Názov:On Disjunction in Modal Logics
Vedúci:RNDr. Damas Gruska, PhD.
Kµúčové slová:modal logic, non-normal, disjunction, distribution, neighbourhood, non-emergence
Abstrakt:[Peter Drábik. On Disjunction in Modal Logics. Master's thesis. FMFI UK, 2007. 56pp] This master's thesis consists of two parts. First part is a survey of basic concepts in modal logics. Syntax and semantics for normal and non-normal modal logics are presented. Then soundness and completeness theory and correspondence theory of normal modal logic are presented. The second part is devoted to investigation of distribution of the modal operator over disjunction, i.e. exploring the properties of formula box(phi or psi) -> (box phi or box psi) in both normal and non-normal modal logics. A class of frames that is defined by this formula (the class of deterministic frames) is characterized. Soundness and strong completeness of the smallest normal modal logic containing this formula with respect to the class of deterministic frames is established. A class of neighbourhood frames defined by this formulas is characterized by the property of non-emergence. Testing of non-emergence of neighbouhoods is investigated.

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