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In propositional logic, a propositional formula is a type of syntactic formula which is well formed. If the values of all variables in a propositional formula are given, it determines a unique truth value. A propositional formula may also be called a propositional expression, a sentence, [1] or a sentential formula.
In propositional calculus, a propositional function or a predicate is a sentence expressed in a way that would assume the value of true or false, except that within the sentence there is a variable (x) that is not defined or specified (thus being a free variable), which leaves the statement undetermined.
The Boolean satisfiability problem (SAT) asks to determine if a propositional formula (example depicted) can be made true by an appropriate assignment ("solution") of truth values to its variables. While it is easy to verify whether a given assignment renders the formula true , [ 1 ] no essentially faster method to find a satisfying assignment ...
An atomic formula is a formula that contains no logical connectives nor quantifiers, or equivalently a formula that has no strict subformulas. The precise form of atomic formulas depends on the formal system under consideration; for propositional logic, for example, the atomic formulas are the propositional variables.
A Horn formula is a propositional formula formed by conjunction of Horn clauses. Horn satisfiability is actually one of the "hardest" or "most expressive" problems which is known to be computable in polynomial time, in the sense that it is a P -complete problem. [ 2 ]
An atomic formula or atom is simply a predicate applied to a tuple of terms; that is, an atomic formula is a formula of the form P (t 1,…, t n) for P a predicate, and the t n terms. All other well-formed formulae are obtained by composing atoms with logical connectives and quantifiers. For example, the formula ∀x. P (x) ∧ ∃y. Q (y, f (x ...
For example, the dual of (A & B ∨ C) would be (¬A ∨ ¬B & ¬C). The dual of a formula φ is notated as φ*. The Duality Principle states that in classical propositional logic, any sentence is equivalent to the negation of its dual.
A superintuitionistic logic is a set L of propositional formulas in a countable set of variables p i satisfying the following properties: 1. all axioms of intuitionistic logic belong to L; 2. if F and G are formulas such that F and F → G both belong to L, then G also belongs to L (closure under modus ponens);