Some articles on atomic formula, formula, atomic formulas, formulas:
... 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 ... According to some terminology, an open formula is formed by combining atomic formulas using only logical connectives, to the exclusion of quantifiers ...
... Given a signature σ, the corresponding formal language is known as the set of σ-formulas ... Each σ-formula is built up out of atomic formulas by means of logical connectives atomic formulas are built from terms using predicate symbols ... The formal definition of the set of σ-formulas proceeds in the other direction first, terms are assembled from the constant and function symbols together ...
Famous quotes containing the words formulas and/or atomic:
“You treat world history as a mathematician does mathematics, in which nothing but laws and formulas exist, no reality, no good and evil, no time, no yesterday, no tomorrow, nothing but an eternal, shallow, mathematical present.”
—Hermann Hesse (18771962)
“The totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest laws of atomic physics or even of pure mathematics and logic, is a man-made fabric which impinges on experience only along the edges. Or, to change the figure, total science is like a field of force whose boundary conditions are experience.”
—Willard Van Orman Quine (b. 1908)