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Higherorder Unification via Explicit Substitutions (Extended Abstract)
 Proceedings of LICS'95
, 1995
"... Higherorder unification is equational unification for βηconversion. But it is not firstorder equational unification, as substitution has to avoid capture. In this paper higherorder unification is reduced to firstorder equational unification in a suitable theory: the &lambda ..."
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Cited by 105 (13 self)
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Higherorder unification is equational unification for &beta;&eta;conversion. But it is not firstorder equational unification, as substitution has to avoid capture. In this paper higherorder unification is reduced to firstorder equational unification in a suitable theory: the &lambda;&sigma;calculus of explicit substitutions.
The Uniform Prooftheoretic Foundation of Linear Logic Programming (Extended Abstract)
 PROCEEDINGS OF THE INTERNATIONAL LOGIC PROGRAMMING SYMPOSIUM
, 1991
"... We present a prooftheoretic analysis of a natural notion of logic programming for Girard's linear logic. This analysis enables us to identify a suitable notion of uniform proof. This in turn enables us to identify choices of classes of definite and goal formulae for which uniform proofs are c ..."
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Cited by 47 (7 self)
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We present a prooftheoretic analysis of a natural notion of logic programming for Girard's linear logic. This analysis enables us to identify a suitable notion of uniform proof. This in turn enables us to identify choices of classes of definite and goal formulae for which uniform proofs are complete and so to obtain the appropriate formulation of resolution proof for such choices. Resolution proofs in linear logic are somewhat difficult to define. This difficulty arises from the need to decompose definite formulae into a form suitable for the use of the linear resolution rule, a rule which requires the selected clause to be deleted after use, and from the presence of the modality ! (of course). We consider a translation  resembling ...
ProofTerms for Classical and Intuitionistic Resolution (Extended Abstract)
, 1996
"... We exploit a system of realizers for classical logic, and a translation from resolution into the sequent calculus, to assess the intuitionistic force of classical resolution for a fragment of intuitionistic logic. This approach is in contrast to formulating locally intuitionistically sound resol ..."
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Cited by 13 (3 self)
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We exploit a system of realizers for classical logic, and a translation from resolution into the sequent calculus, to assess the intuitionistic force of classical resolution for a fragment of intuitionistic logic. This approach is in contrast to formulating locally intuitionistically sound resolution rules. The techniques use the fflcalculus, a development of Parigot's calculus.
ON THE PRACTICAL VALUE OF HERBRAND DISJUNCTIONS
"... Abstract. Herbrand disjunctions are a means for reducing the problem of whether a firstoder formula is valid in an open theory T or not to the problem whether an open formula, one of the so called Herbrand disjunctions, is Tvalid or not. Nevertheless, the set of Herbrand disjunctions, which has to ..."
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Abstract. Herbrand disjunctions are a means for reducing the problem of whether a firstoder formula is valid in an open theory T or not to the problem whether an open formula, one of the so called Herbrand disjunctions, is Tvalid or not. Nevertheless, the set of Herbrand disjunctions, which has to be examined, is undecidable in general. Fore this reason the practical value of Herbrand disjunctions has been estimated negatively (cf. [30]). Relying on completeness proofs which are based on the algebraization technique presented in [30], but taking a more optimistic view, we show how Herbrand disjunctions become the base of a method for building in theories into automatic theorem provers [26]. Surveying newer results we discuss how to treat heterogeneous theories [29] as well as practical implications of different normal form transformations. 1.
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"... We present matrix proof systems for both constant and varyingdomain versions of the firstorder modal logics K, K4, D, D4, T, 84 and 86 based on modal versions of Herbrand's Theorem specifically formulated to support efficient automated proof search. The systems treat the mil modal language ( ..."
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We present matrix proof systems for both constant and varyingdomain versions of the firstorder modal logics K, K4, D, D4, T, 84 and 86 based on modal versions of Herbrand's Theorem specifically formulated to support efficient automated proof search. The systems treat the mil modal language (no normalforming) and admit straightforward structure sharing implementations. A key fsature of our approach is the use of a specialised unification algorithm to reflect the conditions on the accessibility relation for a given logic. The matrix system for one logic differs from the matrix eystem for another only in the nature of this unification algorithm. In addition, proof search may be interpreted as constructing generalised proof trees in an appropriate tableau or sequentbased proof system. This facilitates the use of the matrix systems within interactive environments. 1 Introduction.