Mathematical logic through Python

"An introduction to Mathematical Logic using a unique pedagogical approach in which the students implement the underlying conceps as well as almost all the mathematical proofs in the Python programming language. The textbook is accompanied by an extensive collection of programming tasks, code skeletons, and unit tests. The covered mathematical material includes Propositional Logic and first-order Predicate Logic, culminating in a proof of Gödel's Completeness Theorem. A "sneak peak" into Gödel's Incompleteness Theorem is also provided"--

Cover -- Half-title -- Title page -- Copyright information -- Dedication -- Contents -- Preface -- 0 Introduction and Overview -- 0.1 Our Final Destination: Gödel's Completeness Theorem -- 0.2 Our Pedagogical Approach -- 0.3 How We Travel: Programs That Handle Logic -- 0.4 Our Roadmap -- Part I Propositional Logic -- 1 Propositional Logic Syntax -- 1.1 Propositional Formulas -- 1.2 Parsing -- 1.3 Infinite Sets of Formulas -- 1.A Optional Reading: Polish Notations -- 2 Propositional Logic Semantics -- 2.1 Detour: Semantics of Programming Languages -- 2.2 Models and Truth Values

2.3 Truth Tables -- 2.4 Tautologies, Contradictions, and Satisfiability -- 2.5 Synthesis of Formulas -- 2.A Optional Reading: Conjunctive Normal Form -- 2.B Optional Reading: Satisfiability and Search Problems -- 3 Logical Operators -- 3.1 More Operators -- 3.2 Substitutions -- 3.3 Complete Sets of Operators -- 3.4 Proving Incompleteness -- 4 Proof by Deduction -- 4.1 Inference Rules -- 4.2 Specializations of an Inference Rule -- 4.3 Deductive Proofs -- 4.4 Practice Proving -- 4.5 The Soundness Theorem -- 5 Working with Proofs -- 5.1 Using Lemmas -- 5.2 Modus Ponens -- 5.3 The Deduction Theorem

5.4 Proofs …