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1 | (9) |
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10 | (45) |
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10 | (1) |
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Relational and Operational Structures (Algebras) |
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10 | (1) |
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Subrelational Structures and Subalgebras |
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11 | (2) |
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Intersection, Generators, and Induction from Generators |
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13 | (2) |
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Homomorphisms and Isomorphisms |
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15 | (4) |
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Congruence Relations and Quotient Algebras |
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19 | (6) |
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25 | (3) |
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Subdirect products and the Fundamental Theorem of Universal Algebra |
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28 | (5) |
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Word Algebras and Interpretations |
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33 | (3) |
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Varieties and Equational Definability |
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36 | (1) |
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37 | (2) |
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Examples of Free Algebras |
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39 | (2) |
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41 | (3) |
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The Existence of Free Algebras; Freedom in Varieties and Subdirect classes |
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44 | (3) |
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Birkhoff's Varieties Theorem |
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47 | (2) |
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49 | (2) |
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Logic and Algebra: Algebraic Statements of Soundness and Completeness |
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51 | (4) |
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Order, Lattices, and Boolean Algebras |
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55 | (70) |
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55 | (1) |
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55 | (3) |
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58 | (2) |
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Covering and Hasse Diagrams |
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60 | (3) |
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63 | (4) |
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67 | (3) |
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The Lattice of Congruences |
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70 | (1) |
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71 | (3) |
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74 | (3) |
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77 | (5) |
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82 | (3) |
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Classical Complementation |
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85 | (3) |
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Non-Classical Complementation |
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88 | (4) |
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92 | (6) |
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Non-Classical Distribution |
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98 | (7) |
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105 | (4) |
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Non-Classical Implication |
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109 | (6) |
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115 | (10) |
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125 | (16) |
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125 | (1) |
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125 | (5) |
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130 | (3) |
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Languages as Abstract Structures: Categorial Grammar |
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133 | (3) |
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Substitution Viewed Algebraically (Endomorphisms) |
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136 | (1) |
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137 | (1) |
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Enumerating Strings and Sentences |
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138 | (3) |
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141 | (43) |
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141 | (1) |
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142 | (2) |
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Algebraic Semantics for Sentential Languages |
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144 | (2) |
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146 | (2) |
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Possible Worlds Semantics |
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148 | (4) |
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Logical Matrices and Logical Atlases |
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152 | (3) |
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Interpretations and Valuations |
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155 | (3) |
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Interpreted and Evaluationally Constrained Languages |
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158 | (4) |
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Substitutions, Interpretations, and Valuations |
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162 | (4) |
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166 | (3) |
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169 | (3) |
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172 | (4) |
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176 | (5) |
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181 | (3) |
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184 | (42) |
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184 | (1) |
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The Varieties of Logical Experience |
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185 | (2) |
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187 | (2) |
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189 | (2) |
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Binary Consequence in the Context of Pre-ordered Sets |
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191 | (3) |
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Asymmetric Consequence and Valuations (Completeness) |
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194 | (2) |
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Asymmetric Consequence in the Context of Pre-ordered Groupoids |
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196 | (3) |
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Symmetric Consequence and Valuations (Completeness and Absoluteness) |
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199 | (3) |
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Symmetric Consequence in the Context of Hemi-distributoids |
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202 | (6) |
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Structural (Formal) Consequence |
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208 | (1) |
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Lindenbaum Matrices and Compositional Semantics for Assertional Formal Logics |
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209 | (2) |
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Lindenbaum Atlas and Compositional Semantics for Formal Asymmetric Consequence Logics |
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211 | (2) |
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Scott Atlas and Compositional Semantics for Formal Symmetric Consequence Logics |
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213 | (1) |
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Co-consequence as a Congruence |
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214 | (2) |
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Formal Presentations of Logics (Axiomatizations) |
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216 | (8) |
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224 | (2) |
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226 | (51) |
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226 | (11) |
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226 | (1) |
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Lukasiewicz matrices/submatrices, isomorphisms |
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227 | (3) |
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Godel matrices/more submatrices |
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230 | (1) |
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Sugihara matrices/homomorphisms |
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230 | (2) |
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232 | (1) |
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232 | (1) |
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233 | (1) |
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234 | (3) |
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Relations Among Matrices: Submatrices, Homomorphic Images, and Direct Products |
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237 | (2) |
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Proto-preservation Theorems |
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239 | (4) |
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243 | (3) |
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Varieties Theorem Analogs for Matrices |
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246 | (3) |
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246 | (1) |
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Asymmetric consequence logics |
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247 | (2) |
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Symmetric consequence logics |
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249 | (1) |
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Congruences and Quotient Matrices |
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249 | (5) |
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The Structure of Congruences |
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254 | (3) |
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The Cancellation Property |
