human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "disjunctive bases normal forms and model theory for modal logics"):
  Abstract: We present the concept of a disjunctive basis as a generic framework for normal forms in modal logic based on coalgebra. Disjunctive bases were defined in previous work on completeness for modal fixpoint logics, where they played a central role in the proof of a generic completeness theorem for coalgebraic mu-calculi. Believing the concept has a much wider significance, here we investigate it more thoroughly in its own right. We show that the presence of a disjunctive basis at the "one-step" level entails a number of good properties for a coalgebraic mu-calculus, in particular, a simulation theorem showing that every alternating automaton can be transformed into an equivalent nondeterministic one. Based on this, we prove a Lyndon theorem for the full fixpoint logic, its fixpoint-free fragment and its one-step fragment, a Uniform Interpolation result, for both the full mu-calculus and its fixpoint-free fragment, and a Janin-Walukiewicz-style characterization theorem for the mu-calculus under slightly stronger assumptions. We also raise the questions, when a disjunctive basis exists, and how disjunctive bases are related to Moss' coalgebraic "nabla" modalities. Nabla formulas provide disjunctive bases for many coalgebraic modal logics, but there are cases where disjunctive bases give useful normal forms even when nabla formulas fail to do so, our prime example being graded modal logic. We also show that disjunctive bases are preserved by forming sums of coalgebraic modal logics, providing a tool for modular construction of modal logics admitting disjunctive bases. Finally, we consider the problem of giving a category-theoretic formulation of disjunctive bases, and provide a partial solution.

Includes members:
  Member "uniform interpolation for coalgebraic fixpoint logic":
    also connected through other hyperedges:
      (none)
  Member "monadic second order logic and bisimulation invariance for coalgebras":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "np reasoning in the monotone mu calculus")
  Member "completeness for the coalgebraic cover modality":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "completeness via canonicity in coalgebraic logics")
  Member "exptime tableaux for the coalgebraic mu calculus":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "np reasoning in the monotone mu calculus")
  Member "pspace bounds for rank 1 modal logics":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "optimal satisfiability checking for arithmetic mu calculi")
  Member "coalgebraic automata theory basic results":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "some model theory for the modal mu calculus syntactic characterisations of semantic properties")

Question: Please tell me which class the source paper 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)