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Resolution Theorem Proving
, 1992
"... ground procedure. The first step in constructing the ground procedure is to convert inference problems to a simple normal form. 1 Clausal Normal Form Resolution is a refutation technique. To show that \Sigma j= \Phi resolution derives a contradiction from \Sigma [ f:\Phig. We will simply assume t ..."
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that we are given a finite set of formulas \Gamma and that we wish to show that \Gamma is unsatisfiable. The first step in resolution theorem proving is to put the formulas in \Gamma in a certain normal form. To define this normal form we need some additional terminology. Definition An atomic formula
Resolution Theorem Proving
"... .63>1 Clausal Normal Form Resolution is a refutation technique. To show that \Sigma j= \Phi resolution derives a contradiction from \Sigma [ f:\Phig. We will simply assume that we are given a finite set of formulas \Gamma and that we wish to show that \Gamma is unsatisfiable. The first step in r ..."
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in resolution theorem proving is to put the formulas in \Gamma in a certain normal form. To define this normal form we need some additional terminology. Definition An atomic formula is either a proposition symbol, a predicate application of the form P (t 1 ; \Delta \Delta \Delta ; t n ), or an equation t 1
Nonresolution theorem proving
 Artificial Intelligence
, 1977
"... This talk reviews those efforts in automatic theorem proving, during the past few years, which have emphasized techniques other than resolution. These include: knowledge bases, natural deduction, reduction, (rewrite rules), typing, procedures, advice, controlled forward chaining, algebraic simplific ..."
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Cited by 73 (4 self)
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This talk reviews those efforts in automatic theorem proving, during the past few years, which have emphasized techniques other than resolution. These include: knowledge bases, natural deduction, reduction, (rewrite rules), typing, procedures, advice, controlled forward chaining, algebraic
ZResolution: TheoremProving with Compiled Axioms
 Journal of the ACM
, 1973
"... ABSTRACT. An improved procedure for resolution theorem proving, called Zresolution, is described. The basic idea of Zresolution is to "compile " some of the axioms in a deductive problem. This means to automatically transform the selected axioms into a computer program which carries out ..."
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Cited by 7 (0 self)
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ABSTRACT. An improved procedure for resolution theorem proving, called Zresolution, is described. The basic idea of Zresolution is to "compile " some of the axioms in a deductive problem. This means to automatically transform the selected axioms into a computer program which carries out
Limited Resource Strategy in Resolution Theorem Proving
 JOURNAL OF SYMBOLIC COMPUTATION
, 2000
"... For most applications of firstorder theorem provers a proof should be found within a fixed time limit. When the time limit is set, systems can perform much better by using algorithms other than the ordinary complete ones. In this report we describe the Limited Resource Strategy intended for reasoni ..."
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Cited by 19 (4 self)
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For most applications of firstorder theorem provers a proof should be found within a fixed time limit. When the time limit is set, systems can perform much better by using algorithms other than the ordinary complete ones. In this report we describe the Limited Resource Strategy intended
Conceptual Graphs as Terms: Prospects for Resolution Theorem Proving
 Vrije Universiteit Amsterdam
, 1997
"... This thesis describes an attempt to employ conceptual graphs in a new way. In the past conceptual graphs have always been regarded as existentially quantified logic sentences. The intuition that conceptual graphs generalize feature structures inspires an alternative interpretation of CGs as "de ..."
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Cited by 2 (0 self)
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;descriptions of objects in some domain", which we claim to be at least as appealing and intuitive as the traditional interpretation of CGs as first order logic sentences. With this new interpretation in mind, we examine the prospects of a resolution based theorem prover or logic programming language over a logic
A Nonclausal ConnectionGraph Resolution TheoremProving Program
 in Proc. AAAI82
, 1982
"... A new theoremproving program, combining the use of nonclausal resolution and connection graphs, is described. The use of nonclausal resolution as the inference system eliminates some of the redundancy and unreadability of clausebased systems. The use of a connection graph restricts the search spa ..."
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Cited by 19 (2 self)
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A new theoremproving program, combining the use of nonclausal resolution and connection graphs, is described. The use of nonclausal resolution as the inference system eliminates some of the redundancy and unreadability of clausebased systems. The use of a connection graph restricts the search
The complexity of theoremproving procedures
 IN STOC
, 1971
"... It is shown that any recognition problem solved by a polynomial timebounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a tautology. Here “reduced ” means, roughly speaking, that the first problem can be solved deterministi ..."
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Cited by 1057 (4 self)
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It is shown that any recognition problem solved by a polynomial timebounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a tautology. Here “reduced ” means, roughly speaking, that the first problem can be solved deterministically in polynomial time provided an oracle is available for solving the second. From this notion of reducible, polynomial degrees of difficulty are defined, and it is shown that the problem of determining tautologyhood has the same polynomial degree as the problem of determining whether the first of two given graphs is isomorphic to a subgraph of the second. Other examples are discussed. A method of measuring the complexity of proof procedures for the predicate calculus is introduced and discussed. Throughout this paper, a set of strings 1 means a set of strings on some fixed, large, finite alphabet Σ. This alphabet is large enough to include symbols for all sets described here. All Turing machines are deterministic recognition devices, unless the contrary is explicitly stated.
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