Nonmonotonic logic and temporal projection
Artificial Intelligence
The well-founded semantics for general logic programs
Journal of the ACM (JACM)
Artificial intelligence and mathematical theory of computation
The alternating fixpoint of logic programs with negation
PODS '89 Selected papers of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Artificial Intelligence
Some contributions to the metatheory of the situation calculus
Journal of the ACM (JACM)
Logic programming revisited: logic programs as inductive definitions
ACM Transactions on Computational Logic (TOCL) - Special issue devoted to Robert A. Kowalski
Knowlege in action: logical foundations for specifying and implementing dynamical systems
Knowlege in action: logical foundations for specifying and implementing dynamical systems
Fixpoint semantics for logic programming a survey
Theoretical Computer Science
Logic programs with stable model semantics as a constraint programming paradigm
Annals of Mathematics and Artificial Intelligence
Inductive Definability and the Situation Calculus
ILPS '97 International Seminar on Logic Databases and the Meaning of Change, Transactions and Change in Logic Databases
The description logic handbook: theory, implementation, and applications
The description logic handbook: theory, implementation, and applications
Artificial Intelligence - Special issue on logical formalizations and commonsense reasoning
Elementary induction on abstract structures (Studies in logic and the foundations of mathematics)
Elementary induction on abstract structures (Studies in logic and the foundations of mathematics)
Splitting an operator: Algebraic modularity results for logics with fixpoint semantics
ACM Transactions on Computational Logic (TOCL)
A framework for representing and solving NP search problems
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
Causal theories of action and change
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Satisfiability checking for PC(ID)
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
A logic of nonmonotone inductive definitions
ACM Transactions on Computational Logic (TOCL)
A tool for addressing the ramification problem in spatial databases: A solution implemented in SQL
Expert Systems with Applications: An International Journal
The ramification problem in temporal databases: a solution implemented in SQL
ISMIS'08 Proceedings of the 17th international conference on Foundations of intelligent systems
A tool for ramification reasoning over temporal OWL knowledge bases
International Journal of Knowledge-based and Intelligent Engineering Systems
Grounding FO and FO(ID) with bounds
Journal of Artificial Intelligence Research
The ramification problem in temporal databases: an approach with conflicting constraints
Journal of Intelligent Information Systems
Task modelling using situation calculus
TAMODIA'09 Proceedings of the 8th international conference on Task Models and Diagrams for User Interface Design
The ramification problem in temporal databases: a solution implemented in SQL
Applied Intelligence
Journal of Artificial Intelligence Research
A general representation and approximate inference algorithm for sensing actions
AI'12 Proceedings of the 25th Australasian joint conference on Advances in Artificial Intelligence
An approximative inference method for solving ∃∀SO satisfiability problems
Journal of Artificial Intelligence Research
Constraint Propagation for First-Order Logic and Inductive Definitions
ACM Transactions on Computational Logic (TOCL)
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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.