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John Corcoran (/ ˈ k ɔːr k ər ən / KOR-kər-ən; March 20, 1937 – January 8, 2021) was an American logician, philosopher, mathematician, and historian of logic.He is best known for his philosophical work on concepts such as the nature of inference, relations between conditions, argument-deduction-proof distinctions, the relationship between logic and epistemology, and the place of proof ...
Tarski's World is a computer-based introduction to first-order logic written by Jon Barwise and John Etchemendy.It is named after the mathematical logician Alfred Tarski.The package includes a book, which serves as a textbook and manual, and a computer program which together serve as an introduction to the semantics of logic through games in which simple, three-dimensional worlds are populated ...
The propositional calculus [a] is a branch of logic. [1] It is also called propositional logic, [2] statement logic, [1] sentential calculus, [3] sentential logic, [4] [1] or sometimes zeroth-order logic. [b] [6] [7] [8] Sometimes, it is called first-order propositional logic [9] to contrast it with System F, but it should not be confused with ...
A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables. [1]
Flip-flops can be generalized in at least two ways: by making them 1-of-N instead of 1-of-2, and by adapting them to logic with more than two states. In the special cases of 1-of-3 encoding, or multi-valued ternary logic , such an element may be referred to as a flip-flap-flop .
For all natural numbers n, one has 2·n > 2 + n. is false, because if n is substituted with, for instance, 1, the statement "2·1 > 2 + 1" is false. It is immaterial that "2·n > 2 + n" is true for most natural numbers n: even the existence of a single counterexample is enough to prove the universal quantification false.
in the ternary numeral system, each digit is a trit (trinary digit) having a value of: 0, 1, or 2; in the skew binary number system, only the least-significant non-zero digit can have a value of 2, and the remaining digits have a value of 0 or 1; 1 for true, 2 for false, and 0 for unknown, unknowable/undecidable, irrelevant, or both; [16]
A closely related problem is found in some valid natural language arguments whose most obvious translations are invalid in formal logic. For example, the argument "(1) Fury is a horse; (2) therefore Fury is an animal" is valid but the corresponding argument in formal logic from () to () is invalid. One solution is to add to the argument an ...