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Turnstile Symbol
In mathematical logic and computer science the symbol ⊢ (\vdash) has taken the name turnstile because of its resemblance to a typical turnstile. It is also referred to as tee and is often read as "yields", "proves", "satisfies" or "entails". Interpretations The turnstile represents a binary relation. It has several different interpretations in different contexts: * In epistemology, Per Martin-Löf (1996) analyzes the \vdash symbol thus: "... e combination of Frege's , judgement stroke and , content stroke €” came to be called the assertion sign." Frege's notation for a judgement of some content ::\vdash A :can then be read ::''I know is true''. :In the same vein, a conditional assertion ::P \vdash Q :can be read as: ::''From , I know that '' * In metalogic, the study of formal languages; the turnstile represents syntactic consequence (or "derivability"). This is to say, that it shows that one string can be derived from another in a single step, according to the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Mathematical Logic
Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics. Since its inception, mathematical logic has both contributed to and been motivated by the study of foundations of mathematics. This study began in the late 19th century with the development of axiomatic frameworks for geometry, arithmetic, and Mathematical analysis, analysis. In the early 20th century it was shaped by David Hilbert's Hilbert's program, program to prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |