Abstract
Justification logics connect with modal logics via Realization Theorems. The first such theorem was proved constructively by Artemov, [1]. It showed how to translate an S4 sequent proof, as a whole, into an LP proof. We present a different algorithmic Realization proof for LP/S4, proceeding step by step instead of working on the entire proof, and dividing the argument into two natural parts, one specific to LP/S4, the other widely applicable to justification/modal pairs. This structure makes an implementation easier, and we provide a link to one in Prolog.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Artemov, S.N.: Explicit provability and constructive semantics. Bull. Symbolic Logic 7(1), 1–36 (2001)
Artemov, S.N.: The logic of justification. Rev. Symbolic Logic 1(4), 477–513 (2008)
Artemov, S.N., Yavorskaya (Sidon), T.: First-order logic of proofs. Technical report TR-2011005, City University of New York, May 2011
Feferman, S., Dawson Jr., J.W., Kleene, S.C., Moore, G.H., Solovay, R.M., van Heijenoort, J., Goldfarb, W.D., Parsons, C., Sieg, W. (eds.) Kurt Gödel Collected Works, vol. 5. Oxford (1986–2003)
Fitting, M.C.: Prolog code for S4 realization. See Realization Implemented. http://melvinfitting.org/bookspapers/techreports.html
Fitting, M.C.: The logic of proofs, semantically. Ann. Pure Appl. Logic 132, 1–25 (2005)
Fitting, M.C.: Realizations and LP. Ann. Pure Appl. Logic 161(3), 368–387 (2009). doi:10.1016/j.apal.2009.07.010
Fitting, M.C.: Reasoning with justifications. In: Makinson, D., Malinowski, J., Wansing, H. (eds.) Towards Mathematical Philosophy, Chap. 6. Trends in Logic, vol. 28, pp. 107–123. Springer, Dordrecht (2009)
Fitting, M.C.: Possible world semantics for first order LP. Technical report TR-2011010, CUNY Ph.D. Program in Computer Science, September 2011
Fitting, M.C.: Realization implemented. Technical report TR-2013005, CUNY Ph.D. Program in Computer Science, May 2013
Fitting, M.C.: Realization using the model existence theorem. J. Logic Comput. 26, 213–234 (2013)
Fitting, M.C.: Modal logics, justification logics, and realization. Ann. Pure Appl. Logic 167, 615–648 (2016)
Gödel, K.: Eine Interpretation des intuistionistischen Aussagenkalkuls. Ergebnisse eines mathematischen Kolloquiums 4, 39–40 (1933). Translated as An interpretation of the intuitionistic propositional calculus in [4] I, 296–301
Goetschi, R., Kuznets, R.: Realization for justification logics via nested sequents: modularity through embedding. Ann. Pure Appl. Logic 163(9), 1271–1298 (2012)
Smullyan, R.M.: A unifying principle in quantification theory. Proc. Natl. Acad. Sci. 49(6), 828–832 (1963)
Smullyan, R.M., Logic, F.-O.: First-Order Logic. Springer, Heidelberg (1968). (Revised Edition, Dover Press, New York)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer-Verlag GmbH Germany
About this paper
Cite this paper
Fitting, M. (2017). Quasi-Realization. In: Hansen, H., Murray, S., Sadrzadeh, M., Zeevat, H. (eds) Logic, Language, and Computation. TbiLLC 2015. Lecture Notes in Computer Science(), vol 10148. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-54332-0_17
Download citation
DOI: https://doi.org/10.1007/978-3-662-54332-0_17
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-54331-3
Online ISBN: 978-3-662-54332-0
eBook Packages: Computer ScienceComputer Science (R0)