Abstract
We present an overview of the methods in [10,7,13] and their implementation in the system TINC. This system introduces analytic calculi for large classes of substructural and paraconsistent logics, which it then uses to prove various results about the formalized logics.
Work supported by the FWF project START Y544-N23.
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References
Andreoli, J.-M.: Logic programming with focusing proofs in linear logic. Journal of Logic and Computation 2(3), 297–347 (1992)
Avron, A.: Hypersequents, logical consequence and intermediate logics for concurrency. Annals of Mathematics and Artificial Intelligence 4, 225–248 (1991)
Avron, A., Konikowska, B., Zamansky, A.: Cut-free sequent calculi for C-systems with generalized finite-valued semantics. Journal of Logic and Computation 21(3), 517–540 (2013)
Avron, A., Lev, I.: Non-deterministic multiple-valued structures. Journal of Logic and Computation 15(3), 241–261 (2005)
Baaz, M., Fermüller, C.G., Salzer, G., Zach, R.: MUltlog 1.0: Towards an expert system for many-valued logics. In: McRobbie, M.A., Slaney, J.K. (eds.) CADE 1996. LNCS, vol. 1104, pp. 226–230. Springer, Heidelberg (1996)
Baaz, M., Lahav, O., Zamansky, A.: Finite-valued semantics for canonical labelled calculi. Journal of Automated Reasoning 51(4), 401–430 (2013)
Baldi, P., Ciabattoni, A., Spendier, L.: Standard completeness for extensions of MTL: An automated approach. In: Ong, L., de Queiroz, R. (eds.) WoLLIC 2012. LNCS, vol. 7456, pp. 154–167. Springer, Heidelberg (2012)
Carnielli, W.A., Marcos, J.: A taxonomy of C-systems. In: Carnielli, W.A., Coniglio, M.E., Ottaviano, I.D. (eds.) Paraconsistency: The Logical Way to the Inconsistent, pp. 1–94 (2002)
Chagrov, A., Zakharyaschev, M.: Modal Logic. Clarendon Press, Oxford (1997)
Ciabattoni, A., Galatos, N., Terui, K.: From axioms to analytic rules in nonclassical logics. In: Proceedings of LICS 2008, pp. 229–240 (2008)
Ciabattoni, A., Galatos, N., Terui, K.: MacNeille Completions of FL-algebras. Algebra Universalis 66(4), 405–420 (2011)
Ciabattoni, A., Galatos, N., Terui, K.: Algebraic proof theory for substructural logics: cut-elimination and completions. Annals of Pure and Applied Logic 163(3), 266–290 (2012)
Ciabattoni, A., Lahav, O., Spendier, L., Zamansky, A.: Automated support for the investigation of paraconsistent and other logics. In: Artemov, S., Nerode, A. (eds.) LFCS 2013. LNCS, vol. 7734, pp. 119–133. Springer, Heidelberg (2013)
Ciabattoni, A., Lahav, O., Spendier, L., Zamansky, A.: Taming paraconsistent (and other) logics: An algorithmic approach (submitted 2014)
Ciabattoni, A., Maffezioli, P., Spendier, L.: Hypersequent and labelled calculi for intermediate logics. In: Galmiche, D., Larchey-Wendling, D. (eds.) TABLEAUX 2013. LNCS, vol. 8123, pp. 81–96. Springer, Heidelberg (2013)
Ciabattoni, A., Ramanayake, R.: Structural extensions of display calculi: A general recipe. In: Libkin, L., Kohlenbach, U., de Queiroz, R. (eds.) WoLLIC 2013. LNCS, vol. 8071, pp. 81–95. Springer, Heidelberg (2013)
Cintula, P., Hájek, P., Noguera, C. (eds.): Handbook of Mathematical Fuzzy Logic, vol. 1. Studies in Logic, Mathematical Logic and Foundations, vol. 37. College Publications (2011)
Galatos, N., Jipsen, P., Kowalski, T., Ono, H.: Residuated Lattices: An algebraic glimpse at substructural logics. Studies in Logics and the Foundations of Mathematics. Elsevier (2007)
Jenei, S., Montagna, F.: A proof of standard completeness for Esteva and Godo’s MTL logic. Studia Logica 70(2), 183–192 (2002)
Hájek, P.: Metamathematics of Fuzzy Logic. Springer (1998)
Lahav, O., Zohar, Y.: SAT-based decision procedure for analytic pure sequent calculi. In: Demri, S., Kapur, D., Weidenbach, C. (eds.) IJCAR 2014. LNCS (LNAI), vol. 8562, pp. 76–90. Springer, Heidelberg (2014)
Metcalfe, G., Montagna, F.: Substructural fuzzy logics. Journal of Symbolic Logic 7(3), 834–864 (2007)
Nigam, V., Pimentel, E., Reis, G.: An extended framework for specifying and reasoning about proof systems. Journal of Logic and Computation (accepted)
Ohlbach, H.J.: Computer support for the development and investigation of logics. Logic Journal of the IGPL 4(1), 109–127 (1996)
Tishkovsky, D., Schmidt, R.A., Khodadadi, M.: The tableau prover generator MetTeL2. In: del Cerro, L.F., Herzig, A., Mengin, J. (eds.) JELIA 2012. LNCS, vol. 7519, pp. 492–495. Springer, Heidelberg (2012)
Troelstra, A.S., Schwichtenberg, H.: Basic Proof Theory. Cambridge University Press (2000)
Wenzel, M., Paulson, L.C., Nipkow, T.: The Isabelle Framework. In: Mohamed, O.A., Muñoz, C., Tahar, S. (eds.) TPHOLs 2008. LNCS, vol. 5170, pp. 33–38. Springer, Heidelberg (2008)
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Ciabattoni, A., Spendier, L. (2014). Tools for the Investigation of Substructural and Paraconsistent Logics. In: Fermé, E., Leite, J. (eds) Logics in Artificial Intelligence. JELIA 2014. Lecture Notes in Computer Science(), vol 8761. Springer, Cham. https://doi.org/10.1007/978-3-319-11558-0_2
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