Tense logics based on posets

J 2025

Tense logics based on posets

CHAJDA, Ivan; Helmut LAENGER; Antonio LEDDA; Jan PASEKA; Gandolfo VERGOTTINI et. al.

Basic information

Original name

Tense logics based on posets

Authors

CHAJDA, Ivan; Helmut LAENGER; Antonio LEDDA; Jan PASEKA (203 Czech Republic, belonging to the institution) and Gandolfo VERGOTTINI

Edition

Journal of Logic and Computation, Oxford, Oxford University Press, 2025, 0955-792X

Other information

Language

English

Type of outcome

Article in a journal

Field of Study

10100 1.1 Mathematics

Country of publisher

United Kingdom of Great Britain and Northern Ireland

Confidentiality degree

is not subject to a state or trade secret

References:

URL

Impact factor

Impact factor: 0.700 in 2023

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.1093/logcom/exae081

UT WoS

001382402200001

EID Scopus

2-s2.0-105004259370

Keywords in English

poset; orthomodular poset; Dedekind-MacNeille completion; implication; adjoint operator; adjoint pair; tense operator; tense logic

Abstract

V originále

Quantum mechanics, initially formalized with orthomodular lattices, benefits from a simpler approach using just partially ordered sets (posets). This paper explores how logical connectives are introduced in poset-based logics. Building on prior work by the authors, we delve deeper into 'dynamic' logics where truth values can change over time. We consider time sets with a preference relation and propositions whose truth depends on time. Tense operators, introduced by J.Burgess and extended for various logics, become a valuable tool. This paper proposes several approaches to this topic, aiming to inspire a further stream of research.

Links

GF20-09869L, research and development project

Name: Ortomodularita z různých pohledů

Investor: Czech Science Foundation, Partner Agency (Austria)

Cite

CHAJDA, Ivan; Helmut LAENGER; Antonio LEDDA; Jan PASEKA and Gandolfo VERGOTTINI. Tense logics based on posets. Journal of Logic and Computation. Oxford: Oxford University Press, 2025, vol. 35, No 4, p. 1-31. ISSN 0955-792X. Available from: https://dx.doi.org/10.1093/logcom/exae081.

@article{2485019,
   author = {Chajda, Ivan and Laenger, Helmut and Ledda, Antonio and Paseka, Jan and Vergottini, Gandolfo},
   article_location = {Oxford},
   article_number = {4},
   doi = {http://dx.doi.org/10.1093/logcom/exae081},
   keywords = {poset; orthomodular poset; Dedekind-MacNeille completion; implication; adjoint operator; adjoint pair; tense operator; tense logic},
   language = {eng},
   issn = {0955-792X},
   journal = {Journal of Logic and Computation},
   title = {Tense logics based on posets},
   url = {https://doi.org/10.1093/logcom/exae081},
   volume = {35},
   year = {2025}
}

TY  - JOUR
ID  - 2485019
AU  - Chajda, Ivan - Laenger, Helmut - Ledda, Antonio - Paseka, Jan - Vergottini, Gandolfo
PY  - 2025
TI  - Tense logics based on posets
JF  - Journal of Logic and Computation
VL  - 35
IS  - 4
SP  - 1-31
EP  - 1-31
PB  - Oxford University Press
SN  - 0955792X
KW  - poset
KW  - orthomodular poset
KW  - Dedekind-MacNeille completion
KW  - implication
KW  - adjoint operator
KW  - adjoint pair
KW  - tense operator
KW  - tense logic
UR  - https://doi.org/10.1093/logcom/exae081
N2  - Quantum mechanics, initially formalized with orthomodular lattices, benefits from a simpler approach using just partially ordered sets (posets). This paper explores how logical connectives are introduced in poset-based logics. Building on prior work by the authors, we delve deeper into 'dynamic' logics where truth values can change over time. We consider time sets with a preference relation and propositions whose truth depends on time. Tense operators, introduced by J.Burgess and extended for various logics, become a valuable tool. This paper proposes several approaches to this topic, aiming to inspire a further stream of research.
ER  -

CHAJDA, Ivan; Helmut LAENGER; Antonio LEDDA; Jan PASEKA and Gandolfo VERGOTTINI. Tense logics based on posets. \textit{Journal of Logic and Computation}. Oxford: Oxford University Press, 2025, vol.~35, No~4, p.~1-31. ISSN~0955-792X. Available from: https://dx.doi.org/10.1093/logcom/exae081.

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