Logics. Types of disjunction (most important)

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Logics. Types of disjunction (most important)

Lecture notes, cheat sheets

Directory / Lecture notes, cheat sheets

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27. TYPES OF DISJUNCTION

Non-strict and strict disjunction

Since the connective “or” is used in natural language in two meanings - connective-disjunctive and exclusive-disjunctive, two types of disjunctive judgments should be distinguished:

1) non-strict (weak) disjunction and 2) strict (strong) disjunction.

Nonstrict disjunction - a judgment in which the link "or" is used in a connecting-separating sense (symbol ∨). For example: "Cold weapons can be piercing or cutting" - symbolically р ∨

q. The connective “or” in this case separates, since such types of weapons exist separately, and connects, because there are weapons that simultaneously pierce and cut.

A non-strict disjunction will be true if at least one term of the disjunction is true and false if both of its terms are false.

Strict disjunction - a judgment in which the link "or" is used in a separating sense (symbol - double disjunction). For example: “An act can be intentional or careless,” symbolically

The terms of a strict disjunction, called alternatives, cannot be both true. If an act is committed intentionally, then it cannot be considered negligent, and, conversely, an act committed through negligence cannot be classified as intentional.

A strict disjunction will be true if one term is true and the other term is false; it will be false if both terms are true or both are false. Thus, a proposition of strict disjunction will be true if one alternative is true, and false if both alternatives are false and both are true.

The separating copula in the language is usually expressed using the unions "or", "or". In order to strengthen the disjunction to an alternative meaning, double conjunctions are often used: instead of the expression "p or q" they use "or p, or q", and together "p or q" - "either p or q". Since there are no unambiguous conjunctions for non-strict and strict division in grammar, the question of the type of disjunction in legal and other texts should be decided by a meaningful analysis of the corresponding judgments.

Complete and incomplete disjunction

Complete or closed is a disjunctive judgment that lists all the characteristics or all types of a certain kind.

Symbolically, this judgment can be written as follows: < p ∨

q ∨

r >. For example: “Forests are deciduous, coniferous or mixed.” The completeness of this division (in symbolic notation is indicated by the sign < ... >) is determined by the fact that there are no other types of forests in addition to those indicated.

Incomplete, or open, is a disjunctive judgment that does not list all the characteristics or not all types of a certain kind.. In symbolic notation, the incompleteness of a disjunction can be expressed by an ellipsis: р ∨

q ∨

r ∨ ... In natural language, the incompleteness of a disjunction is expressed by the words: “etc.,” “etc.,” “and the like,” “others,” etc.

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