# An Inferentially Many-Valued Two-Dimensional Notion of Entailment

Carolina Blasio; João Marcos; Heinrich Wansing

Bulletin of the Section of Logic (2017)

- Volume: 46, Issue: 3/4
- ISSN: 0138-0680

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topCarolina Blasio, João Marcos, and Heinrich Wansing. "An Inferentially Many-Valued Two-Dimensional Notion of Entailment." Bulletin of the Section of Logic 46.3/4 (2017): null. <http://eudml.org/doc/295524>.

@article{CarolinaBlasio2017,

abstract = {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.},

author = {Carolina Blasio, João Marcos, Heinrich Wansing},

journal = {Bulletin of the Section of Logic},

keywords = {Inferential many-valuedness; two-dimensional entailment; B-matrices; B-consequence relations; monotonic consequence relations; q-entailment; p-entailment; Suszko Reduction},

language = {eng},

number = {3/4},

pages = {null},

title = {An Inferentially Many-Valued Two-Dimensional Notion of Entailment},

url = {http://eudml.org/doc/295524},

volume = {46},

year = {2017},

}

TY - JOUR

AU - Carolina Blasio

AU - João Marcos

AU - Heinrich Wansing

TI - An Inferentially Many-Valued Two-Dimensional Notion of Entailment

JO - Bulletin of the Section of Logic

PY - 2017

VL - 46

IS - 3/4

SP - null

AB - 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.

LA - eng

KW - Inferential many-valuedness; two-dimensional entailment; B-matrices; B-consequence relations; monotonic consequence relations; q-entailment; p-entailment; Suszko Reduction

UR - http://eudml.org/doc/295524

ER -

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