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: "probabilities on sentences in an expressive logic"
  Abstract: Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive languages like higher-order logic are ideally suited for representing and reasoning about structured knowledge. Uncertain knowledge can be modeled by using graded probabilities rather than binary truth-values. The main technical problem studied in this paper is the following: Given a set of sentences, each having some probability of being true, what probability should be ascribed to other (query) sentences? A natural wish-list, among others, is that the probability distribution (i) is consistent with the knowledge base, (ii) allows for a consistent inference procedure and in particular (iii) reduces to deductive logic in the limit of probabilities being 0 and 1, (iv) allows (Bayesian) inductive reasoning and (v) learning in the limit and in particular (vi) allows confirmation of universally quantified hypotheses/sentences. We translate this wish-list into technical requirements for a prior probability and show that probabilities satisfying all our criteria exist. We also give explicit constructions and several general characterizations of probabilities that satisfy some or all of the criteria and various (counter) examples. We also derive necessary and sufficient conditions for extending beliefs about finitely many sentences to suitable probabilities over all sentences, and in particular least dogmatic or least biased ones. We conclude with a brief outlook on how the developed theory might be used and approximated in autonomous reasoning agents. Our theory is a step towards a globally consistent and empirically satisfactory unification of probability and logic.

Connected through hyperedge HE-1 (induced by source paper "elementary logic in linear space"):
  with members:
    - "on learning to prove"
    - "learning a sat solver from single bit supervision"
    - "gamepad a learning environment for theorem proving"
    - "reinforcement learning of theorem proving"
    - "deep network guided proof search"
    - "holstep a machine learning dataset for higher order logic theorem proving"
    - "analysis of boolean functions"
    - "machine learning of coq proof guidance first experiments"

Connected through hyperedge HE-2 (induced by source paper "on learning to prove"):
  with members:
    - "learning a sat solver from single bit supervision"
    - "gamepad a learning environment for theorem proving"
    - "reinforcement learning of theorem proving"
    - "mastering chess and shogi by self play with a general reinforcement learning algorithm"
    - "holstep a machine learning dataset for higher order logic theorem proving"
    - "tactictoe learning to reason with hol4 tactics"
    - "deepmath deep sequence models for premise selection"
    - "machine learning of coq proof guidance first experiments"

Connected through hyperedge HE-3 (induced by source paper "a formal approach to the problem of logical non omniscience"):
  with members:
    - "why philosophers should care about computational complexity"

Connected through hyperedge HE-4 (induced by source paper "optimal polynomial time estimators a bayesian notion of approximation algorithm"):
  with members:
    - "toward idealized decision theory"
    - "sum of squares proofs and the quest toward optimal algorithms"
    - "resource bounded measure"

Connected through hyperedge HE-5 (induced by source paper "analysis of algorithms and partial algorithms"):
  with members:
    - "asymptotic logical uncertainty and the benford test"
    - "why philosophers should care about computational complexity"

Connected through hyperedge HE-6 (induced by source paper "asymptotic convergence in online learning with unbounded delays"):
  with members:
    - "online learning under delayed feedback"
    - "efficient optimal learning for contextual bandits"

Connected through hyperedge HE-7 (induced by source paper "a probabilistic dependent type system based on non deterministic beta reduction"):
  with members:
    - "church a language for generative models"

Connected through hyperedge HE-8 (induced by source paper "on nicod s condition rules of induction and the raven paradox"):
  with members:
    - "a philosophical treatise of universal induction"

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)