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 "diamonds are not forever liveness in reactive programming with guarded recursion"):
  Abstract: When designing languages for functional reactive programming (FRP) the main challenge is to provide the user with a simple, flexible interface for writing programs on a high level of abstraction while ensuring that all programs can be implemented efficiently in a low-level language. To meet this challenge, a new family of modal FRP languages has been proposed, in which variants of Nakano's guarded fixed point operator are used for writing recursive programs guaranteeing properties such as causality and productivity. As an apparent extension to this it has also been suggested to use Linear Temporal Logic (LTL) as a language for reactive programming through the Curry-Howard isomorphism, allowing properties such as termination, liveness and fairness to be encoded in types. However, these two ideas are in conflict with each other, since the fixed point operator introduces non-termination into the inductive types that are supposed to provide termination guarantees. #R##N#In this paper we show that by regarding the modal time step operator of LTL a submodality of the one used for guarded recursion (rather than equating them), one can obtain a modal type system capable of expressing liveness properties while retaining the power of the guarded fixed point operator. We introduce the language Lively RaTT, a modal FRP language with a guarded fixed point operator and an `until' type constructor as in LTL, and show how to program with events and fair streams. Using a step-indexed Kripke logical relation we prove operational properties of Lively RaTT including productivity and causality as well as the termination and liveness properties expected of types from LTL.

Includes members:
  Member "simply ratt a fitch style modal calculus for reactive programming without space leaks":
    also connected through other hyperedges:
      (none)
  Member "denotational semantics of recursive types in synthetic guarded domain theory":
    also connected through other hyperedges:
      (none)
  Member "a generalized modality for recursion":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "simply ratt a fitch style modal calculus for reactive programming without space leaks")
  Member "modal dependent type theory and dependent right adjoints":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "simply ratt a fitch style modal calculus for reactive programming without space leaks")
  Member "the guarded lambda calculus programming and reasoning with guarded recursion for coinductive types":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "relational reasoning for markov chains in a probabilistic guarded lambda calculus")
  Member "fitch style modal lambda calculi":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "simply ratt a fitch style modal calculus for reactive programming without space leaks")
  Member "guarded cubical type theory":
    also connected through other hyperedges:
      (none)
  Member "guarded dependent type theory with coinductive types":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "coinduction in uniform foundations for corecursive proof search with horn clauses")

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.PL(Programming Languages)