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**Published in:** LIPIcs, Volume 243, 33rd International Conference on Concurrency Theory (CONCUR 2022)

We introduce a non-interleaving structural operational semantics for the applied π-calculus and prove that it satisfies the properties expected of a labelled asynchronous transition system (LATS). LATS have well-studied relations with other standard non-interleaving models, such as Mazurkiewicz traces or event structures, and are a natural extension of labelled transition systems where the independence of transitions is made explicit. We build on a considerable body of literature on located semantics for process algebras and adopt a static view on locations to identify the parallel processes that perform a transition. By lifting, in this way, work on CCS and π-calculus to the applied π-calculus, we lay down a principled foundation for reusing verification techniques such as partial-order reduction and non-interleaving equivalences in the field of security. The key technical device we develop is the notion of located aliases to refer unambiguously to a specific output originating from a specific process. This light mechanism ensures stability, avoiding disjunctive causality problems that parallel extrusion incurs in similar non-interleaving semantics for the π-calculus.

Clément Aubert, Ross Horne, and Christian Johansen. Diamonds for Security: A Non-Interleaving Operational Semantics for the Applied Pi-Calculus. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 30:1-30:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{aubert_et_al:LIPIcs.CONCUR.2022.30, author = {Aubert, Cl\'{e}ment and Horne, Ross and Johansen, Christian}, title = {{Diamonds for Security: A Non-Interleaving Operational Semantics for the Applied Pi-Calculus}}, booktitle = {33rd International Conference on Concurrency Theory (CONCUR 2022)}, pages = {30:1--30:26}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-246-4}, ISSN = {1868-8969}, year = {2022}, volume = {243}, editor = {Klin, Bartek and Lasota, S{\l}awomir and Muscholl, Anca}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2022.30}, URN = {urn:nbn:de:0030-drops-170930}, doi = {10.4230/LIPIcs.CONCUR.2022.30}, annote = {Keywords: Security, Processes, Structural operational semantics, Asynchronous transition systems, Applied pi-calculus} }

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**Published in:** LIPIcs, Volume 228, 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)

Logical time is a partial order over events in distributed systems, constraining which events precede others. Special interest has been given to series-parallel orders since they correspond to formulas constructed via the two operations for "series" and "parallel" composition. For this reason, series-parallel orders have received attention from proof theory, leading to pomset logic, the logic BV, and their extensions. However, logical time does not always form a series-parallel order; indeed, ubiquitous structures in distributed systems are beyond current proof theoretic methods. In this paper, we explore how this restriction can be lifted. We design new logics that work directly on graphs instead of formulas, we develop their proof theory, and we show that our logics are conservative extensions of the logic BV.

Matteo Acclavio, Ross Horne, Sjouke Mauw, and Lutz Straßburger. A Graphical Proof Theory of Logical Time. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 22:1-22:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{acclavio_et_al:LIPIcs.FSCD.2022.22, author = {Acclavio, Matteo and Horne, Ross and Mauw, Sjouke and Stra{\ss}burger, Lutz}, title = {{A Graphical Proof Theory of Logical Time}}, booktitle = {7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)}, pages = {22:1--22:25}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-233-4}, ISSN = {1868-8969}, year = {2022}, volume = {228}, editor = {Felty, Amy P.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.22}, URN = {urn:nbn:de:0030-drops-163037}, doi = {10.4230/LIPIcs.FSCD.2022.22}, annote = {Keywords: proof theory, causality, deep inference} }

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**Published in:** LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020)

We present a structural proof theory for multi-party sessions, exploiting the expressive power of non-commutative logic which can capture explicitly the message sequence order in sessions. The approach in this work uses a more flexible form of subtyping than standard, for example, allowing a single thread to be substituted by multiple parallel threads which fulfil the role of the single thread. The resulting subtype system has the advantage that it can be used to capture compatibility in the multiparty setting (addressing limitations of pairwise duality). We establish standard results: that the type system is algorithmic, that multiparty compatible processes which are race free are also deadlock free, and that subtyping is sound with respect to the substitution principle. Interestingly, each of these results can be established using cut elimination. We remark that global types are optional in this approach to typing sessions; indeed we show that this theory can be presented independently of the concept of global session types, or even named participants.

Ross Horne. Session Subtyping and Multiparty Compatibility Using Circular Sequents. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 12:1-12:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{horne:LIPIcs.CONCUR.2020.12, author = {Horne, Ross}, title = {{Session Subtyping and Multiparty Compatibility Using Circular Sequents}}, booktitle = {31st International Conference on Concurrency Theory (CONCUR 2020)}, pages = {12:1--12:22}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-160-3}, ISSN = {1868-8969}, year = {2020}, volume = {171}, editor = {Konnov, Igor and Kov\'{a}cs, Laura}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.12}, URN = {urn:nbn:de:0030-drops-128245}, doi = {10.4230/LIPIcs.CONCUR.2020.12}, annote = {Keywords: session types, subtyping, compatibility, linear logic, deadlock freedom} }

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**Published in:** LIPIcs, Volume 131, 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)

