Concept

Logical disjunction

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Boolean-valued function

A Boolean-valued function (sometimes called a predicate or a proposition) is a function of the type f : X → B, where X is an arbitrary set and where B is a Boolean domain, i.e. a generic two-element set, (for example B = {0, 1}), whose elements are interpreted as logical values, for example, 0 = false and 1 = true, i.e., a single bit of information. In the formal sciences, mathematics, mathematical logic, statistics, and their applied disciplines, a Boolean-valued function may also be referred to as a characteristic function, indicator function, predicate, or proposition.

Circuit (computer science)

In theoretical computer science, a circuit is a model of computation in which input values proceed through a sequence of gates, each of which computes a function. Circuits of this kind provide a generalization of Boolean circuits and a mathematical model for digital logic circuits. Circuits are defined by the gates they contain and the values the gates can produce. For example, the values in a Boolean circuit are boolean values, and the circuit includes conjunction, disjunction, and negation gates.

OR gate

The OR gate is a digital logic gate that implements logical disjunction. The OR gate returns true if any of its inputs are true; otherwise it returns false. The input and output states are normally represented by different voltage levels. Any OR gate can be constructed with two or more inputs. It outputs a 1 if any of these inputs are 1, or outputs a 0 only if all inputs are 0. The inputs and outputs are binary digits ("bits") which have two possible logical states.

Material nonimplication

Material nonimplication or abjunction (Latin ab = "away", junctio= "to join") is the negation of material implication. That is to say that for any two propositions and , the material nonimplication from to is true if and only if the negation of the material implication from to is true. This is more naturally stated as that the material nonimplication from to is true only if is true and is false. It may be written using logical notation as , , or "Lpq" (in Bocheński notation), and is logically equivalent to , and .

Free choice inference

Free choice is a phenomenon in natural language where a linguistic disjunction appears to receive a logical conjunctive interpretation when it interacts with a modal operator. For example, the following English sentences can be interpreted to mean that the addressee can watch a movie and that they can also play video games, depending on their preference: You can watch a movie or play video games. You can watch a movie or you can play video games.

Boolean domain

In mathematics and abstract algebra, a Boolean domain is a set consisting of exactly two elements whose interpretations include false and true. In logic, mathematics and theoretical computer science, a Boolean domain is usually written as {0, 1}, or The algebraic structure that naturally builds on a Boolean domain is the Boolean algebra with two elements. The initial object in the of bounded lattices is a Boolean domain. In computer science, a Boolean variable is a variable that takes values in some Boolean domain.

Yes–no question

In linguistics, a yes–no question, also known as a binary question, a polar question, or a general question, is a question whose expected answer is one of two choices, one that provides an affirmative answer to the question versus one that provides a negative answer to the question. Typically, in English, the choices are either "yes" or "no". Yes–no questions present an exclusive disjunction, namely a pair of alternatives of which only one is a felicitous answer.

Mask (computing)

In computer science, a mask or bitmask is data that is used for bitwise operations, particularly in a bit field. Using a mask, multiple bits in a byte, nibble, word, etc. can be set either on or off, or inverted from on to off (or vice versa) in a single bitwise operation. An additional use of masking involves predication in vector processing, where the bitmask is used to select which element operations in the vector are to be executed (mask bit is enabled) and which are not (mask bit is clear).

Inquisitive semantics

Inquisitive semantics is a framework in logic and natural language semantics. In inquisitive semantics, the semantic content of a sentence captures both the information that the sentence conveys and the issue that it raises. The framework provides a foundation for the linguistic analysis of statements and questions. It was originally developed by Ivano Ciardelli, Jeroen Groenendijk, Salvador Mascarenhas, and Floris Roelofsen. The essential notion in inquisitive semantics is that of an inquisitive proposition.

Short-circuit evaluation

Short-circuit evaluation, minimal evaluation, or McCarthy evaluation (after John McCarthy) is the semantics of some Boolean operators in some programming languages in which the second argument is executed or evaluated only if the first argument does not suffice to determine the value of the expression: when the first argument of the AND function evaluates to false, the overall value must be false; and when the first argument of the OR function evaluates to true, the overall value must be true.