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#Proof Theory

Showing: 31 courses
Hausdorff Center for Mathematics

Graham Leigh: On the Computational Content of Classical Sequent Calculus

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Explore computational interpretations of classical logic through Herbrand's Theorem, focusing on a language-theoretic representation using higher-order recursion schemes in classical sequent calculus.
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9 Lesons
35 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

An Introduction to Tensorial Logic and Dialogue Categories

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An introduction to tensorial logic, exploring its relationship with dialogue games and categories. Refines linear logic and provides insights into dialogical interpretations of proofs and programs.
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1 Lesons
33 minutes
On-Demand
Free-Video
ACM SIGPLAN

Orthologic with Axioms - Proof Theory and Algorithms

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Explore orthologic with axioms, its proof theory, and algorithms. Discover generalized ortholattice reasoning and its applications in verification condition simplification and normalization.
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1 Lesons
20 minutes
On-Demand
Free-Video
ACM SIGPLAN

Interpolation and Quantifiers in Ortholattices

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Explore quantifiers and interpolation in orthologic, examining proof systems, quantifier elimination, and efficient interpolant computation for verification algorithms.
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1 Lesons
16 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

David Cerna: Proof Schema and the Refutational Complexity of Their Cut Structure

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Explore proof schemas, refutational complexity, and cut structures in mathematical logic. Gain insights into CERES, ECA, and 1-SMA concepts for advanced theorem proving techniques.
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14 Lesons
39 minutes
On-Demand
Free-Video
Fields Institute

Topics in Pure Model Theory - Lecture 10

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Explore advanced concepts in pure model theory, including simple theory, invariant types, and symmetry, with expert insights from Itay Kaplan of The Hebrew University of Jerusalem.
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8 Lesons
1 hour 26 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Ulrich Kohlenbach - Extraction of Information from Proofs

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Explore proof theory and its applications in mathematics, focusing on extracting computational content from nonconstructive proofs for practical problem-solving.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Insights into Mathematics

Are All True Mathematical Statements Provable? - Famous Math Problems

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Explores the philosophical question of mathematical truth and provability, challenging conventional views with explicit examples of likely true but unprovable mathematical statements.
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9 Lesons
31 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

From Informal to Formal Mathematics and Back - Tools for Mathematical Transformation

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Tools for transforming informal mathematics to formal and vice versa, aiming to enhance mathematical understanding. Explores Lean blueprint infrastructure and Informal Lean for collaborative formalization projects and customizable proof detailing.
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1 Lesons
42 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Dialectica Categories for All

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Explore dialectica categories and their applications in logic, mathematics, and computer science with expert Valeria de Paiva in this insightful talk.
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1 Lesons
52 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Peculiarities of the Minimalist Foundation for Formal Mathematics

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Explore the unique aspects of the Minimalist Foundation in formal mathematics, examining its peculiarities and implications for mathematical reasoning and proof construction.
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1 Lesons
42 minutes
On-Demand
Free-Video
Institute for Advanced Study

The Value of Errors in Proofs

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Explore the significance of errors in mathematical proofs with Avi Wigderson, delving into their role in advancing quantum information and physics research.
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1 Lesons
1 hour 19 minutes
On-Demand
Free-Video
Fields Institute

The Value of Errors in Proofs

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Explore the significance of errors in mathematical proofs with Avi Wigderson. Gain insights into how mistakes contribute to advancing mathematical understanding and problem-solving techniques.
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1 Lesons
43 minutes
On-Demand
Free-Video
Wrath of Math

Where This Deadly Proof Falls Apart - Analyzing the Irrationality of sqrt(2)

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Explore the classic proof of sqrt(2)'s irrationality and discover its limitations when applied to rational numbers in this insightful mathematical analysis.
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1 Lesons
20 minutes
On-Demand
Free-Video
MUNI Seminar Series

Taming the Monster of Independence in Mathematics

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Explore approaches to settling seemingly independent mathematical problems, focusing on Gödel's incompleteness theorem and the Continuum Hypothesis.
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1 Lesons
54 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Cueology of Proof

