‘Transitivity’ of consequence relations

David Ripley

doi:10.1007/978-3-662-48561-3_27

‘Transitivity’ of consequence relations

David Ripley

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Other › peer-review

2 Citations (Scopus)

Abstract

A binary relation R on a set S is transitive iff for all a, b, c ∈ S, if aRb and bRc, then aRc. This almost never applies to the relations logicians tend to think of as consequence relations; where such relations are relations on a set at all, they are rarely transitive. Yet it is common to hear consequence relations described as ‘transitive’, and to see rules imposed to ensure ‘transitivity’ of these relations. This paper attempts to clarify the situation.

Original language	English
Title of host publication	Logic, Rationality, and Interaction - 5th International Workshop, LORI 2015, Proceedings
Subtitle of host publication	Proceedings of LORI V
Editors	Wen-Fang Wang, Wiebe van der Hoek, Wesley H. Holliday
Publisher	Springer
Pages	328-340
Number of pages	13
ISBN (Print)	9783662485606
DOIs	https://doi.org/10.1007/978-3-662-48561-3_27
Publication status	Published - 2015
Externally published	Yes
Event	5th International Workshop on Logic, Rationality, and Interaction, LORI 2015 - Taipei, Taiwan Duration: 28 Oct 2015 → 31 Oct 2015

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9394
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	5th International Workshop on Logic, Rationality, and Interaction, LORI 2015
Country/Territory	Taiwan
City	Taipei
Period	28/10/15 → 31/10/15

Access to Document

10.1007/978-3-662-48561-3_27

Cite this

Ripley, D. (2015). ‘Transitivity’ of consequence relations. In W.-F. Wang, W. van der Hoek, & W. H. Holliday (Eds.), Logic, Rationality, and Interaction - 5th International Workshop, LORI 2015, Proceedings: Proceedings of LORI V (pp. 328-340). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9394). Springer. https://doi.org/10.1007/978-3-662-48561-3_27

Ripley, David. / ‘Transitivity’ of consequence relations. Logic, Rationality, and Interaction - 5th International Workshop, LORI 2015, Proceedings: Proceedings of LORI V. editor / Wen-Fang Wang ; Wiebe van der Hoek ; Wesley H. Holliday. Springer, 2015. pp. 328-340 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{45e9893fc50f49e5b62dec7986df33bd,

title = "{\textquoteleft}Transitivity{\textquoteright} of consequence relations",

abstract = "A binary relation R on a set S is transitive iff for all a, b, c ∈ S, if aRb and bRc, then aRc. This almost never applies to the relations logicians tend to think of as consequence relations; where such relations are relations on a set at all, they are rarely transitive. Yet it is common to hear consequence relations described as {\textquoteleft}transitive{\textquoteright}, and to see rules imposed to ensure {\textquoteleft}transitivity{\textquoteright} of these relations. This paper attempts to clarify the situation.",

author = "David Ripley",

year = "2015",

doi = "10.1007/978-3-662-48561-3_27",

language = "English",

isbn = "9783662485606",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer",

pages = "328--340",

editor = "Wen-Fang Wang and {van der Hoek}, Wiebe and Holliday, {Wesley H.}",

booktitle = "Logic, Rationality, and Interaction - 5th International Workshop, LORI 2015, Proceedings",

note = "5th International Workshop on Logic, Rationality, and Interaction, LORI 2015 ; Conference date: 28-10-2015 Through 31-10-2015",

}

Ripley, D 2015, ‘Transitivity’ of consequence relations. in W-F Wang, W van der Hoek & WH Holliday (eds), Logic, Rationality, and Interaction - 5th International Workshop, LORI 2015, Proceedings: Proceedings of LORI V. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9394, Springer, pp. 328-340, 5th International Workshop on Logic, Rationality, and Interaction, LORI 2015, Taipei, Taiwan, 28/10/15. https://doi.org/10.1007/978-3-662-48561-3_27

‘Transitivity’ of consequence relations. / Ripley, David.
Logic, Rationality, and Interaction - 5th International Workshop, LORI 2015, Proceedings: Proceedings of LORI V. ed. / Wen-Fang Wang; Wiebe van der Hoek; Wesley H. Holliday. Springer, 2015. p. 328-340 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9394).

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Other › peer-review

TY - GEN

T1 - ‘Transitivity’ of consequence relations

AU - Ripley, David

PY - 2015

Y1 - 2015

N2 - A binary relation R on a set S is transitive iff for all a, b, c ∈ S, if aRb and bRc, then aRc. This almost never applies to the relations logicians tend to think of as consequence relations; where such relations are relations on a set at all, they are rarely transitive. Yet it is common to hear consequence relations described as ‘transitive’, and to see rules imposed to ensure ‘transitivity’ of these relations. This paper attempts to clarify the situation.

AB - A binary relation R on a set S is transitive iff for all a, b, c ∈ S, if aRb and bRc, then aRc. This almost never applies to the relations logicians tend to think of as consequence relations; where such relations are relations on a set at all, they are rarely transitive. Yet it is common to hear consequence relations described as ‘transitive’, and to see rules imposed to ensure ‘transitivity’ of these relations. This paper attempts to clarify the situation.

UR - http://www.scopus.com/inward/record.url?scp=84951081318&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-48561-3_27

DO - 10.1007/978-3-662-48561-3_27

M3 - Conference Paper

AN - SCOPUS:84951081318

SN - 9783662485606

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 328

EP - 340

BT - Logic, Rationality, and Interaction - 5th International Workshop, LORI 2015, Proceedings

A2 - Wang, Wen-Fang

A2 - van der Hoek, Wiebe

A2 - Holliday, Wesley H.

PB - Springer

T2 - 5th International Workshop on Logic, Rationality, and Interaction, LORI 2015

Y2 - 28 October 2015 through 31 October 2015

ER -

Ripley D. ‘Transitivity’ of consequence relations. In Wang WF, van der Hoek W, Holliday WH, editors, Logic, Rationality, and Interaction - 5th International Workshop, LORI 2015, Proceedings: Proceedings of LORI V. Springer. 2015. p. 328-340. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-662-48561-3_27

‘Transitivity’ of consequence relations

Abstract

Publication series

Conference

Access to Document

Other files and links

Cite this