What Are Justification Logics?

• Autorzy: Fitting Melvin

Identyfikatory

DOI

10.3233/FI-2019-1782

• Języki publikacji: EN

Abstrakty

EN

Justification logic began with Sergei Artemov’s work providing an arithmetic semantics for intuitionistic logic. As part of that work, a small number of explicit modal logics were introduced—logics in which there was a structure of terms that kept track of not just what was a necessary truth, but why it was necessary. These explicit modal logics were connected with standard modal logics such as S4, T, K, and others using Realization Theorems, essentially saying that modal operators concealed an underlying informational structure. Since Artemov’s work, the phenomenon of justification logic has turned out to be very broad. For instance, I have shown that infinitely many modal logics have justification counterparts. In this paper I will sketch the basics and try to give some of the ideas behind formal justification proofs, justification semantics, and realization theorems.

Słowa kluczowe

EN

BHK semantics; intuitionistic logic; justification logic; logic of proofs; modal logic; realization

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2019
• Tom: Vol. 165, nr 3-4
• Strony: 193--203
• Opis fizyczny: Bibliogr. 15 poz., rys.

Twórcy

autor

Fitting Melvin

• Graduate Center of the City University of New York, Department of Computer Science, 365 Fifth Avenue, New York, NY 10016, USA

Bibliografia

• [1] Gödel K. Vortrag bei Zilsel, 1938. Translated as Lecture at Zilsel’s in [15] III, 62-113.
• [2] Artemov SN. Explicit Provability and Constructive Semantics. The Bulletin of Symbolic Logic, 2001. 7(1):1-36.
• [3] Artemov SN. The Logic of Justification. The Review of Symbolic Logic, 2008. 1(4):477-513. doi:10.1017/S1755020308090060.
• [4] Pacuit E. A Note on Some Explicit Modal Logics. In: Proceedings of the 5th Panhellenic Logic Symposium. University of Athens, Athens, Greece, 2005 pp. 117-125.
• [5] Rubtsova NM. On Realization of S5-modality by Evidence Terms. Journal of Logic and Computation, 2006. 16(5):671-684. doi:10.1093/logcom/exl030.
• [6] Fitting MC. Modal Logics, Justification Logics, and Realization. Annals of Pure and Applied Logic, 2016. 167:615-648. doi:10.1016/j.apal.2016.03.005. URL http://www.sciencedirect.com/science/article/pii/S016800721630029X.
• [7] Fitting MC. A Semantic Proof of the Realizability of Modal Logic in the Logic of Proofs. Technical Report TR-2003010, CUNY Ph.D. Program in Computer Science, 2003. URL http://academicworks.cuny.edu/gc_cs_tr/.
• [8] Fitting MC. Justification Logics and Realization. Technical Report TR-2014004, CUNY Ph.D. Program in Computer Science, 2014. URL http://academicworks.cuny.edu/gc_cs_tr/.
• [9] Fitting MC. Quasi-Realization. In: Hansen HH, Murray SE, Sadrzadeh M, Zeevat H (eds.), Logic, Language, and Computation, volume 10148 of Lecture Notes in Computer Science. Springer, 2016 pp. 313-332. 11th International Tbilisi Symposium, TbiLLC, Tbilisi, Georgia, September 21-26, 2015.
• [10] Fitting MC. Realization Implemented. Technical Report TR-2013005, CUNY Ph.D. Program in Computer Science, 2013. URL http://academicworks.cuny.edu/gc_cs_tr/.
• [11] Fitting MC. The Logic of Proofs, Semantically. Annals of Pure and Applied Logic, 2005. 132:1-25.
• [12] Lemmon EJ, Scott DS. The ‘Lemmon Notes’: An Introduction to Modal Logic. Amer. Phil. Quart., Monograph 11, Oxford. Blackwell, 1977. Edited by Krister Segerberg.
• [13] Shamkanov DS. A Realization theorem for the Gödel-Löb provability logic. Russian Academy of Sciences Sbornik Mathematics, 2016. 207(9):1-17. doi:10.1070/SM8667.
• [14] Artemov SN, Fitting M. Justification Logic. In: Zalta EN (ed.), The Stanford Encyclopedia of Philosophy. 2012. URL http://plato.stanford.edu/archives/fall2012/entries/logic-justification/.
• [15] Feferman S, Dawson Jr JW, Kleene SC, Moore GH, Solovay RM, van Heijenoort J, Goldfarb WD, Parsons C, Sieg W (eds.). Kurt Gödel Collected Works. Oxford, 1986-2003. Five volumes.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).