language consisting of the true quantified Boolean formulas. A (fully) quantified Boolean formula is a formula in quantified propositional logic (also...

Boolean formula. In other words, it asks whether the formula's variables can be consistently replaced by the values TRUE or FALSE to make the formula...

A formula game is an artificial game represented by a fully quantified Boolean formula such as ∃ x 1 ∀ x 2 ∃ x 3 … ψ {\displaystyle \exists x_{1}\forall...

(the recognition of true quantified Boolean formulas) that is PSPACE-complete. Analogously, dependency quantified boolean formulas encode computation with...

intersection and union of sets. A quantified propositional function is a statement; thus, like statements, quantified functions can be negated. The ¬  ...

satisfies that property. A formula where a quantifier takes widest scope is called a quantified formula. A quantified formula must contain a bound variable...

logic, where a tautology is defined as a propositional formula that is true under any possible Boolean valuation of its propositional variables. A key property...

universal quantifier into an existential quantifier and negating the quantified formula. That is, ¬ ∀ x P ( x ) is equivalent to ∃ x ¬ P ( x ) {\displaystyle...

In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {−1...

P-complete. This is also often the case for showing that the True quantified Boolean formula problem is PSPACE-complete. This is because the need for memory...

NP-complete nor Undecidable. For instance, the language of true quantified Boolean formulas is decidable in polynomial space, but not in non-deterministic...

impredicative quantification, System F. Parigot (1997) showed how this calculus can be extended to admit classical logic. True quantified Boolean formula Second-order...

Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and...

truth value. Quantifiers can be applied to variables in a formula. The variable x in the previous formula can be universally quantified, for instance...

verification. QBFEVAL is a biennial competition of solvers for true quantified Boolean formulas, which have applications to model checking. SV-COMP is an annual...

In propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid...

connective Logical matrix Product term True quantified Boolean formula Truth table Predicate logic Atomic formula Atomic sentence Domain of discourse Empty...

c)\|} The completeness of the Boolean algebra is required to define truth values for quantified formulas. If φ(x) is a formula with free variable x (and possibly...

may also be used to evaluate fully quantified Boolean formulae in which the formula being quantified is a 2-CNF formula. A number of exact and approximate...

mathematical logic, a sentence (or closed formula) of a predicate logic is a Boolean-valued well-formed formula with no free variables. A sentence can be...

languages, any expression can be evaluated in a context that expects a Boolean data type. Typically (though this varies by programming language) expressions...

a formula. This is how we define logical connectives in propositional logic: ¬Φ is True iff Φ is False. (Φ ∧ Ψ) is True iff Φ is True and Ψ is True. (Φ...

from Cornell University Kochi University (disambiguation) True quantified Boolean formula, also known as QSAT Kusat, a village in Oman This disambiguation...

to a canonical Boolean, ie. an integer with a value of either 0 or 1 and no other. Although any integer other than 0 is logically true in C and 1 is not...

interpreted as material implication, a formula P → Q {\displaystyle P\to Q} is true unless P {\displaystyle P} is true and Q {\displaystyle Q} is false. Material...

two-element Boolean algebra is the Boolean algebra whose underlying set (or universe or carrier) B is the Boolean domain. The elements of the Boolean domain...

quantified Boolean formulas. A (fully) quantified Boolean formula is a formula in quantified propositional logic where every variable is quantified (or bound)...

statements, so one can speak about n-ary logical connectives. The boolean constants True and False can be thought of as zero-ary operators. Negation is a...

{L}}} , an interpretation, valuation, Boolean valuation, or case, is an assignment of semantic values to each formula of L {\displaystyle {\mathcal {L}}}...

Boolean arithmetic; The primary algebra (Chapter 6 of LoF), whose models include the two-element Boolean algebra (hereinafter abbreviated 2), Boolean...