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Title: Modele otoczeniowe i topologiczne dla klasycznych i intuicjonistycznych logik modalnych
Authors: Witczak, Tomasz
Advisor: Połacik, Tomasz
Keywords: logika modalna; przestrzenie topologiczne; semantyki światów możliwych
Issue Date: 2020
Publisher: Katowice : Uniwersytet Śląski
Abstract: We may speak about syntax. From this point of view any logic can be considered as as the set of axioms and rules. Here we are interested in formal proofs and deduction systems. Second, we can also think about semantics, namely, about some models in which it is possible to de ne the notions of truth and falsity. As for the logical calculi, we are working with propositional logics. Thus, we are not so much interested in quanti ers. Our logics are non-classical. Of course, there are many kinds of non-classical logic and many reasons for which certain system can be considered as nonclassical. In our case, there are two main ways which are notoriously combined. On the one hand, we are interested in intuitionistic, superintuitionistic and subintuitionistic systems. This means that we narrow down the set of axioms and rules of classical logic. On the other hand, we use modal operators to de ne and analyse the ideas of necessity and possibility. As a result, we often obtain classical and intuitionistic modal logics. Our semantic models are mostly neighborhood, topological and relational. These three approaches are also combined. For this reason, we may speak about bi-relational and relational-neighborhood structures. Moreover, we go beyond the standard notion of topology in order to study its various generalizations. Finally, our aim is to investigate several non-classical calculi using all the tools mentioned above. We are interested in the issues of completeness (axiomatization), nite model property, bisimulation and decidability. Moreover, we analyse some purely topological properties of the structures in question. The philosophical aspect is also important.
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