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$Mathematical Documents want to Active Digital Math ... - Kwarc$

Conclusion ◮ Mmt simple, scalable, but expressive representation language for logical knowledge ◮ Meaningful representations while abstracting from foundations ◮ Integration of model and proof theory-based frameworks ◮ Abstraction layer on top of logical systems ◮ connects logical systems and LKM services ◮ facilitates translations between logical systems 50
Simple Things I Cannot Do ◮ Kripke models: elementary completeness proof currently: using involved topos theory ◮ L: representation of Henkin models of higher-order logic problem: models non-standard ◮ L: translation of sorted to unsorted logics problem: translation of types to subtypes ◮ Mmt: translation of LF encoded in LF to LF problem: conflation of type hierarchy levels ◮ Mmt: extra-logical declarations, e.g., notations, tactics problem: very specific to systems ◮ Mmt implementation: type reconstruction for LF problem: hard to reuse existing code 51
Page 1 and 2: Representing Logics and Logic Trans
Page 3 and 4: Premise Set/model theory Type/proof
Page 5 and 6: What is Logic? ◮ Field of mathema
Page 7 and 8: Representing Logics and Logic Trans
Page 9 and 10: Model Theory ◮ Propositions conta
Page 11 and 12: Motivation (1) ◮ Model and proof
Page 13 and 14: Logical Knowledge Management (LKM)
Page 15 and 16: Motivation (2) ◮ Give a generic s
Page 17 and 18: Overview (1) Set/model theory Type/
Page 19 and 20: Part 1: Combining Model and Proof T
Page 21 and 22: 1. Institutions with Proofs σ : Σ
Page 23 and 24: 1. Institutions with Proofs, formal
Page 25 and 26: 2. Model theory for dependent type
Page 27 and 28: 2. Model theory for dependent type
Page 29 and 30: 3. The Logic L, syntax and models
Page 31 and 32: 4. Representation example: first-or
Page 33 and 34: 4., 5. Representing Logics and Tran
Page 35 and 36: Conclusion ◮ L combines advantage
Page 37 and 38: Mmt: A Knowledge Representation Lan
Page 39 and 40: Meta-Theories ◮ Meta-relation bet
Page 41 and 42: Document and Theory Level Document
Page 43 and 44: Statement and Object Level ◮ Cons
Page 45 and 46: Foundations ◮ Well-formedness of
Page 47 and 48: Scalability ◮ Flexible flattening
Page 49: Future Work: Practice ◮ API: Scal

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