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Abstract: The quantifer-free propositional linear ane logic (i.e. linear logic with the weakening) is decidable. Recently, Lafont and Scedrov proved that multiplicative fragment of second-order linear logic is undecidable. In this paper we show that the second order linear ane logic is undecidable too. At the same time it turns out that even its multiplicative fragment is undecidable. Moreover, we obtain the whole class of undecidability second order logics which lie between Lambek calculus (LC) and... (Update)
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.... semantics has been used in [Laf95] to show that second order multiplicative additive logic is undecidable, and subsequently in [LS95, Kan95, Kop95b], to show that various fragments of second order linear logic are undecidable. The proof of theorem 1 works with smaller...
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The Finite Model Property For Various Fragments Of Linear Logic - Lafont (1997) (Correct)
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0.2: Linear Logic and Noncommutativity in the Calculus of Structures - Straßburger (2003) (Correct)
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BibTeX entry: (Update)
A. P. Kopylov. The undecidability of second order linear affine logic. Manuscript. 1995. http://citeseer.ist.psu.edu/kopylov95undecidability.html More
@misc{ kopylov96,
author = "Alexei Kopylov",
title = "The undecidability of second order linear ane logic",
year = 1995,
month = "August",
url = "citeseer.ist.psu.edu/kopylov95undecidability.html" }
Citations (may not include all citations):982 Theoretical Computer Science (context) - Girard - 1987
54 Phase semantics and sequent calculus for pure noncommutative.. (context) - Abrusci - 1991
43 Recursive unsolvability of Post's problem of 'tag' and other.. (context) - Minsky - 1961
19 The Undecidability of Second Order Multiplicative Linear Log.. - Lafont, Scedrov - 1995
19 The Undecidability of Second Order Linear Logic without Expo.. - Lafont - 1995
12 The Direct Simulation of Minsky machine in Linear logic (context) - Kanovich - 1995
12 The Finite Model Property for Various Fragments of Linear Lo.. - Lafont
11 Decision Problem for Second Order Linear Logic - Lincoln, Scedrov et al. - 1995
2 How to program an innite abacus (context) - Lambek - 1961
1 CSLI lecture notes; no (context) - Troelstra, Linear - 1992
1 Second order Lambek is undecidable (context) - Kanovich - 1995
1 th Annual IEEE Symposium on Logic in Computer Science (context) - Kopylov, Linear - 1995
Documents on the same site (http://www.cs.cornell.edu/People/kopylov/papers/): More
Markov's Principle for Propositional Type Theory - Kopylov, Nogin (2001) (Correct)
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