Abstract
We provide a graphical representation of proofs in the product-free Lambek calculus, called term graphs, that is related to several other proof net presentations. The advantage of term graphs is that they are very simple compared to the others. We use this advantage to provide an NP-completeness proof of the product-free Lambek Calculus that uses the reduction of [1]. Our proof is more intuitive due to the fact that term graphs allow arguments that are graphical in nature rather than using the algebraic arguments of [1].
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References
Savateev, Y.: Product-free lambek calculus is NP-complete. CUNY Technical Report (September 2008)
Lambek, J.: The mathematics of sentence structure. American Mathematical Monthly 65(3), 154–170 (1958)
Pentus, M.: Product-free lambek calculus and context-free grammars. The Journal of Symbolic Logic 62(2), 648–660 (1997)
Tiede, H.J.: Deductive Systems and Grammars: Proofs as Grammatical Structures. PhD thesis, Indiana University (1999)
Fowler, T.: Efficient parsing with the Product-Free lambek calculus. In: Proceedings of The 22nd International Conference on Computational Linguistics (2008)
Fowler, T.: A polynomial time algorithm for parsing with the bounded order lambek calculus. In: Ebert, C., Jäger, G., Michaelis, J. (eds.) MOL 10. LNCS, vol. 6149, pp. 36–43. Springer, Heidelberg (2010)
Penn, G.: A graph-theoretic approach to sequent derivability in the lambek calculus. Electronic Notes in Theoretical Computer Science 53, 274–295 (2004)
Perrier, G.: Intuitionistic multiplicative proof nets as models of directed acyclic graph descriptions. In: Nieuwenhuis, R., Voronkov, A. (eds.) LPAR 2001. LNCS (LNAI), vol. 2250, pp. 233–248. Springer, Heidelberg (2001)
Lamarche, F.: From proof nets to games. Electronic Notes in Theoretical Computer Science 3 (1996)
Penn, G.: A Graph-Theoretic approach to sequent derivability in the lambek calculus. In: Proceedings of Formal Grammar ’01 and the 7th Meeting on Mathematics of Language. Helsinki, Finland (2001)
Lamarche, F.: Proof nets for intuitionistic linear logic: Essential nets. Technical Report 00347336, INRIA (2008)
Roorda, D.: Resource logics: proof-theoretical investigations. PhD thesis, Universiteit van Amsterdam (1991)
de Groote, P.: An algebraic correctness criterion for intuitionistic multiplicative proof-nets. Theoretical Computer Science 224(1-2), 115–134 (1999)
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Fowler, T.A.D. (2011). Term Graphs and the NP-Completeness of the Product-Free Lambek Calculus. In: de Groote, P., Egg, M., Kallmeyer, L. (eds) Formal Grammar. FG 2009. Lecture Notes in Computer Science(), vol 5591. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20169-1_10
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DOI: https://doi.org/10.1007/978-3-642-20169-1_10
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