Logics

Front Cover......Page scandjvutmpdd7_0001.djvu
Back Cover......Page scandjvutmpdd8_0001.djvu
Title......Page scandjvutmpddd_0001.djvu
Copyright......Page scandjvutmpdde_0001.djvu
Dedication......Page scandjvutmpddf_0001.djvu
Contents......Page scandjvutmpde0_0001.djvu
Preface......Page scandjvutmpde4_0001.djvu
Part I: Informal Logic......Page scandjvutmp94.djvu
1 – Informal Logic......Page scandjvutmpde7_0001.djvu
1.1  What is Logic......Page 17
1.2  Validity and Counterexamples......Page scandjvutmp5c_0001.djvu
1.3  Relevance......Page scandjvutmpdf1_0001.djvu
1.4  Argument Indicators......Page scandjvutmp6c_0001.djvu
1.5  Use and Mention......Page scandjvutmpdfd_0001.djvu
Part II: Classical Proposaitional Logic......Page scandjvutmp96.djvu
2 – Classical Propositional Logic: Syntax......Page scandjvutmp5f_0001.djvu
2.1  Argument Forms......Page 39
2.2  Formalization......Page scandjvutmp66_0001.djvu
2.3  Formation Rules......Page scandjvutmpe0e_0001.djvu
3 – Classical Propositional Logic: Semantics......Page scandjvutmp6a_0001.djvu
3.1  Truth Conditions......Page 53
3.2  Truth Tables......Page scandjvutmpe23_0001.djvu
3.3  Semantic Trees......Page scandjvutmp75_0001.djvu
3.4  Valuations and Possible Situations......Page scandjvutmpe3c_0001.djvu
4 – Classical Propositional Logic: Inference......Page scandjvutmpe43_0001.djvu
4.1  Chains of Inference......Page 93
4.2  Simple Formal Inference Rules......Page scandjvutmpe46_0001.djvu
4.3  Hypothetical Derivations......Page scandjvutmp79_0001.djvu
4.4  Theorems and Shortcuts......Page scandjvutmpe5a_0001.djvu
4.5  Alternative Proof Techniques and the Limitations of Proofs......Page scandjvutmpe60_0001.djvu
5 – Classical Propositional Logic: Metatheory......Page scandjvutmpe65_0001.djvu
5.1  Introduction to Metalogic......Page 127
5.2  Conditional Proof......Page scandjvutmpe6a_0001.djvu
5.3  Reduction ad Absurdum......Page scandjvutmp8b.djvu
5.4  Mixed Strategies......Page scandjvutmp8c.djvu
5.5  Mathematical Induction......Page scandjvutmpa0_0001.djvu
5.6  Algorithms......Page scandjvutmpa5_0001.djvu
5.7  Decidability......Page scandjvutmpa9_0001.djvu
5.8  Soundness of the Tree Test......Page scandjvutmpae_0001.djvu
5.9  Completeness of the Tree Test......Page scandjvutmpb2_0001.djvu
5.10  Soundness and Completeness of  the Natural Deduction Rules......Page scandjvutmpb5_0001.djvu
Part III: Classical Predicate Logic......Page scandjvutmpc3_0001.djvu
6 – Classical Predicate Logic: Syntax......Page scandjvutmpc5_0001.djvu
6.1  Quantifiers, Predicates, and Names......Page 175
6.2  Syntax for Predicate Logic......Page scandjvutmpcf_0001.djvu
6.3  Identity......Page scandjvutmpd2_0001.djvu
6.4  Functions......Page scandjvutmpd8_0001.djvu
7 – Classical Predicate Logic: Semantics......Page scandjvutmpdd_0001.djvu
7.1  Sets and n-Tuples......Page 199
7.2  Semantics for Predicate Logic......Page scandjvutmpe0_0001.djvu
7.3  Using the Semantics......Page scandjvutmpef_0001.djvu
7.4  Trees for Predicate Logic......Page scandjvutmpf5_0001.djvu
8 – Classical Predicate Logic: Inference......Page scandjvutmp105_0001.djvu
