Algebraic Approach to Tense Operators

B 2015

Algebraic Approach to Tense Operators

PASEKA, Jan a Ivan CHAJDA

Základní údaje

Originální název

Algebraic Approach to Tense Operators

Autoři

PASEKA, Jan (203 Česká republika, garant, domácí) a Ivan CHAJDA (203 Česká republika)

Vydání

Lemgo, 204 s. Research and Exposition 35, 2015

Nakladatel

Heldermann Verlag

Další údaje

Jazyk

angličtina

Typ výsledku

Odborná kniha

Obor

10101 Pure mathematics

Stát vydavatele

Německo

Utajení

není předmětem státního či obchodního tajemství

Forma vydání

tištěná verze "print"

Kód RIV

RIV/00216224:14310/15:00081655

Organizační jednotka

Přírodovědecká fakulta

ISBN

978-3-88538-235-5

Klíčová slova anglicky

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

Štítky

AKR

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 18. 3. 2016 16:36, prof. RNDr. Jan Paseka, CSc.

Anotace

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.

Návaznosti

EE2.3.20.0051, projekt VaV

Název: Algebraické metody v kvantové logice

GA15-15286S, projekt VaV

Název: Algebraické, vícehodnotové a kvantové struktury pro modelování neurčitosti

Investor: Grantová agentura ČR, Algebraické, vícehodnotové a kvantové struktury pro modelování neurčitosti

GF15-34697L, projekt VaV

Název: Nové přístupy k reziduovaným posetům

Investor: Grantová agentura ČR, New approaches to residuated posets, Partnerská agentura (Rakousko)

Citovat

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

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