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Abstract:
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The thesis consists of five chapters. In the introductory chapter some relational-operational structures building of sets of formulas in calculi RA^+ and R^+ are presented. These structures are used in other chapters in making of the canonical frames of Kripke’ type for semantic of positive fragments of relevant propositional calculi. In Chapter 1, the semantic of these positive fragments, which is a mixture of known Routley & Meyer’s and Maksimova’s semantics, is presented. A new way for the semantic of negation in relevant logics is introduced in Chapter 2. It this way semantic completeness theorems for a large class of expansions of the logic R_min are proved. It is shown that Routley & Meyer’s semantic for the logic R is a special case of that semantic. Relevant modal logics are studied in Chapter 3. A semantic of Kripke’s type by which a completeness of a large class of modal logics whose basics are different relevant calculi with or without negation is introduced. A characterization of a large class modal i.e. Hintikka, schemas is given too. They contain almost all modal schemas characterized by formulas of the first order. Moreover, it is proved that the only known semantic for the calculus R_⊙ is a special case of the semantic given in this chapter. Semantics of relevant calculi which are not distributive are studied in Chapter 4. It is shown that semantics of non-distributive relevant logics radically change Kripke’s semantic. |