Multi-modal systems of restricted depth

Main Article Content

Manuel Sierra A.


multi-modal logic, reasoners with restrictions, language with restrictions.


They are presented as extensions of the classical propositional logic, the hierarchy of deductive systems SMM–n with n > 1. SMM–n is the multi–modal system of depth–n. The system SMM–1 is the classical propositional logic. The system SMM–(n + 1) it can be seen as the result of applying the necesariedad rule, associated to the reasoners with enough reasoning capacity, once to the theorems of the system SMM–n. The system SMM is of the union of the systems of the hierarchy, and it can be seen as the system of logic multimodal Km with restrictions. The systems SMM–n are characterized with a semantics to the style Kripke, in the one which, the longitude of the chains of possible worlds is restricted.

MSC: 03BXX, 03B05, 03B45


Download data is not yet available.
Abstract 447 | PDF (Español) Downloads 171


[1] Wolfgang Lenzen. Recent work in epistemic logic. Acta Philosophica Fennica, ISSN 0355–1792, 30(1), 1978.

[2] Jaakko Hintikka. Knowledge and Belief–An Introduction to the Logic of the Two Notions, ISBN 978–1904987086. College Publications, 2005.

[3] Saul Kripke. Semantical analysis of modal logic. Zeitschrift f¨ur Mathematische Logik und Grundlagen der Mathematik, ISSN 0044–3050, 9, 67–96 (1963).

[4] Max Freund. L´ogica epist´emica. Enciclopedia iberoamericana de filosof´ıa, ISBN 84-8164-045-X. Editorial Trotta S. A. Madrid, 1995.

[5] Max J. Cresswell. Logics and languages. ISBN 978–0416769500, Methuen young books, 1973.

[6] Jaakko Hintikka. Impossible posible worlds vindicated. Journal of Philosophical Logic, ISSN 0022–3611, 4(3), 475–484 (1975).

[7] Nicholas Rescher and Robert Brandon. The logic of inconsistency: a study in nonstandard possible–world semantics and ontology, ISBN 978–0631115816. Oxford: Blackwell, 1980.

[8] Hector J. Levesque. A logic of implicit and explicit belief . Proceedings of National Conference on Artificial Intelligence, ISBN 978–0865760806, 1984.

[9] Marco Schaerf and Marco Cadoli. Tractable reasoning via approximation. Artificial Intelligence, ISSN 0004–3702, 74(2), 1995.

[10] Marcelo Finger and Renata Wassermann. Logics for approximate reasoning: approximating classical logic “from above”. Brazilian Symposium on Artificial Intelligence 16, ISBN 3540001247, 2507, 21–30 (2002).

[11] Guilherme de Souza Rabello and Marcelo Finger. Approximations of Modal Logics: K and beyond. Annals of Pure and Applied Logic, ISSN 0168–0072, 152(1– 3), 161–173 (2008).

[12] Kurt Konolige. A Deduction Model of belief , ISBN 0934613087. Pitman Publishing: London and Morgan Kaufmann., 1986.

[13] Xavier Caicedo. Elementos de l´ogica y calculabilidad, ISBN 9706251905. Editorial Universidad de los Andes, 1990.

[14] A. G. Hamilton. Lógica para matem´aticos, ISBN 8428311013. Editorial Paraninfo S.A., 1981.

[15] Leon Henkin. The completeness of the first–order functional calculus. The journal of symbolic logic, ISSN 0022–4812, 14(3), 159–166 (1949).

[16] David Kaplan. Review of Kripke. The Journal of Symbolic Logic, ISSN 0022–3611, 31(1), 120–122 (1966).

[17] Brian Chellas. Modal logic: an introduction, ISBN 978–0521295154. Cambridge University Press, 1980.