LEADER 02343nam 2200493 450 001 9910683352003321 005 20230730235910.0 010 $a9789811986338$b(electronic bk.) 010 $z9789811986321 024 7 $a10.1007/978-981-19-8633-8 035 $a(MiAaPQ)EBC7220716 035 $a(Au-PeEL)EBL7220716 035 $a(OCoLC)1374428501 035 $a(DE-He213)978-981-19-8633-8 035 $a(PPN)269097295 035 $a(EXLCZ)9926347427400041 100 $a20230730d2023 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aR-Calculus, IV $epropositional logic /$fWei Li and Yuefei Sui 205 $a1st ed. 2023. 210 1$aSingapore :$cSpringer,$d[2023] 210 4$dİ2023 215 $a1 online resource (264 pages) 225 1 $aPerspectives in Formal Induction, Revision and Evolution,$x2731-3697 311 08$aPrint version: Li, Wei R-Calculus, IV: Propositional Logic Singapore : Springer,c2023 9789811986321 320 $aIncludes bibliographical references. 327 $aIntroduction -- R-calculus for simplified propositional logics -- R-calculi for tableau/Gentzen deduction systems -- R-calculi RQ1Q2/RQ1Q2 -- R-calculi RQ1iQ2j/RQ1iQ2j -- R-Calculi: RY1Q1iY2Q2j/RY1Q1iY2Q2j -- R-calculi for supersequents -- R-calculi for propositional logic. 330 $aThis fourth volume of the book series combines propositional logic and R-calculus for a new point of view to consider belief revision. It gives the R-calculi for propositional logic, description logics, propositional modal logic, logic programming, ?-propositional logic, semantic networks, and three-valued logic, etc.. Applications of R-calculus in logic of supersequents are also given. This book offers a rich blend of theory and practice. It is suitable for students, researchers and practitioners in the field of logic. . 410 0$aPerspectives in Formal Induction, Revision and Evolution,$x2731-3697 606 $aPropositional calculus 615 0$aPropositional calculus. 676 $a810 700 $aLi$b Wei$0721674 702 $aSui$b Yuefei 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910683352003321 996 $aR-Calculus, IV$93419637 997 $aUNINA LEADER 04931nam 2200649Ia 450 001 9910830908403321 005 20230421054211.0 010 $a1-283-59289-4 010 $a9786613905345 010 $a1-118-49178-5 010 $a1-118-49176-9 010 $a1-118-49177-7 035 $a(CKB)2670000000237810 035 $a(EBL)1011370 035 $a(OCoLC)809539052 035 $a(SSID)ssj0000715402 035 $a(PQKBManifestationID)11454833 035 $a(PQKBTitleCode)TC0000715402 035 $a(PQKBWorkID)10700962 035 $a(PQKB)10726895 035 $a(MiAaPQ)EBC1011370 035 $a(EXLCZ)992670000000237810 100 $a19970708d1997 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aLinear models$b[electronic resource] /$fS. R. Searle 210 $aNew York $cWiley$dc1997 215 $a1 online resource (560 p.) 225 0 $aWiley classics library 300 $aDescription based upon print version of record. 311 $a0-471-76950-9 311 $a0-471-18499-3 327 $aLinear Models; Contents; 1. Generalized Inverse Matrices; 1. Introduction; a. Definition and existence; b. An algorithm; 2. Solving linear equations; a. Consistent equations; b. Obtaining solutions; c. Properties of solutions; 3. The Penrose inverse; 4. Other definitions; 5. Symmetric matrices; a. Properties of a generalized inverse; b. Two methods of derivation; 6. Arbitrariness in a generalized inverse; 7. Other results; 8. Exercises; 2. Distributions and Quadratic Forms; 1. Introduction; 2. Symmetric matrices; 3. Positive definiteness; 4. Distributions; a. Multivariate density functions 327 $ab. Momentsc. Linear transformations; d. Moment generating functions; e. Univariate normal; f. Multivariate normal; (i) Density function; (ii) Aitken's integral; (iii) Moment generating function; (iv) Marginal distributions; (v) Conditional distributions; (vi) Independence; g. Central ?2, F and t; h. Non-central ?2; i. Non-central F; j . Other non-central distributions; 5. Distribution of quadratic forms; a. Cumulants; b. Distributions; c. Independence; 6. Bilinear forms; 7. The singular normal distribution; 8. Exercises; 3. Regression, or the Full Rank Model; 1. Introduction; a. The model 327 $ab. Observationsc. Estimation; d. Example; e. The general case of k x-vartables; f. Example (continued); g. Intercept and no-intercept models; h. Example (continued); 2. Deviations from means; 3. Four methods of estimation; a. Ordinary least squares; b. Generalized least squares; c. Maximum likelihood; d. The best linear unbiased estimator (b.l.u.e.); 4. Consequences of estimation; a. Unbiasedness; b. Variances; c. Estimating E(y); d. Residual error sum of squares; e. Estimating the residual error variance; f. Partitioning the total sum of squares; g. Multiple correlation 327 $ah. Example (continued)5. Distributional properties; a. y is normal; b. b is normal; c. b and ?2 are independent; d. SSE/?2 has a ?2-distribution; e. Non-central ?2's; f. F-distributions; g. Analyses of variance; h. Pure error; i. Tests of hypotheses; j . Example (continued); k. Confidence intervals; l. Example (continued); 6. The general linear hypothesis; a. Testing linear hypotheses; b. Estimation under the null hypothesis; c. Four common hypotheses; (i) H: b = 0; (ii) H: b = b0; (iii) H: ?'b = m; (iv) H: bq = 0; d. Reduced models; (i) K'b = m; (ii) K'b = 0; (iii) bq = 0; 7. Related topics 327 $aa. The likelihood ratio testb. Type I and II errors; c. The power of a test; d. Examining residuals; 8. Summary of regression calculations; 9. Exercises; 4. Introducing Linear Models: Regression on Dummy Variables; 1. Regression on allocated codes; a. Allocated codes; b. Difficulties and criticism; c. Grouped variables; d. Unbalanced data; 2. Regression on dummy (0, 1) variables; a. Factors and levels; b. The regression; 3. Describing linear models; a. A 1-way classification; b. A 2-way classification; c. A 3-way classification; d. Main effects and interactions; (i) Main effects 327 $a(ii) Interactions 330 $aThis 1971 classic on linear models is once again available--as a Wiley Classics Library Edition. It features material that can be understood by any statistician who understands matrix algebra and basic statistical methods. 410 0$aWiley Series in Probability and Statistics - Applied Probability and Statistics Section 606 $aLinear models (Statistics) 606 $aStatistics 615 0$aLinear models (Statistics) 615 0$aStatistics. 676 $a519.5 676 $a519.538 700 $aSearle$b S. R$g(Shayle R.),$f1928-$0105121 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910830908403321 996 $aLinear models$9197209 997 $aUNINA