☝️ Fatemeh Shirmohammadzadeh Maleki, one of the 12 laureates of the CIMPA-ICTP Research in Pairs programme, is a professor at Iranian Research Institute of Philosophy, Iran.
This course was filmed at CIMPA (Nice, France).
"Subintuitionistic Logics" (1/4)
Abstract: In this course, we will give an introduction to subintuitionistic logics. This course will be prepared for 4 sessions, each for about 2 hours. We start by giving a brief introduction to intuitionistic logic and reviewing the preliminary notions. By considering Kripke semantics and Neighborhood semantics for modal logics, we will introduce Kripke Semantics and Neighborhood Semantics for intuitionistic logic (IPC). First, we consider subintuitionistic logics with Kripke models. The basic system, which is called F, is characterized by the class of Kripke models in which no assumption of truth preservation is made. An extension of F, which is called BPC, is complete for the class of transitive, irreflexive Kripke models with truth preservation. Then, we introduce weaker subintuitionistic logics interpreted over two types of neighborhood models. In the NB-neighborhood frames the neighborhoods are pairs (X, Y ) of sets of worlds. In N-neighborhood frames the neighborhoods are sets of worlds. The NB-neighbourhood semantics is best suited to study the basic logic WF, the N neighbourhood semantics is more suitable for obtaining modal companions with respect to the G¨odel type translation discovered for subintuitionistic logics with Kripke models. We clarify the exact relationship between the two types of frames. Thereby modal companions for various logics will be recognized. Specifically, we will introduce a logic which has basic monotonic logic with necessitation as its modal companion. Many of the extensions of the basic logics will be discussed and characterized. The NB-neighborhood semantics will be used to create a diary modal companion 1 for the basic logic WF for which the usual type of modal companion does not exist. The remaining time will be devoted to conservativity results for IPC with regard to classes of implications in some of these subintuitionistic logics with Kripke and Neighborhood semantics.
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