The Consistency and Complexity of Multiplicative Additive System Virtual

Horne, Ross

doi:10.7561/sacs.2015.2.245

Cited by 9 publications

(25 citation statements)

References 52 publications

(68 reference statements)

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“…A natural extension of this observation is to consider whether the ideal and filter semantics, introduced in the previous section for causal attack trees, have an underlying logical system. A logical system sound with respect to each of the ideal and filter semantics is indeed enabled by an extension of linear logic with a non-commutative operator, called MAV [8]. We briefly introduce the system MAV, which is expressed using a generalisation of the sequent calculus, called the calculus of structures.…”

Section: Logical Systems For Specialising Causal Attack Treesmentioning

confidence: 99%

“…An established result [8], is a generalisation of cut elimination to the setting of MAV, which implies the transitivity of implication and consistency of MAV.…”

Section: A Conservative Extension Of Mall With Sequential Compositionmentioning

confidence: 99%

“…However, since contraction and weakening are omitted from linear logic, the multiplicative and additive operators are distinguished. For more details on MALL, we recommend the paper on MAV [8], the logical system used later in this paper, which begins by introducing MALL. The mix rule is not essential for plain attack trees, but enables conservative extensions introduced in later sections.…”

Section: A Brief Overview Of Multiplicative Additive Linear Logicmentioning

confidence: 99%

“…The proofs rely on the following definition and lemma, which is used for proving cut elimination for MAV (Theorem 37) proven in related work [8].…”

Section: Embeddings Of Causal Attack Trees In Non-commutative Logicmentioning

confidence: 99%

“…The logical semantics we propose is based on an extension of linear logic [6] with a non-commutative operator representing sequentiality, called MAV [7,8]. A philosophical benefit of having a logical semantics for causal attack trees is that a logical system provides an objective justification for a choice of semantics.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Semantics for Specialising Attack Trees based on Linear Logic

Horne

Mauw

Tiu

2017

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Attack trees profile the sub-goals of the proponent of an attack. Attack trees have a variety of semantics depending on the kind of question posed about the attack, where questions are captured by an attribute domain. We observe that one of the most general semantics for attack trees, the multiset semantics, coincides with a semantics expressed using linear logic propositions. The semantics can be used to compare attack trees to determine whether one attack tree is a specialisation of another attack tree. Building on these observations, we propose two new semantics for an extension of attack trees named causal attack trees. Such attack trees are extended with an operator capturing the causal order of sub-goals in an attack. These two semantics extend the multiset semantics to sets of series-parallel graphs closed under certain graph homomorphisms, where each semantics respects a class of attribute domains. We define a sound logical system with respect to each of these semantics, by using a recently introduced extension of linear logic, called MAV, featuring a non-commutative operator. The non-commutative operator models causal dependencies in causal attack trees. Similarly to linear logic for attack trees, implication defines a decidable preorder for specialising causal attack trees that soundly respects a class of attribute domains.

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Section: Logical Systems For Specialising Causal Attack Treesmentioning

confidence: 99%

“…An established result [8], is a generalisation of cut elimination to the setting of MAV, which implies the transitivity of implication and consistency of MAV.…”

Section: A Conservative Extension Of Mall With Sequential Compositionmentioning

confidence: 99%

Section: A Brief Overview Of Multiplicative Additive Linear Logicmentioning

confidence: 99%

“…The proofs rely on the following definition and lemma, which is used for proving cut elimination for MAV (Theorem 37) proven in related work [8].…”

Section: Embeddings Of Causal Attack Trees In Non-commutative Logicmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Semantics for Specialising Attack Trees based on Linear Logic

Horne

Mauw

Tiu

2017

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The Attacker Does not Always Hold the Initiative: Attack Trees with External Refinement

Horne

Mauw

Tiu

2019

Graphical Models for Security

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Attack trees provide a structure to an attack scenario, where disjunctions represent choices decomposing attacker's goals into smaller subgoals. This paper investigates the nature of choices in attack trees. For some choices, the attacker has the initiative, but for other choices either the environment or an active defender decides. A semantics for attack trees combining both types of choice is expressed in linear logic and connections with extensive-form games are highlighted. The linear logic semantics defines a specialisation preorder enabling trees, not necessarily equal, to be compared in such a way that all strategies are preserved.

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On Orderings in Security Models

Rowe

2021

Protocols, Strands, and Logic

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The Consistency and Complexity of Multiplicative Additive System Virtual

Cited by 9 publications

References 52 publications

Semantics for Specialising Attack Trees based on Linear Logic

Semantics for Specialising Attack Trees based on Linear Logic

The Attacker Does not Always Hold the Initiative: Attack Trees with External Refinement

On Orderings in Security Models

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