Introduction .................................................... 7
1 Preliminaries ................................................ 17
1.1 Propositional Languages and Substitutions ................ 17
1.2 Logical systems, Leibniz congruences, Lindenbaum-Tarski
algebras, varieties ...................................... 18
1.3 Some important varieties ................................. 25
1.4 Splittings of the lattice of logics ...................... 31
2 Unification and Unification Types ............................ 33
2.1 Syntactic unification of first order terms ............... 33
2.2 E-unification. Unification types ......................... 36
2.3 Unification and unification types in logic ............... 39
2.4 Finitely presented algebras and congruence formulas ...... 42
2.5 Projective algebras ...................................... 46
2.6 An algebraic approach to unification ..................... 48
2.7 Transparent unifiers ..................................... 51
3 Non-Fregean Logics ........................................... 55
3.1 SCI and some SCI-theories ................................ 58
3.2 Basics of unification for SCI-theories ................... 63
3.3 Transparent unifiers for WH-theories and for
many-valued SCI-counterparts ............................. 68
3.4 Filtering unification for invariant WT-theories .......... 78
4 Fregean Logics: Intuitionistic and Intermediate Logics ....... 86
4.1 Semi-constructive logics ................................. 90
4.2 Finitely presented algebras. Filtering unification ....... 92
4.3 The Splitting of ExtINT .................................. 95
4.4 Projective formulas ...................................... 97
4.5 Projective approximations and admissible rules in
intuitionistic logic .................................... 102
4.6 The logic КС, Gödel logics and logics of finite
slices .................................................. 105
5 Normal Modal Logics ......................................... 110
5.1 Weakly Transitive Logics ................................ 115
5.2 Sclf-conjngate and rcsidnatcd operators Galois
connections ............................................. 118
5.3 Unifiable formulas in modal logics ...................... 121
5.4 Finitely presented algebras and unifiers ................ 122
5.5 Transparent unifiers .................................... 123
5.6 Filtering unification in ExtS4 .......................... 134
5.7 The splitting of ExtS4 .................................. 136
6 Multimodal, Tense and Epistemic logics ...................... 140
6.1 Products of modal logics ................................ 147
6.2 Weakly Transitive Multimodal Logics ..................... 149
6.3 Conjugate and residuated operators Galois connections ... 153
6.4 Finitely presented algebras and unifiers ................ 155
6.5 Transparent unifiers .................................... 157
6.6 Applications: Tense, Epistemic, DALLA and other
logics .................................................. 159
6.7 Filtering unification in weakly transitive and
n-confluent logics ...................................... 170
7 Summary and Conclusions ..................................... 175
Bibliography .................................................. 180
Index ......................................................... 187
Index of symbols .............................................. 189
Streszczenie .................................................. 191
Zusammenfassung ............................................... 192
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