Geodesic
An Inferentially Many-Valued Two-Dimensional Notion of Entailment
Bulletin of the Section of Logic, Tome 46 (2017) no. 3-4

Voir la notice de l'article provenant de la source Library of Science

Starting from the notions of q-entailment and p-entailment, a two-dimensional notion of entailment is developed with respect to certain generalized q-matrices referred to as B-matrices. After showing that every purely monotonic singleconclusion consequence relation is characterized by a class of B-matrices with respect to q-entailment as well as with respect to p-entailment, it is observed that, as a result, every such consequence relation has an inferentially four-valued characterization. Next, the canonical form of B-entailment, a two-dimensional multiple-conclusion notion of entailment based on B-matrices, is introduced, providing a uniform framework for studying several different notions of entailment based on designation, antidesignation, and their complements. Moreover, the two-dimensional concept of a B-consequence relation is defined, and an abstract characterization of such relations by classes of B-matrices is obtained. Finally, a contribution to the study of inferential many-valuedness is made by generalizing Suszko’s Thesis and the corresponding reduction to show that any B-consequence relation is, in general, inferentially four-valued.
Keywords: Inferential many-valuedness, two-dimensional entailment, B-matrices, B-consequence relations, monotonic consequence relations, q-entailment, p-entailment, Suszko Reduction 
@article{BSL_2017_46_3-4_a0,
     author = {Blasio, Carolina and Marcos, Jo\~ao and Wansing, Heinrich},
     title = {An {Inferentially} {Many-Valued} {Two-Dimensional} {Notion} of {Entailment}},
     journal = {Bulletin of the Section of Logic},
     publisher = {mathdoc},
     volume = {46},
     number = {3-4},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BSL_2017_46_3-4_a0/}
}
TY  - JOUR
AU  - Blasio, Carolina
AU  - Marcos, João
AU  - Wansing, Heinrich
TI  - An Inferentially Many-Valued Two-Dimensional Notion of Entailment
JO  - Bulletin of the Section of Logic
PY  - 2017
VL  - 46
IS  - 3-4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BSL_2017_46_3-4_a0/
LA  - en
ID  - BSL_2017_46_3-4_a0
ER  - 
%0 Journal Article
%A Blasio, Carolina
%A Marcos, João
%A Wansing, Heinrich
%T An Inferentially Many-Valued Two-Dimensional Notion of Entailment
%J Bulletin of the Section of Logic
%D 2017
%V 46
%N 3-4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BSL_2017_46_3-4_a0/
%G en
%F BSL_2017_46_3-4_a0
Blasio, Carolina; Marcos, João; Wansing, Heinrich. An Inferentially Many-Valued Two-Dimensional Notion of Entailment. Bulletin of the Section of Logic, Tome 46 (2017) no. 3-4. http://geodesic.mathdoc.fr/item/BSL_2017_46_3-4_a0/