Inductive situation calculus

Temporal reasoning has always been a major test case for knowledge representation formalisms. In this paper, we develop an inductive variant of the situation calculus in ID-logic, classical logic extended with inductive definitions. This logic has been proposed recently and is an extension of classi...

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Bibliographic Details
Published in:Artificial intelligence Vol. 171; no. 5; pp. 332 - 360
Main Authors: Denecker, Marc, Ternovska, Eugenia
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.04.2007
Elsevier
Subjects:
Applied sciences
Artificial intelligence
Computer science; control theory; systems
Exact sciences and technology
Inductive definitions
Knowledge representation
Situation calculus
Inductive definitions
Situation calculus
Knowledge representation
Induction
Partial ordering
Case based reasoning
Predicate calculus
Inductive learning
Modularity
Temporal logic
Circumscription
Temporal reasoning
Discrete time
Causality
Inductive logic programming
Artificial intelligence
ISSN:0004-3702, 1872-7921
Online Access:Get full text
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Summary:Temporal reasoning has always been a major test case for knowledge representation formalisms. In this paper, we develop an inductive variant of the situation calculus in ID-logic, classical logic extended with inductive definitions. This logic has been proposed recently and is an extension of classical logic. It allows for a uniform representation of various forms of definitions, including monotone inductive definitions and non-monotone forms of inductive definitions such as iterated induction and induction over well-founded posets. We show that the role of such complex forms of definitions is not limited to mathematics but extends to commonsense knowledge representation. In the ID-logic axiomatization of the situation calculus, fluents and causality predicates are defined by simultaneous induction on the well-founded poset of situations. The inductive approach allows us to solve the ramification problem for the situation calculus in a uniform and modular way. Our solution is among the most general solutions for the ramification problem in the situation calculus. Using previously developed modularity techniques, we show that the basic variant of the inductive situation calculus without ramification rules is equivalent to Reiter-style situation calculus.
ISSN:0004-3702
1872-7921
DOI:10.1016/j.artint.2007.02.002