unit of the additive disjunction, based on particular labels and constraints, and proves the soundness and completeness of this calculus wrt the Kripke resource semantics with an emphasis on countermodel construction.

Characterizing Provability in

This work proposes a characterization of provability in BI’s Pointer Logic that is based on semantic structures called resource graphs that capture PL models by considering heaps as resources and by using a labelling process.

The Logic of Bunched Implications

A logic BI in which a multiplicative (or linear) and an additive (or intuitionistic) implication live side-by-side is introduced and computational interpretations, based on sharing, at both the propositional and predicate levels are discussed.

The semantics of BI and resource tableaux

A theory of semantic tableaux for BI is developed, providing an elegant basis for efficient theorem proving tools for BI, and two new strong results for propositional BI are proved: its decidability and the finite model property with respect to topological semantics.

Intuitionistic Propositional Logic is Polynomial-Space Complete

Adjunct Elimination Through Games in Static Ambient Logic

This proof is directed by the intuition that adjuncts can be eliminated when the corresponding moves are not useful in winning the game, and is modular with respect to the operators of the logic, providing a general technique for determining which combinations of operators admit adjunct elimination.

A Calculus and logic of resources and processes

This work presents a calculus of resources and processes, based on a development of Milner’s synchronous calculus of communication systems, SCCS, that uses an explicit model of resource and provides a logical characterization of bisimulation between resource processes which is compositional in the concurrent and local structure of systems.

The semantics and proof theory of the logic of bunched implications

  • D. Pym
  • Philosophy, Computer Science
    Applied logic series
  • 2002
This book discusses Propositional BI as a Sequent Calculus as well as Topological Kripke Semantics for Predicate BI and its applications in Algebraic, Topological, Categorical and Resource Semantics.