A Prolog technology theorem prover: implementation by an extended Prolog computer
Journal of Automated Reasoning
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
Knowledge Representation, Reasoning, and Declarative Problem Solving
Knowledge Representation, Reasoning, and Declarative Problem Solving
The Well-Founded Semantics Is the Principle of Inductive Definition
JELIA '98 Proceedings of the European Workshop on Logics in Artificial Intelligence
A logic of nonmonotone inductive definitions
ACM Transactions on Computational Logic (TOCL)
The Second Answer Set Programming Competition
LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
A framework for representing and solving NP search problems
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
Towards a logical reconstruction of a theory for locally closed databases
ACM Transactions on Database Systems (TODS)
An approximation of action theories of AL and its application to conformant planning
LPNMR'05 Proceedings of the 8th international conference on Logic Programming and Nonmonotonic Reasoning
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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The fragment ∃∀SO(ID) of second order logic extended with inductive definitions is expressive, and many interesting problems, such as conformant planning, can be naturally expressed as finite domain satisfiability problems of this logic. Such satisfiability problems are computationally hard (Σ2P). In this paper, we develop an approximate, sound but incomplete method for solving such problems that transforms a ∃∀SO(ID) to a ∃SO(ID) problem. The finite domain satisfiability problem for the latter language is in NP and can be handled by several existing solvers. We show that this provides an effective method for solving practically useful problems, such as common examples of conformant planning. We also propose a more complete translation to ∃SO(FP), existential SO extended with nested inductive and coinductive definitions.