An informational semantics for logical consequence


  • Marcos Antonio Alves UNESP



Logical consequence, Informational logical consequence, information probability


In semantic terms, the logical consequence is usually defined from the truth value of the premises and conclusion: this is true in every situation in which the former are true. It can be understood that, in these cases, the conclusion does not contain more information than the set of premises. Based on this idea, we develop, in this article, a definition of informational logical consequence, based on the notion of information suggested in the Mathematical Theory of Communication. We show some results, such as that, despite being inconsistent, the system underlying this notion is not trivial and that the logic underlying the informational logical consequence is not classical, but some kind of paraconsistent logic.


Alves, M. A. 2012. Lógica e informação: uma análise da consequência lógica a partir de uma perspectiva quantitativa da informação. Tese (Doutorado em Filosofia), 211 f. Instituto de Filosofia e Ciências Humanas, Universidade Estadual de Campinas, Campinas.

Da Costa, N. C. A. 1993. Lógica indutiva e probabilidade. 2.ed. São Paulo: Ed. HUCITEC.

D’Agostino & Floridi, L. 2009. The Enduring Scandal of Deduction: Is Propositional Logic Really Uninformative? Synthese 167(2): 271-315.

D’Ottaviano, I. M. L. 1992. A Lógica Clássica e o Surgimento das Lógicas Não-Clássicas. In: F. R. R. Évora (ed.), Século XIX: o nascimento da ciência contemporânea, p.65-93. Coleção CLE, v.11. Campinas: Universidade Estadual de Campinas/CLE.

Haack, S. 2002. Filosofia das Lógicas. Trad. C. A. Mortari & L. H. A. Dutra. São Paulo: Editora UNESP.

Hintikka, J. 1970. Surface Information and Depth Information. In: J. Hintikka & P. Suppes (eds.), Information and Inference, p.263-297. Dordrecht: Reidel.

Mates, B. 1968. Lógica Elementar. Trad. L. Hegenberg & O. S. Mota. São Paulo: Companhia Editora Nacional/Editora da Universidade de São Paulo.

Mendelson, E. 1964. Introduction to Logic. New York: D. Van Nostrand Company.

Shannon, C. & Weaver, W. 1949. The Mathematical Theory of Information. Urbana: University of Illinois Press.

Shoenfield, J. 1967. Mathematical Logic. Reading, MA: Addison Wesley Publishing Company.

Tarski, A. 1983 [1956]. On the Concept of Logical Consequence. In: Logic, Semantics, Metamathematics, p.409-420. Oxford: Clarendon Press.





Special Issue: The Logical Alien