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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 SchöenfinkelBernays fragment: Partial Instantiation and Hypergraph Algorithms
 Proceedings of 8th subcommission &quot;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...
Tau: A WebDeployed Hybrid Prover for FirstOrder Logic with Identity, with Optional Inductive Proof
, 2005
"... We outline Tau, a practical and extensible hybrid theorem prover for firstorder predicate calculus with identity. Tau is flexible and userconfigurable, accepts the KIF Language, is implemented in Java, and has multiple user interfaces. Tau combines rulebased problem rewriting with Model Eliminati ..."
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We outline Tau, a practical and extensible hybrid theorem prover for firstorder predicate calculus with identity. Tau is flexible and userconfigurable, accepts the KIF Language, is implemented in Java, and has multiple user interfaces. Tau combines rulebased problem rewriting with Model Elimination, uses Brand’s Modification Method to implement identity, and accepts userconfigurable heuristic search to speed the search for proofs. Tau optionally implements mathematical induction. Formulas are input and output in KIF or infix FOPC, and other external forms can be added. Tau can be operated from a Web interface or from a commandline interface. Tau is implemented entirely in Java and can run on any system for which a current Java Virtual Machine is available.
Partial Instantiation Theorem Proving for Distributed Resource Location
"... In this paper, we present a partial instantiation theorem prover (INSTANT) which handles sentences in firstorder logic in clausal or nonclausal form. INSTANT uses a variant of the GSAT algorithm for determining the satisfiability of a propositional sentence to increase its speed. The algorithm use ..."
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In this paper, we present a partial instantiation theorem prover (INSTANT) which handles sentences in firstorder logic in clausal or nonclausal form. INSTANT uses a variant of the GSAT algorithm for determining the satisfiability of a propositional sentence to increase its speed. The algorithm used in INSTANT can be parallelized with good speedup to improve performance. INSTANT is designed for matching requests for resources with available resources over a network. Environments in which distributed resource location takes place through matching of requests and advertisements include CORBA's Object Trading Service and communication between agents using KIF and KQML. 1 Introduction Theorem provers are used today in a variety of applications such as verification of hardware and software, solving resource allocation and scheduling problems [1], and answering queries posed to knowledge bases. All of these applications could benefit from improvements in theorem prover speed, but for appli...
Deduction by Combining Semantic Tableaux and Integer Programming
, 1996
"... . In this paper we propose to extend the current capabilities of automated reasoning systems by making use of techniques from integer programming. We describe the architecture of an automated reasoning system based on a Herbrand procedure (enumeration of formula instances) on clauses. The input are ..."
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. In this paper we propose to extend the current capabilities of automated reasoning systems by making use of techniques from integer programming. We describe the architecture of an automated reasoning system based on a Herbrand procedure (enumeration of formula instances) on clauses. The input are arbitrary sentences of firstorder logic. The translation into clauses is done incrementally and is controlled by a semantic tableau procedure using unification. This amounts to an incremental polynomial CNF transformation which at the same time encodes part of the tableau structure and, therefore, tableauspecific refinements that reduce the search space. Checking propositional unsatisfiability of the resulting sequence of clauses can either be done with a symbolic inference system such as the DavisPutnam procedure or it can be done using integer programming. If the latter is used a number of advantages become apparent. Introduction In this paper we propose to extend the current capabilit...