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 "decidability of type checking in the calculus of algebraic constructions with size annotations"):
  Abstract: Since Val Tannen's pioneer work on the combination of simply-typed lambda-calculus and first-order rewriting (LICS'88), many authors have contributed to this subject by extending it to richer typed lambda-calculi and rewriting paradigms, culminating in calculi like the Calculus of Algebraic Constructions. These works provide theoretical foundations for type-theoretic proof assistants where functions and predicates are defined by oriented higher-order equations. This kind of definitions subsumes induction-based definitions, is easier to write and provides more automation. On the other hand, checking that user-defined rewrite rules are strongly normalizing and confluent, and preserve the decidability of type-checking when combined with beta-reduction, is more difficult. Most termination criteria rely on the term structure. In a previous work, we extended to dependent types and higher-order rewriting, the notion of ``sized types'' studied by several authors in the simpler framework of ML-like languages, and proved that it preserves strong normalization. The main contribution of the present paper is twofold. First, we prove that, in the Calculus of Algebraic Constructions with size annotations, the problems of type inference and type-checking are decidable, provided that the sets of constraints generated by size annotations are satisfiable and admit most general solutions. Second, we prove the later properties for a size algebra rich enough for capturing usual induction-based definitions and much more.

Includes members:
  Member "a type based termination criterion for dependently typed higher order rewrite systems":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "size based termination of higher order rewriting")
  Member "rewriting modulo in deduction modulo":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "termination of rewrite relations on λ terms based on girard s notion of reducibility")
  Member "inductive types in the calculus of algebraic constructions":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "elaborating inductive definitions and course of values induction in cedille")
  Member "definitions by rewriting in the calculus of constructions":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "a modular termination method for second order computation")

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)