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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Vydané v:	Artificial intelligence Ročník 171; číslo 5; s. 332 - 360
Hlavní autori:	Denecker, Marc, Ternovska, Eugenia
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Amsterdam Elsevier B.V 01.04.2007 Elsevier
Predmet:	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
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Abstract	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.
AbstractList	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.
Author	Ternovska, Eugenia Denecker, Marc
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Keywords	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
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Snippet	Temporal reasoning has always been a major test case for knowledge representation formalisms. In this paper, we develop an inductive variant of the situation...
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SubjectTerms	Applied sciences Artificial intelligence Computer science; control theory; systems Exact sciences and technology Inductive definitions Knowledge representation Situation calculus
Title	Inductive situation calculus
URI	https://dx.doi.org/10.1016/j.artint.2007.02.002
Volume	171
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