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A key element of the proof is the use of Gödel numbering to construct a "Gödel sentence" for the theory, which encodes a statement of its own incompleteness: "This theory can't prove this statement"; or "I am not provable in this system". Either this statement and its negation are both unprovable (the theory is incomplete) or both provable ...
Logic plays a fundamental role in computer science. Some of the key areas of logic that are particularly significant are computability theory (formerly called recursion theory), modal logic and category theory. The theory of computation is based on concepts defined by logicians and mathematicians such as Alonzo Church and Alan Turing.
Another generalization of the conventional flip-flop is a memory element for multi-valued logic. In this case the memory element retains exactly one of the logic states until the control inputs induce a change. [33] In addition, a multiple-valued clock can also be used, leading to new possible clock transitions. [34]
A key distinction is between deductive and non-deductive arguments. Logical reasoning is a mental activity that aims to arrive at a conclusion in a rigorous way. It happens in the form of inferences or arguments by starting from a set of premises and reasoning to a conclusion supported by these premises.
The history of computational thinking as a concept dates back at least to the 1950s but most ideas are much older. [6] [3] Computational thinking involves ideas like abstraction, data representation, and logically organizing data, which are also prevalent in other kinds of thinking, such as scientific thinking, engineering thinking, systems thinking, design thinking, model-based thinking, and ...
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Karnaugh maps are used to simplify real-world logic requirements so that they can be implemented using the minimal number of logic gates. A sum-of-products expression (SOP) can always be implemented using AND gates feeding into an OR gate , and a product-of-sums expression (POS) leads to OR gates feeding an AND gate.
Example of an early argument map, from Richard Whately's Elements of Logic (1852 edition). Argumentation theory is the interdisciplinary study of how conclusions can be supported or undermined by premises through logical reasoning.