國立虎尾科技大學 |

Decidability of Logical Theories and Their Combination

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Decidability of Logical Theories and Their Combination/ by João Rasga, Cristina Sernadas.
作者:	Rasga, João.
其他作者:	Sernadas, Cristina.
面頁冊數:	XIII, 178 p. 70 illus., 1 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Philosophy of Mathematics. -
電子資源:	https://doi.org/10.1007/978-3-030-56554-1
ISBN:	9783030565541

Decidability of Logical Theories and Their Combination
Rasga, João.

Decidability of Logical Theories and Their Combination[electronic resource] /by João Rasga, Cristina Sernadas. - 1st ed. 2020. - XIII, 178 p. 70 illus., 1 illus. in color.online resource. - Studies in Universal Logic,2297-0282. - Studies in Universal Logic,.

Chapter 1: First Order Logic -- Chapter 2: Reasoning with Theories -- Chapter 3: Decidability Results on Theories -- Chapter 4: Quantifier Elimination -- Chapter 5: Combination of Theories -- Appendix: Basics of Computability -- Bibliography -- Table of Symbols -- Subject Index.

This textbook provides a self-contained introduction to decidability of first-order theories and their combination. The technical material is presented in a systematic and universal way and illustrated with plenty of examples and a range of proposed exercises. After an overview of basic first-order logic concepts, the authors discuss some model-theoretic notions like embeddings, diagrams, and elementary substructures. The text then goes on to explore an applicable way to deduce logical consequences from a given theory and presents sufficient conditions for a theory to be decidable. The chapters that follow focus on quantifier elimination, decidability of the combination of first-order theories and the basics of computability theory. The inclusion of a chapter on Gentzen calculus, cut elimination, and Craig interpolation, as well as a chapter on combination of theories and preservation of decidability, help to set this volume apart from similar books in the field. Decidability of Logical Theories and their Combination is ideal for graduate students of Mathematics and is equally suitable for Computer Science, Philosophy and Physics students who are interested in gaining a deeper understanding of the subject. The book is also directed to researchers that intend to get acquainted with first-order theories and their combination.

ISBN: 9783030565541

Standard No.: 10.1007/978-3-030-56554-1doiSubjects--Topical Terms:

1108410
Philosophy of Mathematics.

LC Class. No.: QA8.9-10.3

Dewey Class. No.: 511.3

Decidability of Logical Theories and Their Combination
LDR:03089nam a22004215i 4500 001 1018401
003 DE-He213
005 20201020133744.0
007 cr nn 008mamaa
008 210318s2020 gw | s |||| 0|eng d
020 $a 9783030565541 $9 978-3-030-56554-1
024 7 $a 10.1007/978-3-030-56554-1 $2 doi
035 $a 978-3-030-56554-1
050 4 $a QA8.9-10.3
072 7 $a PBC $2 bicssc
072 7 $a MAT018000 $2 bisacsh
072 7 $a PBC $2 thema
072 7 $a PBCD $2 thema
082 0 4 $a 511.3 $2 23
100 1 $a Rasga, João. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1313388
245 1 0 $a Decidability of Logical Theories and Their Combination $h [electronic resource] / $c by João Rasga, Cristina Sernadas.
250 $a 1st ed. 2020.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Birkhäuser, $c 2020.
300 $a XIII, 178 p. 70 illus., 1 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Studies in Universal Logic, $x 2297-0282
505 0 $a Chapter 1: First Order Logic -- Chapter 2: Reasoning with Theories -- Chapter 3: Decidability Results on Theories -- Chapter 4: Quantifier Elimination -- Chapter 5: Combination of Theories -- Appendix: Basics of Computability -- Bibliography -- Table of Symbols -- Subject Index.
520 $a This textbook provides a self-contained introduction to decidability of first-order theories and their combination. The technical material is presented in a systematic and universal way and illustrated with plenty of examples and a range of proposed exercises. After an overview of basic first-order logic concepts, the authors discuss some model-theoretic notions like embeddings, diagrams, and elementary substructures. The text then goes on to explore an applicable way to deduce logical consequences from a given theory and presents sufficient conditions for a theory to be decidable. The chapters that follow focus on quantifier elimination, decidability of the combination of first-order theories and the basics of computability theory. The inclusion of a chapter on Gentzen calculus, cut elimination, and Craig interpolation, as well as a chapter on combination of theories and preservation of decidability, help to set this volume apart from similar books in the field. Decidability of Logical Theories and their Combination is ideal for graduate students of Mathematics and is equally suitable for Computer Science, Philosophy and Physics students who are interested in gaining a deeper understanding of the subject. The book is also directed to researchers that intend to get acquainted with first-order theories and their combination.
650 2 4 $a Philosophy of Mathematics. $3 1108410
650 2 4 $a Mathematical Logic and Formal Languages. $3 670059
650 1 4 $a Mathematical Logic and Foundations. $3 669393
650 0 $a Mathematics—Philosophy. $3 1254283
650 0 $a Mathematical logic. $2 bicssc $3 810627
700 1 $a Sernadas, Cristina. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 679077
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030565534
776 0 8 $i Printed edition: $z 9783030565558
776 0 8 $i Printed edition: $z 9783030565565
830 0 $a Studies in Universal Logic, $x 2297-0282 $3 1257651
856 4 0 $u https://doi.org/10.1007/978-3-030-56554-1
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)