Algebraic Approach to Tense Operators

B 2015

Algebraic Approach to Tense Operators

PASEKA, Jan and Ivan CHAJDA

Basic information

Original name

Algebraic Approach to Tense Operators

Authors

PASEKA, Jan (203 Czech Republic, guarantor, belonging to the institution) and Ivan CHAJDA (203 Czech Republic)

Edition

Lemgo, 204 pp. Research and Exposition 35, 2015

Publisher

Heldermann Verlag

Other information

Language

English

Type of outcome

Odborná kniha

Field of Study

10101 Pure mathematics

Country of publisher

Germany

Confidentiality degree

není předmětem státního či obchodního tajemství

Publication form

printed version "print"

RIV identification code

RIV/00216224:14310/15:00081655

Organization unit

Faculty of Science

ISBN

978-3-88538-235-5

Keywords in English

tense logic; tense operator; quantifier; modal operator; dynamic order algebra; tense algebra

Abstract

V originále

Propositional logics usually do not incorporate the dimension of time. However, even Aristotle already mentioned that time plays an important role in the evaluation of truth values of propositions. After Aristotle's time, a lot was created by men and, nowadays, logic is not an exceptional area for human reasoning. From the 1940's on, computers were built and the era of the Artificial Intelligence gently started. Nowadays, practically any more advanced product contains some kind of processor which decides situations in a way similar to that of a human being. However, for such technical devices the forecast for truth values of propositions in the future is not only a speculation. Due to the constructions and the technical possibilities, we can often compute these values, and propositions concerning the near future are of great importance. This has motivated many authors to investigate the so-called temporal logic, i.e., the logic where time is considered as a variable of the propositional formula. The logical language of tense logic contains, in addition to the ususal truth-functional operators, four the so-called tense operators. The aim of the monograph is to present an algebraic approach to an axiomatization of tense operators which are the most powerful tools in every tense logic.The authors hope that their monograph will be an incentive for further research.

Links

EE2.3.20.0051, research and development project

Name: Algebraické metody v kvantové logice

GA15-15286S, research and development project

Name: Algebraické, vícehodnotové a kvantové struktury pro modelování neurčitosti

Investor: Czech Science Foundation

GF15-34697L, research and development project

Name: Nové přístupy k reziduovaným posetům

Investor: Czech Science Foundation, Partner Agency (Austria)

Citovat

PASEKA, Jan and Ivan CHAJDA. Algebraic Approach to Tense Operators. Lemgo: Heldermann Verlag, 2015, 204 pp. Research and Exposition 35. ISBN 978-3-88538-235-5.

@book{1339756,
   author = {Paseka, Jan and Chajda, Ivan},
   address = {Lemgo},
   keywords = {tense logic; tense operator; quantifier; modal operator; dynamic order algebra; tense algebra},
   howpublished = {tištěná verze "print"},
   language = {eng},
   location = {Lemgo},
   isbn = {978-3-88538-235-5},
   publisher = {Heldermann Verlag},
   title = {Algebraic Approach to Tense Operators},
   year = {2015}
}

TY  - BOOK
ID  - 1339756
AU  - Paseka, Jan - Chajda, Ivan
PY  - 2015
TI  - Algebraic Approach to Tense Operators
VL  - Research and Exposition 35
PB  - Heldermann Verlag
CY  - Lemgo
SN  - 9783885382355
KW  - tense logic
KW  - tense operator
KW  - quantifier
KW  - modal operator
KW  - dynamic order algebra
KW  - tense algebra
N2  - Propositional logics usually do not incorporate the dimension of time. However, even Aristotle already mentioned that time plays an important role in the evaluation of truth values of propositions. After Aristotle's time, a lot was created by men and, nowadays, logic is not an exceptional area for human reasoning. From the 1940's on, computers were built and the era of the Artificial Intelligence gently started. Nowadays, practically any more advanced product contains some kind of processor which decides situations in a way similar to that of a human being. However, for such technical devices the forecast for truth values of propositions in the future is not only a speculation. Due to the constructions and the technical possibilities, we can often compute these values, and propositions concerning the near future are of great importance. This has motivated many authors to investigate the so-called temporal logic, i.e., the logic where time is considered as a variable of the propositional formula. The logical language of tense logic contains, in addition to the ususal truth-functional operators, four the so-called tense operators. The aim of the monograph is to present an algebraic approach to an axiomatization of tense operators which are the most powerful tools in every tense logic.The authors hope that their monograph will be an incentive for further research.
ER  -

PASEKA, Jan and Ivan CHAJDA. \textit{Algebraic Approach to Tense Operators}. Lemgo: Heldermann Verlag, 2015, 204 pp. Research and Exposition 35. ISBN~978-3-88538-235-5.

Detailed Information on Publication Record