Propositional Logic and the Algebra of Boole - N J Wildberger
Overview of propositional logic, exploring atomic statements, connectives, truth values, and techniques for analysis. Covers tautologies, contradictions, truth tables, and equivalences, with a focus on Boole's algebraic approach.
Turing Award Recipient Dana S. Scott - Reflections on Logic and Computer Science - Part 4
Explore Dana S Scott's contributions to computer science, including his work on LCF, Scott Domains, and Category Theory Type Theory, in this insightful interview segment.
Graham Leigh: On the Computational Content of Classical Sequent Calculus
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.
Constructive Mathematics in Univalent Type Theory
Explore constructive mathematics within univalent type theory, delving into advanced concepts and their applications in modern mathematical foundations.
An Introduction to Tensorial Logic and Dialogue Categories
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.
Cyclic Modal Proofs
Exploring cyclic proof theory for modal fixed point logic, its applications in deriving completeness results, and its advantages over traditional finite tree proofs in applied logic.
What Makes a Proof Acceptable?
Explore the criteria for acceptable mathematical proofs, examining rigor, clarity, and convincing arguments in this thought-provoking lecture by Andrew Granville.
Algebraic Structures in Logic and Query Evaluation - Part 2
Explore advanced algebraic structures in logic and their applications to database query evaluation, building on fundamental concepts.
Logic and Probabilistic Circuits - Lecture 1
Explore logical reasoning and probabilistic modeling techniques, focusing on their applications in database theory and artificial intelligence.
Algebraic Structures in Logic and Query Evaluation - Part 1
Explore algebraic structures' role in logic and query evaluation, focusing on their applications in database theory and AI algorithms.
Inference Rules via the Algebra of Boole - MathFoundations 275
Explore propositional logic inference rules using Boolean algebra, simplifying complex logical concepts and eliminating the need for memorization. Includes application to a Lewis Carroll puzzle.
A Brief History of Logic: From Leibniz to Boole - Math Foundations 254
Explore the evolution of logic from Leibniz to Boole, covering key thinkers and innovations in systematic reasoning, diagram representations, and the introduction of mathematics to classical logic.
A Brief History of Logic: Aristotle and Deduction - Math Foundations 251
Explore Aristotle's foundational work in logic, including syllogisms, logical forms, and deductive reasoning, tracing its development from ancient Greece to its lasting impact on modern philosophy.
Semiring Semantics
Explore semiring semantics in logic, evaluating statements with values beyond true/false. Learn applications in database queries, provenance analysis, and extensions to various logical systems.
Consistency, Acyclicity, and Positive Semirings
Explore local vs. global consistency in probability distributions and relational databases, generalizing results using K-relations over positive semirings and acyclic hypergraphs.
Gödel's Proof of God - A Logician's Perspective
Explore Gödel's ontological argument for God's existence through a logician's lens, examining key concepts and the proof's structure.
An Approximate Skolem Function Counter
Explores an algorithm for counting Skolem functions in quantified Boolean formulas, addressing challenges in synthesis problems and providing PAC guarantees for approximate counting.
War Time Proofs and Futuristic Programs
Exploring Gödel's Dialectica interpretation and its connection to linear logic type theory, revealing how past mathematical ideas influence modern programming languages and type systems.
Compiling FO Sentences to Circuits - Upper Bounds and Lower Bounds on the Size of the Circuit
Explores compilation of Boolean formulas into circuits, focusing on provenance of FO sentences. Examines size complexity and limitations of various circuit types for model counting.
Algorithmic Aspects of Semiring Provenance for Stratified Datalog
Explores semiring provenance for stratified datalog, focusing on efficient computation of greatest fixed points in absorptive semirings and circuit representations for polynomial annotations.
Logical Interfaces to Data, Beyond Views
Explores alternative interfaces to data beyond views, discussing query-answering specifications and instance interchangeability for user classes. Examines convertibility between interface types.