Disjunction in the context of Boolean algebra (logic)

⭐ Core Definition: Disjunction

In logic, disjunction (also known as logical disjunction, logical or, logical addition, or inclusive disjunction) is a logical connective typically notated as $\lor$ and read aloud as "or". For instance, the English language sentence "it is sunny or it is warm" can be represented in logic using the disjunctive formula $S\lor W$ , assuming that $S$ abbreviates "it is sunny" and $W$ abbreviates "it is warm".

In classical logic, disjunction is given a truth functional semantics according to which a formula $\phi \lor \psi$ is true unless both $\phi$ and $\psi$ are false. Because this semantics allows a disjunctive formula to be true when both of its disjuncts are true, it is an inclusive interpretation of disjunction, in contrast with exclusive disjunction. Classical proof theoretical treatments are often given in terms of rules such as disjunction introduction and disjunction elimination. Disjunction has also been given numerous non-classical treatments, motivated by problems including Aristotle's sea battle argument, Heisenberg's uncertainty principle, as well as the numerous mismatches between classical disjunction and its nearest equivalents in natural languages.

↓ Menu

Disjunction in the context of False dilemma

A false dilemma, also referred to as false dichotomy or false binary, is an informal fallacy based on a premise that erroneously limits what options are available. The source of the fallacy lies not in an invalid form of inference but in a false premise. This premise has the form of a disjunctive claim: it asserts that one among a number of alternatives must be true. This disjunction is problematic because it oversimplifies the choice by excluding viable alternatives, presenting the viewer with only two absolute choices when, in fact, there could be many.

False dilemmas often have the form of treating two contraries, which may both be false, as contradictories, of which one is necessarily true. Various inferential schemes are associated with false dilemmas, for example, the constructive dilemma, the destructive dilemma or the disjunctive syllogism. False dilemmas are usually discussed in terms of deductive arguments, but they can also occur as defeasible arguments.

View the full Wikipedia page for False dilemma

↑ Return to Menu

Disjunction in the context of Boolean logic

In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted by 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as conjunction (and) denoted as $\land$ , disjunction (or) denoted as $\lor$ , and negation (not) denoted as $\neg$ . Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction, and division. Boolean algebra is therefore a formal way of describing logical operations in the same way that elementary algebra describes numerical operations.

Boolean algebra was introduced by George Boole in his first book The Mathematical Analysis of Logic (1847), and set forth more fully in his An Investigation of the Laws of Thought (1854). According to Huntington, the term Boolean algebra was first suggested by Henry M. Sheffer in 1913, although Charles Sanders Peirce gave the title "A Boolian [sic] Algebra with One Constant" to the first chapter of his "The Simplest Mathematics" in 1880. Boolean algebra has been fundamental in the development of digital electronics, and is provided for in all modern programming languages. It is also used in set theory and statistics.

View the full Wikipedia page for Boolean logic

↑ Return to Menu

Disjunction in the context of Boolean algebra (logic)

Disjunction Study page number 1 of 1

Play TriviaQuestions Online!

Skip to study material about Disjunction in the context of "Boolean algebra (logic)"

⭐ Core Definition: Disjunction

Disjunction in the context of False dilemma

Disjunction in the context of Boolean logic