Probabilistic choice, where each branch of a choice is weighted according to a probability distribution, is an established approach for modelling processes, quantifying uncertainty in the environment and other sources of randomness. This paper uncovers new insight showing probabilistic choice has a purely logical interpretation as an operator in an extension of linear logic. By forbidding projection and injection, we reveal additive operators between the standard with and plus operators of linear logic. We call these operators the sub-additives. The attention of the reader is drawn to two sub-additive operators: the first being sound with respect to probabilistic choice; while the second arises due to the fact that probabilistic choice cannot be self-dual, hence has a de Morgan dual counterpart. The proof theoretic justification for the sub-additives is a cut elimination result, employing a technique called decomposition. The justification from the perspective of modelling probabilistic concurrent processes is that implication is sound with respect to established notions of probabilistic refinement, and is fully compositional.

Ross Horne. The Sub-Additives: A Proof Theory for Probabilistic Choice extending Linear Logic. In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 131, pp. 23:1-23:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{horne:LIPIcs.FSCD.2019.23, author = {Horne, Ross}, title = {{The Sub-Additives: A Proof Theory for Probabilistic Choice extending Linear Logic}}, booktitle = {4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)}, pages = {23:1--23:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-107-8}, ISSN = {1868-8969}, year = {2019}, volume = {131}, editor = {Geuvers, Herman}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2019.23}, URN = {urn:nbn:de:0030-drops-105300}, doi = {10.4230/LIPIcs.FSCD.2019.23}, annote = {Keywords: calculus of structures, probabilistic choice, probabilistic refinement} }

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**Published in:** LIPIcs, Volume 85, 28th International Conference on Concurrency Theory (CONCUR 2017)

Open bisimilarity is a strong bisimulation congruence for the pi-calculus. In open bisimilarity, free names in processes are treated as variables that may be instantiated; in contrast to late bisimilarity where free names are constants. An established modal logic due to Milner, Parrow, and Walker characterises late bisimilarity, that is, two processes satisfy the same set of formulae if and only if they are bisimilar. We propose an intuitionistic variation of this modal logic and prove that it characterises open bisimilarity. The soundness proof is mechanised in Abella. The completeness proof provides an algorithm for generating distinguishing formulae, useful for explaining and certifying whenever processes are non-bisimilar.

Ki Yung Ahn, Ross Horne, and Alwen Tiu. A Characterisation of Open Bisimilarity using an Intuitionistic Modal Logic. In 28th International Conference on Concurrency Theory (CONCUR 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 85, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{ahn_et_al:LIPIcs.CONCUR.2017.7, author = {Ahn, Ki Yung and Horne, Ross and Tiu, Alwen}, title = {{A Characterisation of Open Bisimilarity using an Intuitionistic Modal Logic}}, booktitle = {28th International Conference on Concurrency Theory (CONCUR 2017)}, pages = {7:1--7:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-048-4}, ISSN = {1868-8969}, year = {2017}, volume = {85}, editor = {Meyer, Roland and Nestmann, Uwe}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2017.7}, URN = {urn:nbn:de:0030-drops-77899}, doi = {10.4230/LIPIcs.CONCUR.2017.7}, annote = {Keywords: bisimulation, modal logic, intuitionistic logic} }

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**Published in:** LIPIcs, Volume 59, 27th International Conference on Concurrency Theory (CONCUR 2016)

We present an expressive but decidable first-order system (named MAV1) defined by using the calculus of structures, a generalisation of the sequent calculus. In addition to first-order universal and existential quantifiers the system incorporates a de Morgan dual pair of nominal quantifiers called `new' and `wen', distinct from the self-dual Gabbay-Pitts and Miller-Tiu nominal quantifiers. The novelty of the operators `new' and `wen' is they are polarised in the sense that `new' distributes over positive operators while `wen' distributes over negative operators. This greater control of bookkeeping enables private names to be modelled in processes embedded as predicates in MAV1. Modelling processes as predicates in MAV1 has the advantage that linear implication defines a precongruence over processes that fully respects causality and branching. The transitivity of this precongruence is established by novel techniques for handling first-order quantifiers in the cut elimination proof.

Ross Horne, Alwen Tiu, Bogdan Aman, and Gabriel Ciobanu. Private Names in Non-Commutative Logic. In 27th International Conference on Concurrency Theory (CONCUR 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 59, pp. 31:1-31:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{horne_et_al:LIPIcs.CONCUR.2016.31, author = {Horne, Ross and Tiu, Alwen and Aman, Bogdan and Ciobanu, Gabriel}, title = {{Private Names in Non-Commutative Logic}}, booktitle = {27th International Conference on Concurrency Theory (CONCUR 2016)}, pages = {31:1--31:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-017-0}, ISSN = {1868-8969}, year = {2016}, volume = {59}, editor = {Desharnais, Jos\'{e}e and Jagadeesan, Radha}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2016.31}, URN = {urn:nbn:de:0030-drops-61759}, doi = {10.4230/LIPIcs.CONCUR.2016.31}, annote = {Keywords: process calculi, calculus of structures, nominal logic, causal consistency} }

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