An approximative inference method for solving ∃∀SO satisfiability problems

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 ($\Sigma^P_2$). 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.Acceptance rate: 33%status: publishe

An approximative inference method for solving ∃∀SO satisfiability problems

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 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 first-order logic to transform such an ∃∀SO satisfiability problem to an ∃SO satisfiability problem (second-order logic, extended with with inductive definitions). The finite domain satisfiability problem for the latter language is in NP and can be handled by several existing solvers. Next, we look at an extension of first-order logic with inductive definitions (FO(ID)). Inductive definitions are a powerful knowledge representation tool, and this %motives 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.status: publishe