Logics. Complex connective propositions (most important)

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Logics. Complex connective propositions (most important)

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25. COMPLEX CONNECTIVE JUDGMENTS

A complex proposition is one that consists of several simple ones connected by logical connectives.. The following types of complex judgments are distinguished:

1) connecting, 2) dividing, 3) conditional, 4) equivalent. The truth of such complex judgments is determined by the truth of their simple constituents.

Connective (conjunctive) judgments

A connective, or conjunctive, is a proposition consisting of several simple ones connected by the logical connective “and”. For example, the proposition “Theft and fraud are intentional crimes” is a connecting proposition consisting of two simple ones: “Theft is an intentional crime,” “Fraud is an intentional crime.” If the first is denoted р, and the second - q, then the connecting proposition can be expressed symbolically as р ∧

qWhere р и q - members of the conjunction (or conjuncts), ∧ - symbol of the conjunction.

In natural language, the conjunctive connective can also be represented by such expressions as "a", "but", "as well", "like", "although", "however", "despite", "at the same time", etc. For example, "When the court determines the amount of damages to be compensated, not only the damages (R), but also the specific situation in which the losses were caused (Q), as well as the financial situation of the employee (r)". Symbolically this judgment can be expressed as follows: р ∧

q ∧ r.

A connecting proposition can be expressed in one of three structures.

Two subjects and one predicate (S' and S″ are Р).

For example, "Confiscation of property and deprivation of title are additional criminal sanctions."

One subject and two predicates (S is P' and P″).

For example, "Crime is a socially dangerous and illegal act."

Two subjects and two predicates (S' and S″ are P´ and P″). For example, “Fundamental human rights and freedoms are inalienable and belong to everyone from birth.”

The truth of a connecting proposition is determined by the truth of its constituent simple propositions. A connecting proposition is true only if its simple parts are true. If at least one simple proposition is false, then the conjunction as a whole is also false.

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