Abstract
Our account is formulated in the language of the situation calculus, the most established special-purpose knowledge representation formalism for reasoning about dynamical systems. Originally postulated by McCarthy, and later revised by Reiter, it is a dialect of first-order logic with distinguished sorts. So we begin with a brief recap of standard first-order and second-order logic, before turning to the situation calculus.
You can prove anything you want by coldly logical reason—if you pick the proper postulates.
– Isaac Asimov, I, Robot
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Notes
- 1.
Proofs are omitted almost entirely in this book. The bibliographic sections at the end of every chapter detail where formal statements (and their proofs by extension) can be found.
- 2.
Regression is a form of query rewriting [231], and can be seen as the sentential solution to pre-image computation for state-based abstractions seen in model checking [46].
- 3.
Since their work, a number of other special cases have been studied [160].
- 4.
There are numerous nonmonotonic accounts that rely on a controlled extension to predicates—often referred to as model minimization—to overcome the need to specify every qualifier and condition, e.g., [3, 87].
- 5.
This can be contrasted to a model checking approach, where the application of interest is captured directly as a propositional, first-order or modal structure [107, 227].
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Belle, V. (2023). From Predicate Calculus to the Situation Calculus. In: Toward Robots That Reason: Logic, Probability & Causal Laws. Synthesis Lectures on Artificial Intelligence and Machine Learning. Springer, Cham. https://doi.org/10.1007/978-3-031-21003-7_3
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DOI: https://doi.org/10.1007/978-3-031-21003-7_3
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