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: "interpolation in local theory extensions"
  Abstract: In this paper we study interpolation in local extensions of a base theory. We#N#identify situations in which it is possible to obtain interpolants in a#N#hierarchical manner, by using a prover and a procedure for generating#N#interpolants in the base theory as black-boxes. We present several examples of#N#theory extensions in which interpolants can be computed this way, and discuss#N#applications in verification, knowledge representation, and modular reasoning#N#in combinations of local theories.

Connected through hyperedge HE-1 (induced by source paper "nil learning nonlinear interpolants"):
  with members:
    - "sharper and simpler nonlinear interpolants for program verification"
    - "on interpolation and symbol elimination in theory extensions"
    - "interpolation synthesis for quadratic polynomial inequalities and combination with euf"
    - "generating non linear interpolants by semidefinite programming"

Connected through hyperedge HE-2 (induced by source paper "nonlinear craig interpolant generation"):
  with members:
    - "generating non linear interpolants by semidefinite programming"
    - "a hybrid approach for synthesizing optimal controllers of hybrid systems a case study of the oil pump industrial example"

Connected through hyperedge HE-3 (induced by source paper "on invariant synthesis for parametric systems"):
  with members:
    - "on interpolation and symbol elimination in theory extensions"
    - "backward reachability of array based systems by smt solving termination and invariant synthesis"

Connected through hyperedge HE-4 (induced by source paper "on interpolation and symbol elimination in theory extensions"):
  with members:
    - "a pspace complete first order fragment of computability logic"
    - "interpolant based transition relation approximation"
    - "polynomial time computation via local inference relations"

Connected through hyperedge HE-5 (induced by source paper "on first order model based reasoning"):
  with members:
    - "semantically guided evolution of mathcal shi aboxes"
    - "dual hoops have unique halving"
    - "otter 3 3 reference manual"

Connected through hyperedge HE-6 (induced by source paper "locality and applications to subsumption testing and interpolation in mathcal el and some of its extensions"):
  with members:
    - "polynomial time computation via local inference relations"

Connected through hyperedge HE-7 (induced by source paper "quantifier free interpolation of a theory of arrays"):
  with members:
    - "ground interpolation for the theory of equality"
    - "from strong amalgamability to modularity of quantifier free interpolation"
    - "new results on rewrite based satisfiability procedures"
    - "efficient generation of craig interpolants in satisfiability modulo theories"

Connected through hyperedge HE-8 (induced by source paper "from strong amalgamability to modularity of quantifier free interpolation"):
  with members:
    - "quantifier free interpolation of a theory of arrays"
    - "ground interpolation for the theory of equality"

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)