Generalized Galois logics: relational semantics of nonclassical logical calculi
Nonclassical logics have played an increasing role in recent years in disciplines ranging from mathematics and computer science to linguistics and philosophy. Generalized Galois Logics develops a uniform framework of relational semantics to mediate between logical calculi and their semantics through algebra. This volume addresses normal modal logics such as K and S5, and substructural logics, including relevance logics, linear logic, and Lambek calculi. The authors also treat less-familiar and new logical systems with equal deftness.
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distributive lattices with families of operations
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accessibility relation argument place axiom binary Boolean algebra bounded lattice calculus canonical frame canonical model canonical structure canonical valuation carrier set classical logic clopen cocones combinatory complete family conjunction consecution constants contains defined definition denoted disjunction distributive lattice dual duality elements equations equivalence classes example family of operations finite first-order formulas frame conditions function fusion Galois connections hence holds homomorphism ideals implies intensional isomorphism join-irreducible filters Let us assume Lindenbaum algebra maps maximal meet semi-lattice negation ngGl nondistributive nonempty normal modal logics notation notion ordered set partial distribution type partial order pgGl poset pre-order Priestley space prime filters properties propositions provable prove reader as problem relevance logics representation residuation satisfies semantics semi-lattice sequent calculus simplified soundness and completeness stable sets Stone spaces structural rules subsets theories tion tonicity type topology true ultrafilters unary