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Abstract: Existentially quantified variables are the source of non decidability for second order linear logic without exponentials (MALL2). We present a decision procedure for a fragment of MALL2 based on a canonical instantiation of these variables and using inference permutability in proofs. We also establish that this fragment is PSPACE-complete. Introduction The decision problem for second order linear logic without exponentials (MALL2) has given rise recently to many papers and results. P.... (Update)
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BibTeX entry: (Update)
@article{ perrier99pspacecomplete,
author = "G. Perrier",
title = "A {PSPACE}-complete fragment of second-order linear logic",
journal = "Theoretical Computer Science",
volume = "224",
number = "1--2",
pages = "267--289",
year = "1999",
url = "citeseer.ist.psu.edu/perrier99pspacecomplete.html" }
Citations (may not include all citations):142 Logic programming with focusing proofs in linear logic - Andreoli - 1992
96 Decision Problems for Propositional Linear Logic - Lincoln, Mitchell et al. - 1990
30 Games Semantics for Full Propositional Linear logic (context) - Lamarche - 1995
20 Foundations of proof search strategies design in linear logi.. - Galmiche, Perrier - 1994
19 The undecidability of second order linear logic without expo.. - Lafont
19 The undecidability of second order multiplicative linear log.. - Lafont, Scedrov - 1995
15 On proof normalisation in linear logic (context) - Galmiche, Perrier - 1994
11 Parsing with Polymorphism (context) - Emms - 1993
11 Decision problems for second order linear logic - Lincoln, Scedrov et al. - 1995
4 An undecidability result for polymorphic Lambek calculus (context) - Emms - 1995
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