Title......Page 1 Contents......Page 3 Preface......Page 7 1. Propositional languages......Page 9 2. Logical calculi......Page 10 3. Closure bases......Page 14 4. Consequence operations from a complete lattice......Page 15 5. A bit more about the lattice of structural consequence......Page 16 6. Structural completeness......Page 23 7. Rules of inference and inferential bases......Page 24 8. More on structural completeness......Page 26 9. Some examples......Page 28 10. More on inferential bases. Proofs......Page 33 11. Basic definitions and theorems......Page 37 12. Deductive systems and well-determined logics......Page 39 13. Are Łukasiewicz logics well-determined?......Page 40 14. Well determined modal logics......Page 42 15. Surprisingly enough, relevant logics are not well-determined......Page 44 16. Theories vs truth-valuations......Page 45 17. Epistemic valuations for L......Page 47 18. Epistemic valuation for L~......Page 48 19. Neighborhood valuations......Page 50 20. Relational valuations......Page 51 21. Completeness lemma......Page 53 22. Consequence with Lindenbaum property......Page 54 23. Inferential bases for K, H, Jmin, J, and some useful theorems......Page 57 24. An inferential base for N and some adequacy theorems. The method of canonical frames......Page 60 25. Canonical frames for modal logics......Page 64 26. Are all classical modal systems natural? System K4.3W......Page 66 27. The problem of completeness......Page 68 28. Some preparatory results......Page 71 29. Conditions for a consequence to be finitary......Page 73 30. All Łn, n є ω are standard: an example of application of theorem 29.1.......Page 75 31. Matrices and matrix semantics......Page 77 32. First two completeness theorems......Page 79 33. Simple matrices and two more completeness theorems......Page 80 34. Łoś-Suszco's theorem......Page 81 35. A few comments on Łoś-Suszco's theorem......Page 84 36. Ramified matrices and ramified logics......Page 86 37. Implicative logics......Page 89 38. More on algebraic semantics......Page 91 39. Properly l-algebraic logics......Page 93 40. A bit of philosophy......Page 95 41. Some operations on matrices......Page 99 42. Reduced products of matrices......Page 101 43. Czelakowski's theorems......Page 102 44. The proof of Czelakowski's theorems......Page 103 45. Some more conditions for a logic to be standard......Page 107 46. Some corollaries to theorem 43.1......Page 108 47. Matr*(C) for equivalential logics......Page 110 48. Subdirectly irreducible matrices......Page 113 52. K--standard referential matrices......Page 117 53. Referential matrices vs neighborhood frames......Page 119 54. Referential matrices vrs relational frames......Page 121 55. Comparing the relative strength of different semantics......Page 122 49. Referential algebras......Page 125 50. Selfextensional logics......Page 128 51. An useful lemma......Page 130 56. A syntactical test for strong finiteness......Page 133 57. The lattices of strengthenings of a strongly finite consequences......Page 135 58. Hereditary properties......Page 137 59. Degree of maximality......Page 141 60. Some applications of Theorem 59.3......Page 143 61. Two algebraic lattices......Page 145 62. Finitely axiomatizable theories and finitely based logics......Page 146 63. Axiomatizable theories and parafinitely based logics......Page 147 64. A generalized version of Herrop's theorem and some problems concerning decidability......Page 148 65. Finite approximability and finite model property......Page 151 66. Definitional extensions......Page 153 67. Definability......Page 156 68. Definitional variants......Page 157 Bibliography......Page 161 A-C......Page 173 D-E-F......Page 174 H-I-K-L......Page 175 M......Page 176 N-P-Q-R......Page 177 S......Page 178 T-U-V......Page 179