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257 | (5) |
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262 | (4) |
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266 | (4) |
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Normal Characteristic Matrices for Consequence Logics |
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270 | (1) |
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271 | (2) |
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When is a Logic ``Algebraizable''? |
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273 | (4) |
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277 | (44) |
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Partially Ordered Sets with Implication(s) |
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277 | (10) |
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277 | (1) |
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278 | (9) |
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287 | (1) |
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288 | (5) |
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Finite Distributive Lattices |
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293 | (2) |
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The Problem of a General Representation for Distributive Lattices |
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295 | (2) |
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Stone's Representation Theorem for Distributive Lattices |
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297 | (3) |
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300 | (2) |
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Filters and Homomorphisms |
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302 | (1) |
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Maximal Filters and Prime Filters |
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302 | (1) |
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Stone's Representation Theorem for Boolean Algebras |
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303 | (2) |
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Maximal Filters and Two-Valued Homomorphisms |
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305 | (8) |
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Distributive Lattices with Operators |
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313 | (4) |
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317 | (4) |
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Classical Propositional Logic |
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321 | (35) |
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321 | (1) |
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The Equivalence of (Unital) Boolean Logic and Frege Logic |
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322 | (2) |
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324 | (2) |
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Compactness Theorems for Classical Propositional Logic |
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326 | (7) |
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333 | (1) |
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Axiomatic Calculi for Classical Propositional Logic |
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334 | (1) |
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Primitive Vocabulary and Definitional Completeness |
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335 | (2) |
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337 | (4) |
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341 | (5) |
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Asymmetrical Sequent Calculus for Classical Propositional Logic |
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346 | (2) |
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Fragments of Classical Propositional Logic |
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348 | (1) |
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The Implicative Fragment of Classical Propositional Logic: Semi-Boolean Algebras |
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349 | (1) |
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Axiomatizing the Implicative Fragment of Classical Propositional Logic |
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350 | (2) |
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The Positive Fragment of Classical Propositional Logic |
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352 | (4) |
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Modal Logic and Closure Algebras |
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356 | (24) |
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356 | (2) |
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Boolean Algebras with a Normal Unitary Operator |
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358 | (3) |
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Free Boolean Algebras with a Normal Unitary Operator and Modal Logic |
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361 | (1) |
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The Kripke Semantics for Modal Logic |
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361 | (2) |
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363 | (1) |
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Topological Representation of Closure Algebras |
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364 | (3) |
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The Absolute Semantics for S5 |
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367 | (1) |
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367 | (2) |
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Alternation Property for S4 and Compactness |
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369 | (1) |
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Algebraic Decision Procedures for Modal Logic |
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370 | (5) |
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375 | (5) |
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Intuitionistic Logic and Heyting Algebras |
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380 | (14) |
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380 | (1) |
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381 | (2) |
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383 | (1) |
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Representation of Heyting Algebras using Quasi-ordered Sets |
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383 | (1) |
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Topological Representation of Heyting Algebras |
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384 | (2) |
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Embedding Heyting Algebras into Closure Algebras |
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386 | (1) |
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386 | (1) |
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Alternation Property for H |
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387 | (1) |
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Algebraic Decision Procedures for Intuitionistic Logic |
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388 | (2) |
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390 | (4) |
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Gaggles: General Galois Logics |
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394 | (37) |
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394 | (1) |
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Residuation and Galois Connections |
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395 | (3) |
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Definitions of Distributoid and Tonoid |
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398 | (2) |
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Representation of Distributoids |
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400 | (6) |
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Partially Ordered Residuated Groupoids |
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406 | (2) |
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408 | (1) |
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Representation of Gaggles |
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409 | (3) |
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Modifications for Distributoids and Gaggles with Identities and Constants |
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412 | (2) |
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414 | (1) |
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415 | (2) |
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417 | (3) |
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420 | (1) |
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Representation of Positive Binary Gaggles |
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421 | (1) |
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422 | (3) |
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Implication in relevance logic |
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423 | (1) |
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Implication in intuitionistic logic |
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424 | (1) |
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424 | (1) |
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425 | (5) |
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The gaggle treatment of negation |
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425 | (1) |
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Negation in intuitionistic logic |
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426 | (1) |
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Negation in relevance logic |
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427 | (2) |
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Negation in classical logic |
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429 | (1) |
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430 | (1) |
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Representations and Duality |
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431 | (14) |
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Representations and Duality |
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431 | (2) |
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433 | (2) |
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Duality for Boolean Algebras |
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435 | (3) |
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Duality for Distributive Lattices |
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438 | (3) |
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Extensions of Stone's and Priestley's Results |
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441 | (4) |
References |
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445 | (10) |
Index |
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455 | |