On the Expressive Power of Graph Logic

Marcinkowski, Jerzy

doi:10.1007/11874683_32

Cited by 4 publications

(6 citation statements)

References 5 publications

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“…Marcinkowski [9] settled this conjecture positively. The property he constructs crucially relies on the presence of an unbounded set of labels in the graphs considered, and on the ability of formulas of GL and (an enhanced) monadic second-order logic, which he calls MSO+ to quantify over labels.…”

Section: Introductionmentioning

confidence: 92%

“…It is not the case that GL can be translated into MS 1 and in Section 6 we construct an example exhibiting this. The question left open from [6] and [9] is whether there is a sentence of MS 2 that is not equivalent to any sentence of GL. This is the question we answer in the present paper.…”

Section: Whereα[x → A] Denotes the Map That Agrees Withα At All Valuementioning

confidence: 99%

“…We allow atomic formulas E σ (t 1 , t 2 ) for each σ ∈ Σ ∪ L and also allow equality testing and quantification over labels. Thus, for σ, τ ∈ Σ ∪ L, we have atomic formulas σ = τ and for any formula ϕ, we can form the formula ∃lϕ for l ∈ L. Marcinkowski [9] termed this extended logic GL+ and proved that it was strictly weaker than MSO+, the corresponding extension of MS 2 . Our result strengthens his.…”

Section: Whereα[x → A] Denotes the Map That Agrees Withα At All Valuementioning

confidence: 99%

“…It was shown in [6] that the same is true of GL. The correspondence between MSO and finite automata extends further to Σ-labelled trees, and it remains an open question (see [9]) whether GL can express all regular tree languages. In Section 6, we show that one suggested candidate for separation-the class of binary trees with an even number of leaves-is definable in GL.…”

Section: Whereα[x → A] Denotes the Map That Agrees Withα At All Valuementioning

confidence: 99%

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Separating Graph Logic from MSO

Antonopoulos

Dawar

2009

Foundations of Software Science and Computational Structures

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Abstract. Graph logic (GL) is a spatial logic for querying graphs introduced by Cardelli et al. It has been observed that in terms of expressive power, this logic is a fragment of Monadic Second Order Logic (MSO), with quantification over sets of edges. We show that the containment is proper by exhibiting a property that is not GL definable but is definable in MSO, even in the absence of quantification over labels. Moreover, this holds when the graphs are restricted to be forests and thus strengthens in several ways a result of Marcinkowski. As a consequence we also obtain that Separation Logic, with a separating conjunction but without the magic wand, is strictly weaker than MSO over memory heaps, settling an open question of Brochenin et al.

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Section: Introductionmentioning

confidence: 92%

Section: Whereα[x → A] Denotes the Map That Agrees Withα At All Valuementioning

confidence: 99%

Section: Whereα[x → A] Denotes the Map That Agrees Withα At All Valuementioning

confidence: 99%

Section: Whereα[x → A] Denotes the Map That Agrees Withα At All Valuementioning

confidence: 99%

See 2 more Smart Citations

Separating Graph Logic from MSO

Antonopoulos

Dawar

2009

Foundations of Software Science and Computational Structures

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“…These games have been adapted for some versions of separation logic, see e.g. [AD09,Ant10] based on similar games on spatial logics [DGG04,Mar06,DGG07].…”

Section: Sl( * ) Versus 1msolmentioning

confidence: 99%

Separation logics and modalities: a survey

Demri

Deters

2015

Journal of Applied Non-Classical Logics

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Like modal logic, temporal logic, or description logic, separation logic has become a popular class of logical formalisms in computer science, conceived as assertion languages for Hoarestyle proof systems with the goal to perform automatic program analysis. In a broad sense, separation logic is often understood as a programming language, an assertion language and a family of rules involving Hoare triples. In this survey, we present similarities between separation logic as an assertion language and modal and temporal logics. Moreover, we propose a selection of landmark results about decidability, complexity and expressive power.

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On the Almighty Wand

Brochenin

Demri

Lozes

2008

Computer Science Logic

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We investigate decidability, complexity and expressive power issues for (first-order) separation logic with one record field (herein called SL) and its fragments. SL can specify properties about the memory heap of programs with singly-linked lists. Separation logic with two record fields is known to be undecidable by reduction of finite satisfiability for classical predicate logic with one binary relation. Surprisingly, we show that second-order logic is as expressive as SL and as a by-product we get undecidability of SL. This is refined by showing that SL without the separating conjunction is as expressive as SL, whence undecidable too. As a consequence of this deep result, in SL the magic wand can simulate the separating conjunction. By contrast, we establish that SL without the magic wand is decidable with non-elementary complexity by reduction from satisfiability for the first-order theory over finite words. Equivalence between second-order logic and separation logic extends to the case with more than one selector.

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On the Expressive Power of Graph Logic

Cited by 4 publications

References 5 publications

Separating Graph Logic from MSO

Separating Graph Logic from MSO

Separation logics and modalities: a survey

On the Almighty Wand

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