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Preface
Logic, Computability, and Uncomputability
Kostas Arkoudas & Selmer Bringsjord
Preface
Contents
Gödelian Preview
The First Puzzle
Exercises
Solutions
A Second Puzzle
Exercises
Preliminaries
Essential Logic
Sets
Relations and Functions
Finite and Infinite Sets and Alphabets
Exercises
Propositional Languages
Syntax
Semantics
Proof Theory
A Fitch-style Proof Theory
Resolution
Converting to Clausal Form
The Resolution Rule (Propositional Case)
Strategic Resolution and O
TTER
Binary Resolution
UR-Resolution
Hyper-resolution
Set of Support Resolution
Metatheory
Soundness
Completeness
First-Order Languages
Syntax
Semantics
Satisfaction
Exercises
Solutions
Consequence and Other Concepts
Exercises
Solutions to Exercises
Proof Theory
Natural Deduction
Resolution
Converting to Clausal Form
Unification
Unit Resolution
Binary Resolution
Paramodulation
Demodulation
Metatheory
Soundness
Completeness
First Steps
Henkin's Theorem
Augmentation; Completion of Completeness Proof
The Löwenheim-Skolem Theorem
Turing Machines
Definitions
Examples
The Halting Problem
The Undecidability of First-Order Logic
Gödel's First Incompleteness Theorem
Set Theory
Russells's Paradox
Axiomatic Set Theory
Zermelo-Fraenkel Axioms for Set Theory
Exercises
The Continuum Hypothesis
About this document ...
Selmer Bringsjord
1999-04-19
