False (logic) in the context of "False statement"

In logic, specifically in deductive reasoning, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. It is not required for a valid argument to have premises that are actually true, but to have premises that, if they were true, would guarantee the truth of the argument's conclusion. Valid arguments must be clearly expressed by means of sentences called well-formed formulas (also called wffs or simply formulas).

The validity of an argument can be tested, proved or disproved, and depends on its logical form.

A proposition is a central concept in the philosophy of language, semantics, logic, and related fields, often characterized as the primary bearer of truth or falsity. Propositions are the objects denoted by declarative sentences; for example, "The sky is blue" expresses the proposition that the sky is blue. Unlike sentences, propositions are not linguistic expressions, so the English sentence "Snow is white" and the German "Schnee ist weiß" denote the same proposition. Propositions also serve as the objects of belief and other propositional attitudes, such as when someone believes that the sky is blue.

Formally, propositions are often modeled as functions which map a possible world to a truth value. For instance, the proposition that the sky is blue can be modeled as a function which would return the truth value ${\displaystyle T}$ if given the actual world as input, but would return ${\displaystyle F}$ if given some alternate world where the sky is green. However, a number of alternative formalizations have been proposed, notably the structured propositions view.

In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values (true or false). Truth values are used in computing as well as various types of logic.

A truth-bearer is an entity that is said to be either true or false and nothing else. The thesis that some things are true while others are false has led to different theories about the nature of these entities. Since there is divergence of opinion on the matter, the term truth-bearer is used to be neutral among the various theories. Truth-bearer candidates include propositions, sentences, sentence-tokens, statements, beliefs, thoughts, intuitions, utterances, and judgements but different authors exclude one or more of these, deny their existence, argue that they are true only in a derivative sense, assert or assume that the terms are synonymous,or seek to avoid addressing their distinction or do not clarify it.

In mathematical logic, a term is an arrangement of dependent/bound symbols that denotes a mathematical object within an expression/formula. In particular, terms appear as components of a formula. This is analogous to natural language, where a noun phrase refers to an object and a whole sentence refers to a fact.

A first-order term is recursively constructed from constant symbols, variable symbols, and function symbols.An expression formed by applying a predicate symbol to an appropriate number of terms is called an atomic formula, which evaluates to true or false in bivalent logics, given an interpretation.For example, ⁠${\displaystyle (x+1)*(x+1)}$⁠ is a term built from the constant 1, the variable x, and the binary function symbols ⁠${\displaystyle +}$⁠ and ⁠${\displaystyle *}$⁠; it is part of the atomic formula ⁠${\displaystyle (x+1)*(x+1)\geq 0}$⁠ which evaluates to true for each real-numbered value of x.