Investigating Basic Logics and Their Possible Interrelation

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Vaezian, Vahid | 2011

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 41449 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Ardeshir, Mohammad
Abstract:
In logic literature, the phrase “basic logic” can refer to three different logical systems. First, basic propositional logic (BPL) that was introduced by A. Visser in 1981. This logic is a subintuitionistic logic, that can be obtained from intuitionistic logic by a weakening of modus ponens. One decade later, Wim Ruitenberg regarding philosophical critiques of logical connectives, reintroduced BPL and its first order extension, BQC. From then, different aspects of basic logic have been investigated by logicians all over the world. Another logical system with the name “basic logic” is the system that was introduced by G. Sambin and G. Battilotti in 1997. The goal of this system is to provide a common foundation for all usual logics, so they can be obtained as extensions. The third logical system is in the field of fuzzy logic and does not seem to have any relationship with the other two logics. In this thesis we want to introduce Sambin’s basic logic that is not well-known in iran, and then after giving a short summary of visser’s basic logic, investigate their relationship.
Keywords:
Basic Logic ; Sambin Basic Logic ; Visser's Basic Logic ; Relationship Between Basic Logics ; Subintuitionistic Logics ; Substructural Logics

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