20.500.12556/RUL-180895 Topološki vidiki modalnih logik magistrsko delo On the topological aspects of modal logics Relacijska semantika predstavlja že ustaljeni pristop k študiju modalnih logik. Po opredelitvi temeljnih sintaktičnih in semantičnih pojmov si ogledamo nekaj osnovnih korespondenc med lastnostmi relacij in modalnih aksiomov, ki jim ustrezajo. Vpeljemo normalne modalne logike in dokažemo zdravost in polnost za osnovni normalni modalni sistem $\textbf{K}$. Nato pozornost preusmerimo na topološko semantiko modalnega sistema $\textbf{S4}$ in jo s konstrukcijo, ki temelji na snopih, razširimo z logiko prvega reda. Ogledamo si primer sheme, ki jo konkreten primer modela ovrže. Poleg osnovnega modalnega jezika obravnavamo, kjer smiselno, še primere v osnovnem temporalnem jeziku. Relational semantics represents an established approach to the study of modal logics. After defining the fundamental syntactic and semantic notions, we examine some basic correspondences between properties of relations and the modal axioms to which they correspond. We introduce normal modal logics and prove soundness and completeness for the basic normal modal system $\textbf{K}$. We then turn our attention to the topological semantics of the modal system $\textbf{S4}$ and, using a construction based on sheaves, extend it to first-order logic. We also consider an example of a schema refuted by a concrete model. In addition to the basic modal language, we address, where appropriate, examples in the basic temporal language. In addition to the basic modal language, we address, where appropriate, examples in the basic temporal language. modalna logika relacijska semantika topološka semantika logika prvega reda snop temporalna logika modal logic relational semantics topological semantics first-order logic sheaf temporal logic true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2026-03-19 08:15:07 2026-03-19 08:15:12 2026-03-22 03:59:08 0000-00-00 00:00:00 2026 0 0 0000-00-00 NiDoloceno Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 510.6 159528 271817475 21356.pdf 21356.pdf 1 C7E72E2A15B09EF0689249CA1088C179 3045e6c540d0860c3add973b4d6788419468dc989c5599ac57d06ebb2900e5dc 4a0def1b-2363-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=230841 Fakulteta za matematiko in fiziko 0 0 0