Negation in the context of "Declarative sentence"

A premise or premiss is a proposition—a true or false declarative statement—used in an argument to prove the truth of another proposition called the conclusion. Arguments consist of a set of premises and a conclusion.

An argument is meaningful for its conclusion only when all of its premises are true. If one or more premises are false, the argument says nothing about whether the conclusion is true or false. For instance, a false premise on its own does not justify rejecting an argument's conclusion; to assume otherwise is a logical fallacy called denying the antecedent. One way to prove that a proposition is false is to formulate a sound argument with a conclusion that negates that proposition.

Apophatic theology, also known as negative theology, is a form of theological thinking and religious practice which attempts to approach God, the Divine, by negation, to speak only in terms of what may not be said about God. It forms a pair together with cataphatic theology (also known as affirmative theology), which approaches God or the Divine by affirmations or positive statements about what God is.

The apophatic tradition is often, though not always, allied with the approach of mysticism, which aims at the vision of God, the perception of the divine reality beyond the realm of ordinary perception.

In logic, false (Its noun form is falsity) or untrue is the state of possessing negative truth value and is a nullary logical connective. In a truth-functional system of propositional logic, it is one of two postulated truth values, along with its negation, truth. Usual notations of the false are 0 (especially in Boolean logic and computer science), O (in prefix notation, Opq), and the up tack symbol ${\displaystyle \bot }$.

Another approach is used for several formal theories (e.g., intuitionistic propositional calculus), where a propositional constant (i.e. a nullary connective), ${\displaystyle \bot }$, is introduced, the truth value of which being always false in the sense above. It can be treated as an absurd proposition, and is often called absurdity.

Propositional logic is a branch of logic. It is also called statement logic, sentential calculus, propositional calculus, sentential logic, or sometimes zeroth-order logic. Sometimes, it is called first-order propositional logic to contrast it with System F, but it should not be confused with first-order logic. It deals with propositions (which can be true or false) and relations between propositions, including the construction of arguments based on them. Compound propositions are formed by connecting propositions by logical connectives representing the truth functions of conjunction, disjunction, implication, biconditional, and negation. Some sources include other connectives, as in the table below.

Unlike first-order logic, propositional logic does not deal with non-logical objects, predicates about them, or quantifiers. However, all the machinery of propositional logic is included in first-order logic and higher-order logics. In this sense, propositional logic is the foundation of first-order logic and higher-order logic.

Non-classical logics (and sometimes alternative logics or non-Aristotelian logics) are formal systems that differ in a significant way from standard logical systems such as propositional and predicate logic. There are several ways in which this is commonly the case, including by way of extensions, deviations, and variations. The aim of these departures is to make it possible to construct different models of logical consequence and logical truth.

Philosophical logic is understood to encompass and focus on non-classical logics, although the term has other meanings as well. In addition, some parts of theoretical computer science can be thought of as using non-classical reasoning, although this varies according to the subject area. For example, the basic boolean functions (e.g. AND, OR, NOT, etc) in computer science are very much classical in nature, as is clearly the case given that they can be fully described by classical truth tables. However, in contrast, some computerized proof methods may not use classical logic in the reasoning process.