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: "first steps in synthetic guarded domain theory step indexing in the topos of trees"
  Abstract: We present the topos S of trees as a model of guarded recursion. We study the#N#internal dependently-typed higher-order logic of S and show that S models two#N#modal operators, on predicates and types, which serve as guards in recursive#N#definitions of terms, predicates, and types. In particular, we show how to#N#solve recursive type equations involving dependent types. We propose that the#N#internal logic of S provides the right setting for the synthetic construction#N#of abstract versions of step-indexed models of programming languages and#N#program logics. As an example, we show how to construct a model of a#N#programming language with higher-order store and recursive types entirely#N#inside the internal logic of S. Moreover, we give an axiomatic categorical#N#treatment of models of synthetic guarded domain theory and prove that, for any#N#complete Heyting algebra A with a well-founded basis, the topos of sheaves over#N#A forms a model of synthetic guarded domain theory, generalizing the results#N#for S.

Connected through hyperedge HE-1 (induced by source paper "diamonds are not forever liveness in reactive programming with guarded recursion"):
  with members:
    - "simply ratt a fitch style modal calculus for reactive programming without space leaks"
    - "denotational semantics of recursive types in synthetic guarded domain theory"
    - "a generalized modality for recursion"
    - "modal dependent type theory and dependent right adjoints"
    - "the guarded lambda calculus programming and reasoning with guarded recursion for coinductive types"
    - "fitch style modal lambda calculi"
    - "guarded cubical type theory"
    - "guarded dependent type theory with coinductive types"

Connected through hyperedge HE-2 (induced by source paper "coinduction in uniform foundations for corecursive proof search with horn clauses"):
  with members:
    - "coinductive uniform proofs"
    - "towards coinductive theory exploration in horn clause logic position paper"
    - "breaking the loop recursive proofs for coinductive predicates in fibrations"
    - "productive corecursion in logic programming"
    - "guarded dependent type theory with coinductive types"
    - "proof relevant corecursive resolution"
    - "refinement type inference via horn constraint optimization"
    - "sequent calculus in the topos of trees"

Connected through hyperedge HE-3 (induced by source paper "shallow embedding of type theory is morally correct"):
  with members:
    - "pointers in recursion exploring the tropics"
    - "canonicity and normalisation for dependent type theory"
    - "axioms for modelling cubical type theory in a topos"
    - "cubical type theory a constructive interpretation of the univalence axiom"
    - "quotient inductive inductive types"
    - "normalisation by evaluation for type theory in type theory"

Connected through hyperedge HE-4 (induced by source paper "simply ratt a fitch style modal calculus for reactive programming without space leaks"):
  with members:
    - "the clocks they are adjunctions denotational semantics for clocked type theory"
    - "a generalized modality for recursion"
    - "modal dependent type theory and dependent right adjoints"
    - "fitch style modal lambda calculi"

Connected through hyperedge HE-5 (induced by source paper "relational reasoning for markov chains in a probabilistic guarded lambda calculus"):
  with members:
    - "proving uniformity and independence by self composition and coupling"
    - "the guarded lambda calculus programming and reasoning with guarded recursion for coinductive types"
    - "coupling proofs are probabilistic product programs"
    - "a relational logic for higher order programs"
    - "guarded dependent type theory with coinductive types"
    - "differentially private bayesian programming"
    - "relational reasoning via probabilistic coupling"
    - "a lambda calculus foundation for universal probabilistic programming"

Connected through hyperedge HE-6 (induced by source paper "a metalanguage for guarded iteration"):
  with members:
    - "guarded traced categories"
    - "a semantics for hybrid iteration"
    - "guard your daggers and traces properties of guarded co recursion"
    - "the guarded lambda calculus programming and reasoning with guarded recursion for coinductive types"
    - "complete elgot monads and coalgebraic resumptions"
    - "a decidable weakening of compass logic based on cone shaped cardinal directions"
    - "a hoare logic for the coinductive trace based big step semantics of while"
    - "intensionality definability and computation"

Connected through hyperedge HE-7 (induced by source paper "lewis meets brouwer constructive strict implication"):
  with members:
    - "a light modality for recursion"
    - "guard your daggers and traces properties of guarded co recursion"
    - "guarded dependent type theory with coinductive types"
    - "programming and reasoning with guarded recursion for coinductive types"
    - "sequent calculus in the topos of trees"
    - "constructive modalities with provability smack"
    - "epistemic updates on algebras"
    - "canonized rewriting and ground ac completion modulo shostak theories design and implementation"

Connected through hyperedge HE-8 (induced by source paper "denotational semantics of recursive types in synthetic guarded domain theory"):
  with members:
    - "guarded dependent type theory with coinductive types"
    - "cubical type theory a constructive interpretation of the univalence axiom"
    - "quotient inductive inductive types"
    - "guarded cubical type theory path equality for guarded recursion"
    - "general recursion via coinductive types"

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)