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 "on the strong equivalences for lpmln programs"):
  Abstract: By incorporating the methods of Answer Set Programming (ASP) and Markov Logic Networks (MLN), LPMLN becomes a powerful tool for non-monotonic, inconsistent and uncertain knowledge representation and reasoning. To facilitate the applications and extend the understandings of LPMLN, we investigate the strong equivalences between LPMLN programs in this paper, which is regarded as an important property in the field of logic programming. In the field of ASP, two programs P and Q are strongly equivalent, iff for any ASP program R, the programs P and Q extended by R have the same stable models. In other words, an ASP program can be replaced by one of its strong equivalent without considering its context, which helps us to simplify logic programs, enhance inference engines, construct human-friendly knowledge bases etc. Since LPMLN is a combination of ASP and MLN, the notions of strong equivalences in LPMLN is quite different from that in ASP. Firstly, we present the notions of p-strong and w-strong equivalences between LPMLN programs. Secondly, we present a characterization of the notions by generalizing the SE-model approach in ASP. Finally, we show the use of strong equivalences in simplifying LPMLN programs, and present a sufficient and necessary syntactic condition that guarantees the strong equivalence between a single LPMLN rule and the empty program.

Includes members:
  Member "asp core 2 input language format":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "an asp semantics for constraints involving conditional aggregates")
  Member "weight learning in a probabilistic extension of answer set programs":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "strong equivalence for lpmln programs")
  Member "computing lpmln using asp and mln solvers":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "strong equivalence for lpmln programs")
  Member "probabilistic reasoning with answer sets":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "semiring programming a declarative framework for generalized sum product problems")
  Member "discovering classes of strongly equivalent logic programs":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "on uniform equivalence of epistemic logic programs")
  Member "semantical characterizations and complexity of equivalences in answer set programming":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "query inseparability for alc ontologies")
  Member "logic programming with ordered disjunction":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "translating lpod and cr prolog2 into standard answer set programs")

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)