Expressive completeness failure in branching time structures

Amihood Amir

doi:10.1016/0022-0000(87)90003-1

Expressive completeness failure in branching time structures

Amihood Amir

Massachusetts Institute of Technology

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

A propositional logic is expressively complete if there is a finite set of connectives which define all truth tables. Kamp, Stavi, and Gabbay proved that all tense logics over linear time are expressively complete. Amir and Gabbay brought examples of expressively complete non-linear time structures. Gabbay showed that the general time structure is not expressively complete. Here we narrow the gap and prove that for branching time, if the model is an infinite tree with an unbounded branching factor then there is no expressive completeness.

Original language	English
Pages (from-to)	27-42
Number of pages	16
Journal	Journal of Computer and System Sciences
Volume	34
Issue number	1
DOIs	https://doi.org/10.1016/0022-0000(87)90003-1
State	Published - Feb 1987
Externally published	Yes

Access to Document

10.1016/0022-0000(87)90003-1

Cite this

@article{2c3d22b3dcc14ee29ff137fa03524a21,

title = "Expressive completeness failure in branching time structures",

abstract = "A propositional logic is expressively complete if there is a finite set of connectives which define all truth tables. Kamp, Stavi, and Gabbay proved that all tense logics over linear time are expressively complete. Amir and Gabbay brought examples of expressively complete non-linear time structures. Gabbay showed that the general time structure is not expressively complete. Here we narrow the gap and prove that for branching time, if the model is an infinite tree with an unbounded branching factor then there is no expressive completeness.",

author = "Amihood Amir",

year = "1987",

month = feb,

doi = "10.1016/0022-0000(87)90003-1",

language = "אנגלית",

volume = "34",

pages = "27--42",

journal = "Journal of Computer and System Sciences",

issn = "0022-0000",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Expressive completeness failure in branching time structures

AU - Amir, Amihood

PY - 1987/2

Y1 - 1987/2

N2 - A propositional logic is expressively complete if there is a finite set of connectives which define all truth tables. Kamp, Stavi, and Gabbay proved that all tense logics over linear time are expressively complete. Amir and Gabbay brought examples of expressively complete non-linear time structures. Gabbay showed that the general time structure is not expressively complete. Here we narrow the gap and prove that for branching time, if the model is an infinite tree with an unbounded branching factor then there is no expressive completeness.

AB - A propositional logic is expressively complete if there is a finite set of connectives which define all truth tables. Kamp, Stavi, and Gabbay proved that all tense logics over linear time are expressively complete. Amir and Gabbay brought examples of expressively complete non-linear time structures. Gabbay showed that the general time structure is not expressively complete. Here we narrow the gap and prove that for branching time, if the model is an infinite tree with an unbounded branching factor then there is no expressive completeness.

UR - https://www.scopus.com/pages/publications/0023288035

U2 - 10.1016/0022-0000(87)90003-1

DO - 10.1016/0022-0000(87)90003-1

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0023288035

SN - 0022-0000

VL - 34

SP - 27

EP - 42

JO - Journal of Computer and System Sciences

JF - Journal of Computer and System Sciences

IS - 1

ER -

Expressive completeness failure in branching time structures

Abstract

Access to Document

Other files and links

Fingerprint

Cite this