Implicational Tonoid Logics: Algebraic and Relational Semantics

Eunsuk Yang; J. Michael Dunn

doi:10.1007/s11787-021-00288-z

Implicational Tonoid Logics: Algebraic and Relational Semantics

Eunsuk Yang^*
, J. Michael Dunn

^*Corresponding author for this work

Department of Philosophy

Indiana University Bloomington

Research output: Contribution to journal › Journal article › peer-review

12 Scopus citations

Abstract

This paper combines two classes of generalized logics, one of which is the class of weakly implicative logics introduced by Cintula and the other of which is the class of gaggle logics introduced by Dunn. For this purpose we introduce implicational tonoid logics. More precisely, we first define implicational tonoid logics in general and examine their relation to weakly implicative logics. We then provide algebraic semantics for implicational tonoid logics. Finally, we consider relational semantics, called Routley–Meyer–style semantics, for finitary those logics.

Original language	English
Pages (from-to)	435-456
Number of pages	22
Journal	Logica Universalis
Volume	15
Issue number	4
DOIs	https://doi.org/10.1007/s11787-021-00288-z
State	Published - 2021.12

Keywords

(Implicational) tonoid logic
Algebraic semantics
Gaggle logic
Relational semantics
Weakly implicative logic

Quacquarelli Symonds(QS) Subject Topics

Mathematics

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10.1007/s11787-021-00288-z

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@article{a6e5d1aa883e428dae54ab8a16a4338c,

title = "Implicational Tonoid Logics: Algebraic and Relational Semantics",

abstract = "This paper combines two classes of generalized logics, one of which is the class of weakly implicative logics introduced by Cintula and the other of which is the class of gaggle logics introduced by Dunn. For this purpose we introduce implicational tonoid logics. More precisely, we first define implicational tonoid logics in general and examine their relation to weakly implicative logics. We then provide algebraic semantics for implicational tonoid logics. Finally, we consider relational semantics, called Routley–Meyer–style semantics, for finitary those logics.",

keywords = "(Implicational) tonoid logic, Algebraic semantics, Gaggle logic, Relational semantics, Weakly implicative logic",

author = "Eunsuk Yang and Dunn, \{J. Michael\}",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

year = "2021",

month = dec,

doi = "10.1007/s11787-021-00288-z",

language = "English",

volume = "15",

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journal = "Logica Universalis",

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TY - JOUR

T1 - Implicational Tonoid Logics

T2 - Algebraic and Relational Semantics

AU - Yang, Eunsuk

AU - Dunn, J. Michael

PY - 2021/12

Y1 - 2021/12

N2 - This paper combines two classes of generalized logics, one of which is the class of weakly implicative logics introduced by Cintula and the other of which is the class of gaggle logics introduced by Dunn. For this purpose we introduce implicational tonoid logics. More precisely, we first define implicational tonoid logics in general and examine their relation to weakly implicative logics. We then provide algebraic semantics for implicational tonoid logics. Finally, we consider relational semantics, called Routley–Meyer–style semantics, for finitary those logics.

AB - This paper combines two classes of generalized logics, one of which is the class of weakly implicative logics introduced by Cintula and the other of which is the class of gaggle logics introduced by Dunn. For this purpose we introduce implicational tonoid logics. More precisely, we first define implicational tonoid logics in general and examine their relation to weakly implicative logics. We then provide algebraic semantics for implicational tonoid logics. Finally, we consider relational semantics, called Routley–Meyer–style semantics, for finitary those logics.

KW - (Implicational) tonoid logic

KW - Algebraic semantics

KW - Gaggle logic

KW - Relational semantics

KW - Weakly implicative logic

UR - https://www.scopus.com/pages/publications/85115721487

U2 - 10.1007/s11787-021-00288-z

DO - 10.1007/s11787-021-00288-z

M3 - Journal article

AN - SCOPUS:85115721487

SN - 1661-8297

VL - 15

SP - 435

EP - 456

JO - Logica Universalis

JF - Logica Universalis

IS - 4

ER -

Implicational Tonoid Logics: Algebraic and Relational Semantics

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

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