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For example, if , and are variables then the expression ¯ contains three literals and the expression ¯ + ¯ ¯ contains four literals. However, the expression A ¯ C + B ¯ C {\displaystyle {\bar {A}}C+{\bar {B}}C} would also be said to contain four literals, because although two of the literals are identical ( C {\displaystyle C} appears ...
A variant of the 3-satisfiability problem is the one-in-three 3-SAT (also known variously as 1-in-3-SAT and exactly-1 3-SAT). Given a conjunctive normal form with three literals per clause, the problem is to determine whether there exists a truth assignment to the variables so that each clause has exactly one TRUE literal (and thus exactly two ...
The predicate calculus goes a step further than the propositional calculus to an "analysis of the inner structure of propositions" [4] It breaks a simple sentence down into two parts (i) its subject (the object (singular or plural) of discourse) and (ii) a predicate (a verb or possibly verb-clause that asserts a quality or attribute of the object(s)).
In mathematical logic, a propositional variable (also called a sentence letter, [1] sentential variable, or sentential letter) is an input variable (that can either be true or false) of a truth function. Propositional variables are the basic building-blocks of propositional formulas, used in propositional logic and higher-order logics.
The set of variables of a term t is denoted by vars(t). A term that doesn't contain any variables is called a ground term; a term that doesn't contain multiple occurrences of a variable is called a linear term. For example, 2+2 is a ground term and hence also a linear term, x⋅(n+1) is a linear term, n⋅(n+1) is a non-linear
There are many known examples of undecidable problems from ordinary mathematics. The word problem for groups was proved algorithmically unsolvable by Pyotr Novikov in 1955 and independently by W. Boone in 1959. The busy beaver problem, developed by Tibor Radó in 1962, is another well-known example.
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