Toward Robots That Reason: Logic, Probability & Causal Laws

✍ Scribed by Vaishak Belle

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 201
• Series: Synthesis Lectures on Artificial Intelligence and Machine Learning
• Edition: 1
• Category: Library

✦ Synopsis

This book discusses the two fundamental elements that underline the science and design of artificial intelligence (AI) systems: the learning and acquisition of knowledge from observational data, and the reasoning of that knowledge together with whatever information is available about the application at hand. It then presents a mathematical treatment of the core issues that arise when unifying first-order logic and probability, especially in the presence of dynamics, including physical actions, sensing actions and their effects. A model for expressing causal laws describing dynamics is also considered, along with computational ideas for reasoning with such laws over probabilistic logical knowledge.

✦ Table of Contents

Preface
Acknowledgments
Contents
About the Author
1 Introduction
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1.1 A Science of Agency, Deliberation and Learning
1.2 Logic Meets Probability
1.3 Actions
1.4 Some Related Areas
1.5 Computation, Big Data, Acquisition and Causality
1.6 Key Takeaways
1.7 Notes
2 Representation Matters
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2.1 Introduction
2.2 Symbolic Logic
2.2.1 First-Order Logic
2.2.2 Infinite Domains
2.3 Probabilities on Formulas
2.3.1 Probabilities on Atoms
2.3.2 Probabilities on Quantified Formulas
2.3.3 Essentially Propositional Languages
2.3.4 Actions
2.4 Notes
3 From Predicate Calculus to the Situation Calculus
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3.1 Predicate Calculus
3.2 A Theory of Action
3.2.1 Ontology and Assumptions
3.2.2 The Language
3.2.3 Basic Action Theories
3.2.4 Axiomatization: A One-Dimensional Robot
3.2.5 Regression and Progression
3.2.6 A Programming Language
3.3 Technical Devices
3.3.1 Many Initial Situations
3.3.2 mathbbR-Interpretations
3.3.3 Summation
3.3.4 Integration
3.4 Notes
4 Knowledge
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4.1 Truth and Knowledge
4.1.1 Objective and Subjective Sentences
4.1.2 Actions
4.1.3 Sensing
4.2 The Knowledge Macro
4.2.1 Possible Worlds
4.2.2 The Ideal Reasoner
4.2.3 The Epistemic Fluent
4.2.4 Effects of Actions
4.2.5 Axiomatization: Robot Sensing the Wall
4.2.6 Regression and Progression
4.2.7 Knowledge-Based Programming
4.3 Notes
5 Probabilistic Beliefs
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5.1 Beyond Knowledge and Deterministic Acting
5.2 Weights and Likelihoods
5.3 The Belief Macro
5.3.1 The Numeric Epistemic Fluent
5.3.2 Likelihoods
5.3.3 Axiomatization: The One-Dimensional Robot
5.4 Notes
6 Continuous Distributions
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6.1 Belief Reformulated
6.2 From Weights to Densities
6.3 Bayesian Conditioning
6.4 Axiomatization: A Two-Dimensional Robot
6.5 Noisy Acting
6.5.1 Noisy Action Types
6.5.2 The GOLOG Approach
6.5.3 Alternate Action Axioms
6.5.4 A Definition for Belief
6.5.5 Axiomatization: The Robot with Noisy Effectors
6.6 Notes
7 Localization
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7.1 Axiomatization
7.1.1 Environment
7.1.2 Robot: Physical Actions
7.1.3 Robot: Sensors
7.1.4 Initial Constraints
7.2 Properties
7.2.1 Knowing the Orientation
7.2.2 Uncertainty About the Orientation
7.3 Notes
8 Regression and Progression
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8.1 Regression for Discrete Domains
8.2 Regression for General Domains
8.3 Two Special Cases
8.4 Regression over Noisy Actions
8.5 Progression
8.5.1 Invertible Action Theories
8.5.2 Classical Progression
8.5.3 Progressing Degrees of Belief
8.6 Computability of Progression
8.7 Notes
9 Programs
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9.1 From Knowledge-Based to Belief-Based Programs
9.2 The Allegro System
9.2.1 Domain Axiomatization
9.2.2 Belief-Based Programs
9.2.3 Usage
9.3 Mathematical Foundations
9.3.1 Program Semantics
9.4 A Sampling-Based Interpreter
9.5 Notes
10 A Modal Reconstruction
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10.1 The Non-probabilistic Case
10.1.1 Semantics
10.1.2 Properties
10.1.3 Axiomatization: The One-Dimensional Robot
10.1.4 Beyond the Semantics
10.2 Allowing Probabilities
10.2.1 Semantics
10.2.2 Properties
10.2.3 Axiomatization: The Robot with Noisy Effectors
10.3 Notes
11 Conclusions
11.1 Summary
11.2 What About Automated Planning?
11.3 Outlook
11.4 Notes
Bibliography