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Explore the art and science of constructing mathematical proofs, delving into logical reasoning, problem-solving techniques, and the foundations of formal verification.
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1 Lesons
39 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

An Introduction to Differential Linear Logic

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Explore Differential Linear Logic fundamentals, key concepts, and applications in this comprehensive introduction by Marie Kerjean at CIRM's mathematical conference.
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1 Lesons
1 hour 18 minutes
On-Demand
Free-Video
NCCR SwissMAP

An Introduction to Mathematical Logic

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Explore fundamental concepts of mathematical logic, including propositional calculus, first-order logic, and formal reasoning techniques.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

On a Decomposition of WKL

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Explore a mathematical decomposition of WKL!! with Takako Nemoto, delving into type theory, constructive mathematics, and geometric logics.
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1 Lesons
52 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Mechanising Gödel-Löb Provability Logic in HOL Light

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Explore the mechanisation of Gödel–Löb Provability Logic in HOL Light, delving into formal proofs and theorem verification techniques for modal logic systems.
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1 Lesons
59 minutes
On-Demand
Free-Video
BIMSA

Infinitary Combinatorics and Finitary Arithmetic

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Explore recent developments in characterizing Ramsey-type combinatorial principles within reverse mathematics, focusing on proof-theoretic strength analysis.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
ACM SIGPLAN

Focusing on Refinement Typing - A Logically Principled Foundation

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Explore a logically principled foundation for SMT constraint generation in refinement type systems, combining focalized call-by-push-value, bidirectional typing, and value-determined indexes.
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1 Lesons
19 minutes
On-Demand
Free-Video
ACM SIGPLAN

The Complex(ity) Landscape of Checking Infinite Descent

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Explore the complexity of checking Infinite Descent in cyclic proof systems, examining various criteria and their parameterized time complexities to improve automatic verification techniques.
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1 Lesons
18 minutes
On-Demand
Free-Video
Strange Loop Conference

Proof Theory Impressionism - Blurring the Curry-Howard Line

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Exploring approaches to bridge the gap between proof assistants and production languages, focusing on Rust and its potential for incorporating provable system capabilities.
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1 Lesons
35 minutes
On-Demand
Free-Video
ACM SIGPLAN

Explicit Refinement Types - A Type Theory with Embedded Proofs

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Explore λert, a type theory with explicit proof refinement types. Learn about its soundness, denotational semantics, and formalization in Lean 4.
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1 Lesons
29 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Recursive Inequalities in Applied Proof Theory

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Explore recursive inequalities in applied proof theory, delving into advanced mathematical concepts and their practical applications.
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1 Lesons
58 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

From Axioms to Synthetic Inference Rules via Focusing

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Explore the connection between axioms and synthetic inference rules through focusing, as presented by Dale Miller in this mathematical conference talk.
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1 Lesons
47 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Inductive Definitions, Predicativity, and the Mahlo Universe

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Explore inductive definitions, predicativity, and the Mahlo universe in type theory with Peter Dybjer. Gain insights into advanced mathematical concepts and their applications.
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1 Lesons
49 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Structural Rules and Algebraic Properties of Intersection Types

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Explore structural rules and algebraic properties of intersection types in lambda calculus, examining their impact on type assignment systems and programming language theory.
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1 Lesons
56 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Challenges in Formalising Recent Results in Formal Language Theory

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Explore challenges in formalizing recent results linking formal language theory and computational group theory, with insights on making proofs more amenable to formalization.
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1 Lesons
51 minutes
On-Demand
Free-Video
Dyalog User Meetings

Data Parallel Proof Verification in APL - Using Metamath for Mathematical Databases

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Discover how APL enables data-parallel verification of mathematical proofs using Metamath, exploring formal verification methods, proof structures, and efficient processing of large mathematical databases.
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9 Lesons
20 minutes
On-Demand
Free-Video