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 simple proof of the completeness of apal"
  Abstract: We provide a simple proof of the completeness of arbitrary public announcement logic APAL. The proof is an improvement over the proof found in a previous paper.

Connected through hyperedge HE-1 (induced by source paper "positive announcements"):
  with members:
    - "quantifying over boolean announcements"
    - "the undecidability of arbitrary arrow update logic"

Connected through hyperedge HE-2 (induced by source paper "announcement as effort on topological spaces"):
  with members:
    - "on the solvability of inductive problems a study in epistemic topology"
    - "on the solvability of inductive problems a study in epistemic topology"
    - "public announcement logic in geometric frameworks"
    - "complete axiomatizations for reasoning about knowledge and time"
    - "modal logics for topological spaces"
    - "knowledge theoretic properties of topological spaces"
    - "knowledge on treelike spaces"
    - "domain theory and the logic of observable properties"

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)