ON THE MATHEMATICAL FOUNDATIONS OF SYLLOGISTIC ARGUMENT
Project no. 657 · Status: Kapanmış · 2015
Summary
In this thesis, we firstly mentioned examples of the requirements and areas in which the syllogism concept is based, and information on the results of the researchers were given and we emphasized on the contents of the chapters that comprise the thesis. The necessary basic concepts are given in order to facilate the intelligibility of the thesis. In the sequel, a model is constructed that can be defined by the categorical syllogism in Carroll diagrams, which can deduce results from premises and correspond premises and conclusion to a set. This model is determined to be valid for conditional or unconditional syllogisms. The family of these sets are based on different algebraic structures. In addition to these, a reduction consisting of only Sheffer stroke is defined for basic algebra and the Sheffer stroke basic algebras are created and their properties are examined. Categorical syllogisms are associated with this this structure and a Sheffer stroke basic algebra is defined on the family of sets that corresponds to the propositions forming the categorical syllogisms. In line with these developments , a new algorithm is created based on the model which acquire the current syllogisms. The pseudo-code of this algorithm is given and is transferred together with images to see how the program runs. Finally, it was summarized all studies done during the thesis, it was briefly mentioned the conclusions which reach as a result of this study.