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Partial Instantiation Methods for Inference in First Order Logic
 Journal of Automated Reasoning
, 2000
"... Satisfiability algorithms for propositional logic have improved enormously in recently years. This increases the attractiveness of satisfiability methods for first order logic that reduce the problem to a series of groundlevel satisfiability problems. R. Jeroslow introduced a partial instantiati ..."
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Satisfiability algorithms for propositional logic have improved enormously in recently years. This increases the attractiveness of satisfiability methods for first order logic that reduce the problem to a series of groundlevel satisfiability problems. R. Jeroslow introduced a partial instantiation method of this kind that differs radically from the standard resolutionbased methods. This paper lays the theoretical groundwork for an extension of his method that is general enough and efficient enough for general logic programming with indefinite clauses. In particular we improve Jeroslow's approach by (a) extending it to logic with functions, (b) accelerating it through the use of satisfiers, as introduced by Gallo and Rago, and (c) simplifying it to obtain further speedup. We provide a similar development for a "dual" partial instantiation approach defined by Hooker and suggest a primal/dual strategy. We prove correctness of the primal and dual algorithms for full firstorder ...
The Satisfiability problem for the SchÃ¶enfinkelBernays fragment: Partial Instantiation and Hypergraph Algorithms
 Proceedings of 8th subcommission "Magnetic
, 1994
"... A partial instantiation approach to the solution of the satisfiability problem in the SchoenfinkelBernays fragment of 1 st order logic is presented. It is based on a reduction of the problem to a finite sequence of satisfiability problems in the propositional logic and it improves upon the ori ..."
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A partial instantiation approach to the solution of the satisfiability problem in the SchoenfinkelBernays fragment of 1 st order logic is presented. It is based on a reduction of the problem to a finite sequence of satisfiability problems in the propositional logic and it improves upon the original idea of partial instantiation, as proposed by Jeroslow. In the second part of the paper a new interpretation of the partial instantiation approach in terms of Directed Hypergraphs is proposed and a particular implementation for the Datalog case is described in detail. 1 Introduction. The problem of Logical Inference plays a fundamental role in Decision Sciences and has several applications in fields such as decision support systems, logic circuit design, data bases, and programming languages. Although classical approaches to formalize and solve inference problems have been of symbolic nature, in the last few years many scientists in the Operations Research community have studied ...
A Partial Instantiation based First Order Theorem Prover
"... Satisfiability algorithms for propositional logic have improved enormously in recent years. This increases the attractiveness of satisfiability methods for first order logic that reduce the problem to a series of groundlevel satisfiability problems. Partial Instantiation for first order satisfiabil ..."
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Satisfiability algorithms for propositional logic have improved enormously in recent years. This increases the attractiveness of satisfiability methods for first order logic that reduce the problem to a series of groundlevel satisfiability problems. Partial Instantiation for first order satisfiability differs radically from standard resolution based methods. Two approaches to partial instantiation based first order theorem provers have been studied by R. Jeroslow [10] and by Plaisted and Zhu [14]. Hooker and Rago [8, 9] have described improvements of Jeroslow's approach by a) extending it to logic with functions, b) accelerating it through use of satisfiers, as introduced by Gallo and Rago [6] and c) simplifying it to obtain further speedup. The correctness of the Partial Instantiation algorithms described here for full firstorder logic with functions as well as termination on unsatisfiable formulas are shown in [9]. This paper describes the implementation of a theorem prover based o...