Search results
Results From The WOW.Com Content Network
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.
In this example propositional logic assertions are checked using functions to represent the propositions a and b. The following Z3 script checks to see if a ∧ b ¯ ≡ a ¯ ∨ b ¯ {\displaystyle {\overline {a\land b}}\equiv {\overline {a}}\lor {\overline {b}}} :
In logic and computer science, the Davis–Putnam–Logemann–Loveland (DPLL) algorithm is a complete, backtracking-based search algorithm for deciding the satisfiability of propositional logic formulae in conjunctive normal form, i.e. for solving the CNF-SAT problem.
Classical propositional calculus is the standard propositional logic. Its intended semantics is bivalent and its main property is that it is strongly complete, otherwise said that whenever a formula semantically follows from a set of premises, it also follows from that set syntactically. Many different equivalent complete axiom systems have ...
Weights of propositional variables are given in the input of the problem. The weight of an assignment is the sum of weights of true variables. That problem is NP-complete (see Th. 1 of [26]). Other generalizations include satisfiability for first- and second-order logic, constraint satisfaction problems, 0-1 integer programming.
Their definition begins with the arbitrary choice of a set V of propositional variables. The alphabet consists of the letters in V along with the symbols for the propositional connectives and parentheses "(" and ")", all of which are assumed to not be in V. The formulas will be certain expressions (that is, strings of symbols) over this alphabet.
A predicate is a statement or mathematical assertion that contains variables, sometimes referred to as predicate variables, and may be true or false depending on those variables’ value or values. In propositional logic, atomic formulas are sometimes regarded as zero-place predicates. [1] In a sense, these are nullary (i.e. 0-arity) predicates.
In computer science and mathematical logic, satisfiability modulo theories (SMT) is the problem of determining whether a mathematical formula is satisfiable.It generalizes the Boolean satisfiability problem (SAT) to more complex formulas involving real numbers, integers, and/or various data structures such as lists, arrays, bit vectors, and strings.