Defining Cognitive Logics by Non-Classical Tableau Rules

Open access

Abstract

In the paper we propose a new approach to formalization of cognitive logics. By cognitive logics we understand supraclassical, but non-trivial consequence operations, defined in a propositional language. We extend some paradigm of tableau methods, in which classical consequence Cn is defined, to stronger logics - monotonic, as well as non-monotonic ones - by specific use of non-classical tableau rules. So far, in that context tableaus have been treated as a way of formalizing other approaches to supraclassical logics, but we use them autonomically to generate various consequence operations. It requires a description of the hierarchy of non-classical tableau rules that result in different supraclassical consequence operations, so we give it.

Antoniou Grigoris, Nonmonotonic Reasoning, MIT, 1997.

Jarmużek Tomasz, Tkaczyk Marcin, A method of defining paraconsistent tableaus, pp. 295-307, in New Directions in Paraconsistent Logic, J. Y. Beziau, M. Chakraborty and S. Dutta (eds.), vol. 152 of series Springer Proceedings in Mathematics and Statistics, Springer India, 2015.

Jarmużek Tomasz, Formalizacja metod tablicowych dla logik zdań i logik nazw (Formalization of tableau methods for propositional logics and for logics of names), Wydawnictwo UMK, Toruń, 2013.

Jarmużek Tomasz, Tkaczyk Marcin, Modal paraconsistent tableau systems of logic, WSEAS Transactions on Mathematics, vol. 14 (2015), pp. 248-255.

Jarmużek Tomasz, Tableau Metatheorem for Modal Logics, pp. 105-128, in Recent Trends in Philosphical Logic, Trends in Logic, (eds) Roberto Ciuni, Heinrich Wansing, Caroline Willkomennen, Springer Verlag, 2013.

Makinson David, Bridges from Classical to Nonmonotonic Logic, King’s College 2005.

Makinson David, Przedmowa do polskiego wydania (Preface to Polish edition), p. IX, in Od logiki klasycznej do niemonotonicznej, D. Makinson, translated by Tomasz Jarmużek, Wydawnictwo UMK, Toruń 2008.

Olivetti Nicola, Tableaux for Nonmonotonic Logics, pp. 469-529, in D’Agostino M., Gabbay D., Haehnle R., Posegga J. (eds), Handbook of Tableau Methods, Kluwer, 1999.

Tarski Alfred, On the concept of logical consequence, pp. 409-420 in Alfred Tarski, Logic, Semantics, Metamathematics Papers from 1923 to 1938, translated by J.H. Woodger, Oxford: Clarendon Press 1956.

Wójcicki Ryszard, Theory of Logical Calculi Basic Theory of Consequence Operations, Springer 1988.

Studies in Logic, Grammar and Rhetoric

The Journal of University of Bialystok

Journal Information


Cite Score 2017: 0.28

SCImago Journal Rank (SJR) 2017: 0.136
Source Normalized Impact per Paper (SNIP) 2017: 0.293

Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 90 90 7
PDF Downloads 30 30 5