under this interpretation of . Logical constants In the specific cases of propositional logic and predicate logic, the formal languages considered have alphabets that are divided into two sets: the logical symbols (logical constants) and the non-logical symbols. The idea behind this terminology is that logical symbols have the same meaning regardless of the subject matter being studied, while non-logical symbols change in meaning depending on the area of investigation. Logical constants are always given the same meaning by every interpretation of the standard kind, so that only the meanings of the non-logical symbols are changed. Logical constants include quantifier symbols ∀ ("all") and ∃ ("some"), symbols for logical connectives ∧ ("and"), ∨ ("or"), ¬ ("not"), parentheses and other grouping symbols, and (in many treatments) the equality symbol =. General properties of truth-functional interpretations Many of the commonly studied interpretations associate each sentence in a formal language with a single truth value, either True or False. These interpretations are called truth functional; they include the usual interpretations of propositional and first-order logic. The sentences that are made true by a particular assignment are said to be satisfied by that assignment. In classical logic, no sentence can be made both true and false by the same interpretation, although this is not true of glut logics such as LP. Even in classical logic, however, it is possible that the truth value of the same sentence can be different under different interpretations. A sentence is consistent if it is true under at least one interpretation; otherwise it is inconsistent. A sentence φ is said to be logically valid if it is satisfied by every interpretation (if φ is satisfied by every interpretation that satisfies ψ then φ is said to be a logical consequence of ψ). Logical connectives Some of the logical symbols of a language (other than quantifiers) are truth-functional connectives that represent truth functions — functions that take truth values as arguments and return truth values as outputs (in other words, these are operations on truth values of sentences). The truth-functional connectives enable compound sentences to be built up from simpler sentences. In this way, the truth value of the compound sentence is defined as a certain truth function of the truth values of the simpler sentences. The connectives are usually taken to be logical constants, meaning that the meaning of the connectives is always the same, independent of what interpretations