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

Motivation (1) ◮ Model and proof theory complementary (soundness, completeness), but also in philosophical conflict ◮ Successful logical frameworks focusing on one of the two: ◮ institutions, the most successful model theoretical framework ◮ dependent type theory (LF), the most successful proof theoretical framework ◮ Complementary strengths: ◮ institutions: abstraction over concrete syntax, strong support for translations ◮ dependent type theory: elegant syntax, strong support for effective reasoning ◮ Goal: Give a logical framework that combines and subsumes institutions and dependent type theory 12
Logical Knowledge Management (LKM) ◮ Sophisticated LKM services needed for logic on a large scale ◮ module system: distributed development, reuse, encapsulation ◮ storage: efficient retrieval, intelligent search, versioning ◮ display to the user in interactive web-based environments ◮ management of change: dependency analysis, difference-based infrastructure ◮ No comprehensive LKM support in logics and logical frameworks 13
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: Motivation (1) ◮ Model and proof
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 and 50: Future Work: Practice ◮ API: Scal
Page 51: Simple Things I Cannot Do ◮ Kripk

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