A basic epistemic logic and its algebraic model
DOI:
https://doi.org/10.22481/intermaths.v4i2.14133Resumo
In this paper we propose an algebraic model for a modal epistemic logic. Although it is known the existence of algebraic models for modal logics, considering that there are so many different modal logics, so it is not usual to give an algebraic model for each such system. The basic epistemic logic used in the paper is bimodal and we can show that the epistemic algebra introduced in the paper is an adequate model for it.
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W. A. Carnielli and PIZZI, C. Pizzi, Modalità e multimodalità. Milano: Franco Angeli,
A. Chagrov and M. Zakharyachev, Modal logic. Oxford: Clarendon Press, 1997.
B. Chellas, Modal Logic: an introduction. Cambridge: Cambridge University Press, 1980.
J. M. Dunn and G. M. Hardgree, Algebraic methods in philosophical logic. Oxford: Oxford
University Press, 2001.
J. Y. Halpern, “Using reasoning about knowledge to analyze distributed
systems”. Annual Review of Computer Science, v. 2, pp. 37-68, 1987.
https://doi.org/10.1146/annurev.cs.02.060187.000345
J. Y. Halpern and Y. Moses, “A guide to completeness and complexity for modal
logics of knowledge and belief”. Artificial intelligence, v. 54, n. 3, pp. 319-379, 1992.
https://doi.org/10.1016/0004-3702(92)90049-4
J. J. C. Meyer and W. Van der Hoek, Epistemic logic for AI and computer science.
Cambridge: Cambridge University Press, 2004.
F. Miraglia, Cálculo proposicional: uma interação da álgebra e da lógica. Campinas:
UNICAMP/CLE, 1987. (Coleção CLE, v. 1)
C. A. Mortari, Lógicas epistêmicas. In L. H. Dutra(Org.). Nos limites da epistemologia
analítica, p. 17-68, 1999. (Rumos da Epistemologia, v. 1).
RASIOWA, H. Rasiowa and R. Sikorski The mathematics of metamathematics. 2. ed.
Waszawa: PWN - Polish Scientific Publishers, 1968.
H. Rasiowa An algebraic approach to non-classical logics. Amsterdam: North-Holland, 1974.
S. J. Rosenschein, “Formal theories of knowledge in AI and robotics”. New generation
computing, v. 3, n. 4. pp. 345-357, 1985.
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