Semantics for specialising attack trees based on linear logic

Horne, Ross and Mauw, Sjouke and Tiu, Alwen (2017) Semantics for specialising attack trees based on linear logic. Fundamenta Informaticae, 153 (1-2). pp. 57-86. ISSN 0169-2968 (https://doi.org/10.3233/FI-2017-1531)

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Abstract

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.

ORCID iDs

Horne, Ross ORCID logoORCID: https://orcid.org/0000-0003-0162-1901, Mauw, Sjouke and Tiu, Alwen;
  • Item type:Article
    ID code:87794
    Dates:
    Date
    Event
    7 June 2017
    Published
    1 June 2017
    Accepted
    Notes:Horne, Ross, Mauw, Sjouke, and Tiu, Alwen. ‘Semantics for Specialising Attack Trees Based on Linear Logic’. 1 Jan. 2017 : 57 – 86., DOI: 10.3233/FI-2017-1531 Issue title: Methods for Distributed and Concurrent Systems: Special Issue on the occasion of the 60th Birthday of Professor Gabriel Ciobanu
    Subjects:Science > Mathematics
    Science > Mathematics > Electronic computers. Computer science
    Department:Faculty of Science > Computer and Information Sciences
    Depositing user: Pure Administrator
    Date deposited:11 Jan 2024 15:49
    Last modified:11 Nov 2024 14:04
    URI:https://strathprints.strath.ac.uk/id/eprint/87794
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