8.1  Existential Introduction......Page 238
8.2  Existential Elimination......Page scandjvutmp108_0001.djvu
8.3  Universal Elimination......Page scandjvutmp10e_0001.djvu
8.4  Universal Introduction......Page scandjvutmp110_0001.djvu
8.5  Identity......Page scandjvutmp116_0001.djvu
8.6  Functions......Page scandjvutmp118_0001.djvu
9 – Classical Predicate Logic: Soundness, Completeness, and Inexpressibility......Page scandjvutmp11a_0001.djvu
9.1  Soundness of the Tree Test......Page 259
9.2  Completeness of the Tree Test......Page scandjvutmp124_0001.djvu
9.3  Soundness and Completeness of the Rules of Inference......Page scandjvutmp128_0001.djvu
9.4  Inexpressibility......Page scandjvutmp12a_0001.djvu
10 – Classical Predicate Logic: Undecibility......Page scandjvutmp131_0001.djvu
10.1  Abaci......Page 282
10.2  Logical Programming Notation......Page scandjvutmp135_0001.djvu
10.3  The Abacus Program......Page scandjvutmp138_0001.djvu
10.4  Church’s Thesis......Page scandjvutmp140_0001.djvu
10.5  The Halting Problem......Page scandjvutmp145_0001.djvu
10.6  The Undecidability of Predicate Logic......Page scandjvutmp14d_0001.djvu
10.7  How Far Does the Undecidability Extend?......Page scandjvutmp153_0001.djvu
Part IV: Extensions of Classical Logic......Page scandjvutmp156_0001.djvu
11 – Leibnizian Modal Logic......Page scandjvutmp158_0001.djvu
11.1  Modal Operators......Page 321
11.2  Leibnizian Semantics......Page scandjvutmp15b_0001.djvu
11.3  A Natural Model?......Page scandjvutmp4_0001.djvu
11.4  Inference in Leibnizian Logic......Page scandjvutmp7_0001.djvu
12 – Kripkean Modal Logic......Page scandjvutmpd_0001.djvu
12.1  Kripkean Semantics......Page 348
12.2  Inference in Kripkean Logics......Page scandjvutmp17_0001.djvu
12.3  Strict Conditionals......Page scandjvutmp19_0001.djvu
12.4  Lewis Conditionals......Page scandjvutmp1e_0001.djvu
13 – Deontic and Tense Logics......Page scandjvutmp24_0001.djvu
13.1  A Modal Deontic Logic......Page 371
13.2  A Modal Tense Logic......Page scandjvutmp2e_0001.djvu
14 – Higher-Order Logics......Page scandjvutmp3f_0001.djvu
14.1  Higher-Order Logics: Syntax......Page 396
14.2  Second-Order Logic: Semantics......Page scandjvutmp44_0001.djvu
Part V: Nonclassical Logics......Page scandjvutmp4b_0001.djvu
15 – Mildly Nonclassical Logics......Page scandjvutmp4c_0001.djvu
15.1  Free Logics......Page 411
15.2  Multivalued Logics......Page scandjvutmp55_0001.djvu
15.3  Supervaluations......Page scandjvutmp5d_0001_1.djvu
16 – Radically Nonclassical Logics......Page scandjvutmp63_0001.djvu
16.1  Infinite Valued and Fuzzy Logics......Page 434
16.2  Intuitionistic Logics......Page scandjvutmp6a_0001_1.djvu
16.3  Relevance Logics......Page scandjvutmp76_0001_1.djvu
16.4  A Nonmonotonic Logic: Prolog......Page scandjvutmp7e_0001_1.djvu
16.5  Conclusion: Logical Pluralism......Page scandjvutmp8c_0001.djvu
Index......Page scandjvutmp8e_0001.djvu
A-B-C......Page 477
D-E-F......Page scandjvutmp8f_0001.djvu
G-H-I-K-L......Page scandjvutmp90_0001.djvu
M-N-O-P......Page scandjvutmp91_0001.djvu
Q-R-S......Page scandjvutmp92_0001.djvu
T-U-V-W-Y-Z......Page scandjvutmp93_0001.djvu