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National Repository of Grey Literature

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Knowledge changes in dynamic epistemic logic Dančák, Michal ; Peliš, Michal (advisor) ; Urbański, Mariusz (referee) The Logic of Hybrid Action Models is presented in this thesis along with a sound and complete Hilbert style calculus. It is an original multimodal epistemic logic that tries to give the agents (i) a strong method of communication and (ii) a rich vocabulary to communicate about by combining action models with hybrid logics. The language of the resulting logic is rather complex and includes common knowledge, deterministic action updates and all three commonly used hybrid op- erators @, ↓ and E. An overview of both action models and hybrid logics is included. The Hybrid Logic with Partial Denoting Nominals is briefly described and used as a stepping stone. The semantics and the Completeness Theorem of the Logic of Hybrid Action Models form the backbone of this work. 1 Detailed record

Tableaux in non-classical logics Dančák, Michal ; Peliš, Michal (referee) ; Bílková, Marta (advisor) Dalo by se ríct, že jako dukazová metoda jsou sémantické stromy v Cesku nepríliš používané, a to i presto, že ve svete je to nejoblíbenejší dukazový systém pro modální logiku [1]. Vedle základního Hilbertova kalkulu se v ceské literature nejcasteji objevují sekventové kalkuly, prípadne kalkul prirozené dedukce. Presto má metoda sémantických stromu nekolik nezanedbatelných predností a zajímavých témat. Jak už název napovídá, tento kalkul vychází ze sémantiky - dukazy mají predevším sémantický charakter a pro "jednodušší" logiky jsou i velmi intuitivní. Dokazování je zároven i vyvracení. Pri dokazování metodou sémantických stromu vlastne hledáme protipríklad. Jestliže ho nenajdeme, a pokud jsme postupovali správne, tak neexistuje. Na poradí použití pravidel také nezáleží (až na nekolik vyjímek v nekterých logikách, které si pozdeji ukážeme). I díky temto výhodám je tato metoda také velmi vhodná pro strojové zpracování. V této práci jsem se rozhodl zamerit na to, jak se metoda sémantických stromu chová v substrukturální logice BCK (nekdy též FLew). Zacneme základními definicemi a tím, co to vlastne sémantické stromy jsou, dále bude následovat nekolik príkladu, definice logiky BCK a príslušných odvozovacích pravidel. Celá práce bude završena dukazem úplnosti a korektnosti tohoto kalkulu vuci kripkovské... Detailed record

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1	Dančák, Martin

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