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
Computational complexity of planning and approximate planning in the presence of incompleteness
Artificial Intelligence
Knowledge Representation, Reasoning, and Declarative Problem Solving
Knowledge Representation, Reasoning, and Declarative Problem Solving
Polynomial-Length Planning Spans the Polynomial Hierarchy
JELIA '02 Proceedings of the European Conference on Logics in Artificial Intelligence
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
A tractability result for reasoning with incomplete first-order knowledge bases
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Compiling uncertainty away in conformant planning problems with bounded width
Journal of Artificial Intelligence Research
Well-founded semantics and the algebraic theory of non-monotone inductive definitions
LPNMR'07 Proceedings of the 9th international conference on Logic programming and nonmonotonic reasoning
Towards a logical reconstruction of a theory for locally closed databases
ACM Transactions on Database Systems (TODS)
An approximative inference method for solving ∃¬so satisfiability problems
JELIA'10 Proceedings of the 12th European conference on Logics in artificial intelligence
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
Constraint Propagation for First-Order Logic and Inductive Definitions
ACM Transactions on Computational Logic (TOCL)
| Hi-index | 0.00 |
This paper considers the fragment ∃∀SO of second-order logic. 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) and many of these problems are often solved approximately. In this paper, we develop a general approximative method, i.e., a sound but incomplete method, for solving ∃∀SO satisfiability problems. We use a syntactic representation of a constraint propagation method for firstorder logic to transform such an ∃∀SO satisfiability problem to an ∃SO(ID) satisfiability problem (second-order logic, extended with inductive definitions). The finite domain satisfiability problem for the latter language is in NP and can be handled by several existing solvers. Inductive definitions are a powerful knowledge representation tool, and this motivates us to also approximate ∃∀SO(ID) problems. In order to do this, we first show how to perform propagation on such inductive definitions. Next, we use this to approximate ∃∀SO(ID) satisfiability problems. All this provides a general theoretical framework for a number of approximative methods in the literature. Moreover, we also show how we can use this framework for solving practical useful problems, such as conformant planning, in an effective way.