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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 56 (3 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 simplification, builtin associativity and commutativity, models, analogy, and manmachine systems. Examples are given and suggestions are made for future work. 1.
Focusing the inverse method for linear logic
 Proceedings of CSL 2005
, 2005
"... 1.1 Quantification and the subformula property.................. 3 1.2 Ground forward sequent calculus......................... 5 1.3 Lifting to free variables............................... 10 ..."
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Cited by 38 (11 self)
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1.1 Quantification and the subformula property.................. 3 1.2 Ground forward sequent calculus......................... 5 1.3 Lifting to free variables............................... 10
Resolution Methods for Decision Problems and FiniteModel Building
, 1992
"... Contents 1 Introduction 3 1.1 Related work : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 1.2 Structure of the thesis : : : : : : : : : : : : : : : : : : : : : : : : : : 4 2 Terminology 6 2.1 Terms, literals and clauses : : : : : : : : : : : : : : : : : : : : : : : : 6 2.2 Term s ..."
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Cited by 16 (1 self)
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Contents 1 Introduction 3 1.1 Related work : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 1.2 Structure of the thesis : : : : : : : : : : : : : : : : : : : : : : : : : : 4 2 Terminology 6 2.1 Terms, literals and clauses : : : : : : : : : : : : : : : : : : : : : : : : 6 2.2 Term structure and substitutions : : : : : : : : : : : : : : : : : : : : 7 2.3 Subsumption, factors, resolvents, splitting : : : : : : : : : : : : : : : 10 2.4 Herbrand semantics : : : : : : : : : : : : : : : : : : : : : : : : : : : : 12 2.5 Ordinary predicate logic and naming conventions : : : : : : : : : : : 12 3 Completeness of ordering refinements 14 3.1 Proving completeness by lifting : : : : : : : : : : : : : : : : : : : : 15 3.2 Some properties of 'Ø'predicates : : : : : : : : : : : : : : :
The Inverse Method
, 2001
"... this paper every formula is equivalent to a formula in negation normal form ..."
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Cited by 12 (1 self)
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this paper every formula is equivalent to a formula in negation normal form
Knowledge Representation and Classical Logic
, 2007
"... Mathematical logicians had developed the art of formalizing declarative knowledge long before the advent of the computer age. But they were interested primarily in formalizing mathematics. Because of the important role of nonmathematical knowledge in AI, their emphasis was too narrow from the perspe ..."
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Cited by 11 (4 self)
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Mathematical logicians had developed the art of formalizing declarative knowledge long before the advent of the computer age. But they were interested primarily in formalizing mathematics. Because of the important role of nonmathematical knowledge in AI, their emphasis was too narrow from the perspective of knowledge representation, their formal languages were not sufficiently expressive. On the other hand, most logicians were not concerned about the possibility of automated reasoning; from the perspective of knowledge representation, they were often too generous in the choice of syntactic constructs. In spite of these differences, classical mathematical logic has exerted significant influence on knowledge representation research, and it is appropriate to begin this handbook with a discussion of the relationship between these fields. The language of classical logic that is most widely used in the theory of knowledge representation is the language of firstorder (predicate) formulas. These are the formulas that John McCarthy proposed to use for representing declarative knowledge in his advice taker paper [176], and Alan Robinson proposed to prove automatically using resolution [236]. Propositional logic is, of course, the most important subset of firstorder logic; recent
Efficient Intuitionistic Theorem Proving with the Polarized Inverse Method
"... Abstract. The inverse method is a generic proof search procedure applicable to nonclassical logics satisfying cut elimination and the subformula property. In this paper we describe a general architecture and several highlevel optimizations that enable its efficient implementation. Some of these re ..."
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Cited by 6 (3 self)
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Abstract. The inverse method is a generic proof search procedure applicable to nonclassical logics satisfying cut elimination and the subformula property. In this paper we describe a general architecture and several highlevel optimizations that enable its efficient implementation. Some of these rely on logicspecific properties, such as polarization and focusing, which have been shown to hold in a wide range of nonclassical logics. Others, such as rule subsumption and recursive backward subsumption apply in general. We empirically evaluate our techniques on firstorder intuitionistic logic with our implementation Imogen and demonstrate a substantial improvement over all other existing intuitionistic theorem provers on problems from the ILTP problem library. 1
The inverse method for the logic of bunched implications
 In Proceedings of LPAR 2004, volume 3452 of LNAI
, 2005
"... Abstract. The inverse method, due to Maslov, is a forward theorem proving method for cutfree sequent calculi that relies on the subformula property. The Logic of Bunched Implications (BI), due to Pym and O’Hearn, is a logic which freely combines the familiar connectives of intuitionistic logic with ..."
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Cited by 6 (1 self)
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Abstract. The inverse method, due to Maslov, is a forward theorem proving method for cutfree sequent calculi that relies on the subformula property. The Logic of Bunched Implications (BI), due to Pym and O’Hearn, is a logic which freely combines the familiar connectives of intuitionistic logic with multiplicative linear conjunction and its adjoint implication. We present the first formulation of an inverse method for propositional BI without units. We adapt the sequent calculus for BI into a forward calculus. The soundness and completeness of the calculus are proved, and a canonical form for bunches is given. 1
Imogen: Focusing the Polarized Inverse Method for Intuitionistic Propositional Logic
"... Abstract. In this paper we describe Imogen, a theorem prover for intuitionistic propositional logic using the focused inverse method. We represent finegrained control of the search behavior by polarizing the input formula. In manipulating the polarity of atoms and subformulas, we can often improve ..."
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Cited by 5 (3 self)
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Abstract. In this paper we describe Imogen, a theorem prover for intuitionistic propositional logic using the focused inverse method. We represent finegrained control of the search behavior by polarizing the input formula. In manipulating the polarity of atoms and subformulas, we can often improve the search time by several orders of magnitude. We tested our method against seven other systems on the propositional fragment of the ILTP library. We found that our prover outperforms all other provers on a substantial subset of the library. 1