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Mathematical logic, also called 'logistic', 'symbolic logic', the 'algebra of logic', and, more recently, simply 'formal logic', is the set of logical theories elaborated in the course of the nineteenth century with the aid of an artificial notation and a rigorously deductive method. [5]
Formal logic (also known as symbolic logic) is widely used in mathematical logic. It uses a formal approach to study reasoning: it replaces concrete expressions with abstract symbols to examine the logical form of arguments independent of their concrete content. In this sense, it is topic-neutral since it is only concerned with the abstract ...
At the time, the methods employed to design logic circuits (for example, contemporary Konrad Zuse's Z1) were ad hoc in nature and lacked the theoretical discipline that Shannon's paper supplied to later projects. Shannon's work also differered significantly in its approach and theoretical framework compared to the work of Akira Nakashima.
As contrasted with algebraic logic (Boolean logic) that employs arithmetic concepts, symbolic logic begins with a very reduced set of marks (non-arithmetic symbols), a few "logical" axioms that embody the "laws of thought", and rules of inference that dictate how the marks are to be assembled and manipulated – for instance substitution and ...
If one replaces '=' in R1 and R2 with the biconditional, the resulting rules hold in conventional logic. However, conventional logic relies mainly on the rule modus ponens; thus conventional logic is ponential. The equational-ponential dichotomy distills much of what distinguishes mathematical logic from the rest of mathematics.
Langford is famous as co-author of the 1932 book Symbolic Logic and the system of modal logic S5. [3] His doctoral students include Arthur Burks. In the philosophy of language, Langford is known for the Langford substitution test. The test distinguishes used from merely mentioned expressions in a given sentence by translating the sentence into ...
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics .
1952: Symbolic Logic, An Introduction, The Ronald Press Company [6] 1963: "A Logical Analysis of Some Value Concepts", doi:10.2307/2271594 (This paper has over 400 citations.) 1974: Elements of Combinatory Logic, Yale University Press [7] 1975: (with Alan Ross Anderson, Ruth Barcan Marcus, and Richard Milton Martin): The Logical Enterprise.