Abstract
In this article we consider the partition of a set of statements P = P a ∪ P b ∪ P′, where P a, P b, P′ are, correspondingly, sets of statements only being argumented, both being argumented and argumenting, and only argumenting (basic statements). On P are defined two functions of argument and counter-argument selection forming the semantics for logics of argumentation. A four-valued logic of argumentation is proposed. By means of graph theory are formed trees of arguments (argument trees), wood, consisting of them, and some transformations of the wood, such that their result may be both planar and non-planar graph. Argument systems (systems of arguments) are defined together with their characterizations that use analytic tableaux. With the help of argument trees a specification of the idea of hermeneutic (“vicious”) circle is formalized.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
van Benthem, J., Logic and Reasoning: Do the Facts Matter? Studia Logica, 2011, vol. 88, no. 1, pp. 67–84.
Logic and Argumentation van Benthem, J., Eemeren, F.H., Grootendorst, R., and Veltman, F., Eds., Amsterdam: North-Holland, 1996.
Vagin, V.N., Golovina, E.Yu., Zagoryanskaya, A.A., and Fomina, M.V., Dostovernyi i pravdopodobnyi vyvod v intellektual’nykh sistemakh (Reliable and Plausible Inference in Intelligent Systems), Moscow: Fizmatlit, 2008.
Finn, V.K., Standard and Non-Standard Logics of Argumentation, in Iskusstvennyi intellekt: metodologiya primeneniya, filosofiya (Artificial Intelligence: Methodology and Applications, Philosophy), Moscow: KRASAND, 2011, pp. 312–338.
Finn, V.K., On One Variant of Argumentation Logic, Nauchn.-Techn. Inform., Ser. 2, 1996, no. 5–6, pp. 3–19.
Wang, H., Logic, Computers, and Sets. Cp. XII. Many-Sorted Predicate Calculi, New York: Chelsea, 1970, pp. 322–333.
Konig, D., Sur les correspondences multivoques des ensembles, Fundamenta Math., 1926, no. 8, pp. 114–134.
Gadamer, H.-G., Truth and Method New York: The Seabury, 1975; Moscow: Progress, 1988.
Harary, F., Graph Theory Addison-Wesley, 1969; Moscow: Mir, 1973.
Finn, V.K. and Mikheyenkova, M.A., Plausible Reasoning for the Problems of Cognitive Sociology, Logic and Logical Philosophy, 2011, vol. 20, pp. 113–139.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.K. Finn, 2012, published in Nauchno-Tekhnicheskaya Informatsiya, Seriya 2, 2012, No. 11, pp. 20–30.
The article was translated by Prof. D.G. Lakhuti. From the translator: in their article on Developments in Argumentation Theory (Logic and Argumentation, eds. J. van Benthem, F.H. van Eemeren, R. Grootendorst and F. Veltman, North Holland, Amsterdam/Oxford/New York/Tokio, 1996, pp. 9–26) Frans H. van Eemeren and Rob Grootendorst single out four different meanings of the English word argument: (a) a reason, (b) a logical inference of a conclusion from one or more premises, (c) discussion, and (d) a quarrel (p. 9). In Russian there is no word with the same four meanings. In this translation the word argument is used in the sence (a), the word argumentation in the sense (b); we will not need the meanings (c) or, thank God, (d). The verb to argument will be used as meaning to find arguments (in support of a statement), or to build an argumentation.—D. L.
About this article
Cite this article
Finn, V.K. Twelve theses on argumentation systems. Autom. Doc. Math. Linguist. 46, 235–247 (2012). https://doi.org/10.3103/S0005105512060039
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0005105512060039