Linear logic, introduced by J.-Y. Girard, is a refinement of classical logic providing means for controlling the allocation of “resources”. It has aroused considerable interest from both proof theorists and computer scientists. In this paper we investigate methods for automated theorem proving in propositional linear logic. Both the “bottom-up” (tableaux) and “top-down” (resolution) proof strategies are analyzed. Various modifications of sequent rules and efficient search strategies are presented along with the experiments performed with the implemented theorem provers.
Key wordsautomated theorem proving linear logic resolution method
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- 1.Andreoli, J.-M.: Logic programming with focusing proofs in linear logic,J. Logic Computation 2(3) (1992), 297–347.Google Scholar
- 2.Galmiche, D. and Perrier, G.: Automated deduction in additive and multiplicative linear logic, inLFCS'92: Logic at Tver, LNCS 620, Springer-Verlag, Berlin, 1992, pp. 151–162.Google Scholar
- 3.Girard, J.-Y.: Linear logic,Theoret. Comput. Sci. 50 (1987), 1–102.Google Scholar
- 4.Harland, J. A. and Pym, D. J.: On resolution in fragments of classical linear logic, inLPAR'92, LNCS 624, Springer-Verlag, Berlin, 1992, pp. 30–41.Google Scholar
- 5.Hodas, J. and Miller, D.: Logic programming in a fragment of intuitionistic linear logic, inProc. 6th Annual IEEE Symposium on Logic in Computer Science, Amsterdam, July 1991, IEEE Computer Society Press, 1991.Google Scholar
- 6.Kleene, S. C.:Introduction to Metamathemaatics, North-Holland, Amsterdam, 1952.Google Scholar
- 7.Lincoln, P., Mitchel, J., Scedrov, A., and Shankar, N.: Decision problems for propositional linear logic.Ann. Pure Appl. Logic 56(1–3) (1992), 239–311.Google Scholar
- 8.Chirimar, J. and Lipton, J.: Provability in TBLL: A decision procedure, inCSL '91, LNCS 626, Springer-Verlag, Berlin, 1992, pp. 53–67.Google Scholar
- 9.Maslov, S. Ju.: An inverse method of establishing deducibility in the classical predicate calculus,Dokl. Akad. Nauk. SSSR 159 (1964), 17–20; Soviet Math. Dokl.5 (1964) 1420, MR 30 #3005.Google Scholar
- 10.Maslov, S. Ju.: The inverse method for establishing deducibility for logical calculi,Trudy Mat. Inst. Steklov 98 (1968), 26–87;Proc. Steklov. Inst. Math. 98 (1968), 25–96, MR 40 #5416; 43 #4620.Google Scholar
- 11.Maslov, S. Ju.: Proof-search strategies for methods of the resolution type, inMachine Intelligence 6, American Elsevier, 1971, pp. 77–90.Google Scholar
- 12.Mints, G.: Gentzen-type Systems and Resolution Rules. Part I. Propositional Logic, inCOLOG-88, LNCS 417, Springer-Verlag, Berlin, 1990, pp. 198–231.Google Scholar
- 13.Mints, G.: Resolution calculus for the first order linear logic,J. Logic, Language Informat. 2 (1993), 58–93.Google Scholar