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Abstract: We present a general framework for proof search in first-order cut-free sequent calculi and apply it to the specific case of linear logic. In this framework, Herbrand functions are used to encode universal quantification, and unification is used to instantiate existential quantifiers so that the eigenvariable conditions are respected. We present an optimization of this procedure that exploits the permutabilities of the subject logic. We prove the soundness and completeness of several related... (Update)
Context of citations to this paper: More
.... how to apply general proof theoretic techniques to derive an equivalent calculus where Herbrand terms streamline proof search [Lincoln and Shankar, 1994]. Finally, we derive a lifted multi modal sequent inference system, which uses unification (or constraint satisfaction) to...
.... logic programming research, which simply introduce fresh parameters; we must apply a generalization of Herbrand s theorem [Lincoln and Shankar, 1994] and work with quantifier rules that introduce structured terms. More IN MODAL LOGIC PROGRAMMING 3 over, to handle modal...
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BibTeX entry: (Update)
P. Lincoln and N. Shankar. Proof search in first-order linear logic and other cut-free sequent calculi. In Proc. 9th Annual IEEE Symposium on Logic in Computer Science, Paris, 1994. http://citeseer.ist.psu.edu/article/lincoln94proof.html More
@inproceedings{ lincoln94proof,
author = "Patrick Lincoln and Natarajan Shankar",
title = "Proof Search in First-order Linear Logic and Other Cut-free Sequent Calculi",
booktitle = "Ninth Annual Symposium on Logic in Computer Science",
publisher = "IEEE Computer Society Press",
address = "Paris, France",
editor = "S. Abramsky",
pages = "282--291",
year = "1994",
url = "citeseer.ist.psu.edu/article/lincoln94proof.html" }
Citations (may not include all citations):982 Theoretical Computer Science (context) - Girard - 1987
309 Symbolic Logic and Mechanical Theorem Proving (context) - Chang, C-T - 1973
257 Logic programming in a fragment of intuitionistic linear log.. - Hodas, Miller - 1991
142 Logic programming with focusing proofs in linear logic - Andreoli - 1992
96 Decision problems for propositional linear logic - Lincoln, Mitchell et al. - 1992
87 An efficient unification algorithm (context) - Martelli, Montanari - 1982
39 Horn programming in linear logic is NPcomplete (context) - Kanovich - 1992
34 Constant-Only Multiplicative Linear Logic is NP-Complete - Lincoln, Winkler - 1993
32 Proof search in the intuitionisticsequent calculus - Shankar - 1992
30 Permutability of inferences in Gentzen's calculi LK and LJ (context) - Kleene - 1952
21 First order linear logic without modalities is NEXPTIME-hard - Lincoln, Scedrov - 1993
20 Foundations of proof search strategies design in linear logi.. - Galmiche, Perrier - 1994
19 Linearizing intuitionistic implication - Lincoln, Scedrov et al. - 1991
7 Herbrand methods in linear logic (context) - Cerrito - 1992
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