Proof Theory and Semantics of U Logic

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Barzin, Erfan | 2023

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 57062 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Arⅾeshir, Ⅿohaⅿⅿaⅾ
Abstract:
In this thesis, we want to discuss about some aspects of semantics and proof theory of U logic. This logic was introduced by Ardehsir and Vaezian in 2012. U Logic was introduced with intention of unifying Sambin Basic Logic(Sambin in 1997) and Visser Basic Logic(Visser in 1981). These two basic logics are two of the most significant basic logics that were introduced. This thesis begins with addressing U logic proof system. Subsequently, we introduce three algebraic semantics for this logic. The first one was introduced by Girard for Linear logic. The second one was introduced by Sambin for Sambin Basic Logic. Then we introduce the third one specially for U logic. In fact, we have proof system and language of U logic and we are searching for suitable semantics for this proof system
Keywords:
Basic Logic ; Semantics ; Phase Space File ; Proof Theory ; U Logic ; Relational Monoid