human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "a system of interaction and structure ii the need for deep inference"
  Abstract: This paper studies properties of the logic BV, which is an extension of#N#multiplicative linear logic (MLL) with a self-dual non-commutative operator. BV#N#is presented in the calculus of structures, a proof theoretic formalism that#N#supports deep inference, in which inference rules can be applied anywhere#N#inside logical expressions. The use of deep inference results in a simple#N#logical system for MLL extended with the self-dual non-commutative operator,#N#which has been to date not known to be expressible in sequent calculus. In this#N#paper, deep inference is shown to be crucial for the logic BV, that is, any#N#restriction on the ``depth'' of the inference rules of BV would result in a#N#strictly less expressive logical system.

Connected through hyperedge HE-1 (induced by source paper "de morgan dual nominal quantifiers modelling private names in non commutative logic"):
  with members:
    - "subatomic proof systems splittable systems"
    - "private names in non commutative logic"
    - "a deep inference system with a self dual binder which is complete for linear lambda calculus"
    - "interaction and depth against nondeterminism in proof search"
    - "on the proof complexity of deep inference"
    - "a system of interaction and structure"

Connected through hyperedge HE-2 (induced by source paper "proof nets through the lens of graph theory a compilation of remarks"):
  with members:
    - "constrained path finding and structure from acyclicity"
    - "on noncommutative extensions of linear logic"

Connected through hyperedge HE-3 (induced by source paper "subatomic proof systems splittable systems"):
  with members:
    - "a deep inference system with a self dual binder which is complete for linear lambda calculus"
    - "interaction and depth against nondeterminism in proof search"
    - "on the proof complexity of deep inference"
    - "a system of interaction and structure"

Connected through hyperedge HE-4 (induced by source paper "subatomic systems need not be subatomic"):
  with members:
    - "subatomic proof systems splittable systems"
    - "a deep inference system with a self dual binder which is complete for linear lambda calculus"
    - "a system of interaction and structure"

Connected through hyperedge HE-5 (induced by source paper "on noncommutative extensions of linear logic"):
  with members:
    - "dialectica categories for the lambek calculus"
    - "a system of interaction and structure"

Connected through hyperedge HE-6 (induced by source paper "private names in non commutative logic"):
  with members:
    - "a deep inference system with a self dual binder which is complete for linear lambda calculus"
    - "structure preserving bisimilarity supporting an operational petri net semantics of ccsp"
    - "a quasipolynomial cut elimination procedure in deep inference via atomic flows and threshold formulae"
    - "on the proof complexity of deep inference"
    - "a system of interaction and structure"

Connected through hyperedge HE-7 (induced by source paper "a deep inference system with a self dual binder which is complete for linear lambda calculus"):
  with members:
    - "communication and concurrency with logic based restriction inside a calculus of structures"
    - "linear lambda calculus with explicit substitutions as proof search in deep inference"
    - "a system of interaction and structure"
    - "linear encodings of bounded ltl model checking"

Connected through hyperedge HE-8 (induced by source paper "interaction and depth against nondeterminism in proof search"):
  with members:
    - "on the proof complexity of deep inference"
    - "a system of interaction and structure"

Question: Please tell me which class the center node belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.LO(Logic in Computer Science)