Skip to content
Topos Uranos
English

Level 1 · 28 lessons

Mathematical Logic I: Propositional Logic

Syntax, deduction and semantics of classical propositional calculus.

Course content

Unit 0Course overview

  1. 01Syllabus of Mathematical Logic I

Unit 1Language

  1. 02Language: introduction
  2. 03What is mathematical logic
  3. 04The language of propositional logicWith account
  4. 05Induction on the natural numbers and on formulasWith account
  5. 06Formalization of natural languageWith account
  6. 07Language: synthesis and challengesWith account

Unit 2Deduction

  1. 08Deduction: introductionSubscriptionWith account
  2. 09Formal deductive systemsSubscriptionWith account
  3. 10Four deduction techniquesSubscriptionWith account
  4. 11The symmetries of the connectivesSubscriptionWith account
  5. 12The techniques of classical logicSubscriptionWith account
  6. 13De Morgan’s laws and the distributive lawsSubscriptionWith account
  7. 14Deduction: synthesis and challengesSubscriptionWith account

Unit 3Semantics

  1. 15Semantics: introductionSubscriptionWith account
  2. 16Semantics of propositional logicSubscriptionWith account
  3. 17Semantic consequence and equivalenceSubscriptionWith account
  4. 18Generalized De Morgan and distributive lawsSubscriptionWith account
  5. 19Functional completenessSubscriptionWith account
  6. 20Normal formsSubscriptionWith account
  7. 21The normal form algorithm and its applicationsSubscriptionWith account
  8. 22Semantics: synthesis and challengesSubscriptionWith account

Unit 4Metatheory

  1. 23Metatheory: introductionSubscriptionWith account
  2. 24Soundness and completenessSubscriptionWith account
  3. 25The compactness theoremSubscriptionWith account
  4. 26The resolution methodSubscriptionWith account
  5. 27Metatheory: synthesis and challengesSubscriptionWith account

Unit 5Course closing

  1. 28Final review of Mathematical Logic ISubscriptionWith account