Toward Robots That Reason: Logic, Probability & Causal Laws

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