_index.md (3661B)
1 +++ 2 title = 'Logic and Modeling' 3 +++ 4 5 # Logic and Modeling 6 Here's the [online book](http://avigad.github.io/logic_and_proof/propositional_logic.html). 7 8 Also, [here's my Anki deck](logic-modelling.apkg). 9 10 [The one-page cheat sheet](the-one-page-cheat-sheet). 11 12 - [Propositional logic](propositional-logic) 13 - [Notation review](propositional-logic#notation-review) 14 - [Rules of inference](propositional-logic#rules-of-inference) 15 - [Forward and backward reasoning](propositional-logic#forward-and-backward-reasoning) 16 - [Proof by contradiction](propositional-logic#proof-by-contradiction) 17 - [Vocab definitions](propositional-logic#vocab-definitions) 18 - [Classical reasoning](propositional-logic#classical-reasoning) 19 - [Syntax vs Semantics](propositional-logic#syntax-vs-semantics) 20 - [Soundness and completeness](propositional-logic#soundness-and-completeness) 21 - [First order logic](first-order-logic) 22 - [Functions, predicates, relations](first-order-logic#functions-predicates-relations) 23 - [Quantifiers, binding](first-order-logic#quantifiers-binding) 24 - [Natural deduction rules](first-order-logic#natural-deduction-rules) 25 - [Relativization and sorts](first-order-logic#relativization-and-sorts) 26 - [Models](first-order-logic#models) 27 - [Interpreting formulas without quantifiers](first-order-logic#interpreting-formulas-without-quantifiers) 28 - [Interpretation of formulas with quantifiers and free variables](first-order-logic#interpretation-of-formulas-with-quantifiers-and-free-variables) 29 - [Interpreting terms in model with environment](first-order-logic#interpreting-terms-in-model-with-environment) 30 - [Semantical entailment in predicate logic](first-order-logic#semantical-entailment-in-predicate-logic) 31 - [Logical equivalence](first-order-logic#logical-equivalence) 32 - [Satisfiability, validity, consistency](first-order-logic#satisfiability-validity-consistency) 33 - [Translating into predicate logic](first-order-logic#translating-into-predicate-logic) 34 - [Rules for quantifiers and connectives](first-order-logic#rules-for-quantifiers-and-connectives) 35 - [Semantics of first order logic](first-order-logic#semantics-of-first-order-logic) 36 - [Sets](sets) 37 - [Relations](sets#relations) 38 - [Order types](sets#order-types) 39 - [Natural numbers & induction](sets#natural-numbers-induction) 40 - [Recursive definitions](sets#recursive-definitions) 41 - [Modal logic](modal-logic) 42 - [Truth in worlds](modal-logic#truth-in-worlds) 43 - [Truth in Kripke models](modal-logic#truth-in-kripke-models) 44 - [Semantic implication/entailment](modal-logic#semantic-implication-entailment) 45 - [Frames](modal-logic#frames) 46 - [Meta-Theorems of Predicate Logic](meta-theorems-of-predicate-logic) 47 - [Definability and Undefinability results](definability-and-undefinability-results) 48 - [for model cardinality](definability-and-undefinability-results#for-model-cardinality) 49 - [for reachability](definability-and-undefinability-results#for-reachability) 50 - [General overview](definability-and-undefinability-results#general-overview) 51 - [Decidability and Undecidability](decidability-and-undecidability) 52 - [Decision problems](decidability-and-undecidability#decision-problems) 53 - [Termination problem](decidability-and-undecidability#termination-problem) 54 - [Post's Correspondence Problem](decidability-and-undecidability#posts-correspondence-problem) 55 - [Undecidability of Validity and Provability](decidability-and-undecidability#undecidability-of-validity-and-provability) 56 - [Undecidability of Satisfiability](decidability-and-undecidability#undecidability-of-satisfiability) 57 - [Incompleteness theorem](incompleteness-theorem)