A declarative sentence with exact truth value is called a proposition. This proposition can take a "value", which is called truth value. There are only two kinds of truth values: true and false, which are represented by t (or 1) and f (or 0) respectively.
All sentences without judgment content, such as imperative sentences (or imperative sentences), exclamatory sentences, interrogative sentences and ambiguous sentences, cannot be used as propositions.
Atomic proposition (simple proposition): A proposition that cannot be decomposed into simpler propositions.
Compound proposition: a proposition that can be decomposed into simpler propositions. These simple propositions are composed of related words and punctuation marks such as or, and, no, if, if and only if.
Let P be an arbitrary proposition, and the compound proposition "non-P" (or "negation of P") is called the negation of P, which is recorded as? p，“？” This is a negative conjunction. P is true if and only if? P is fake.
Let P and Q be any two propositions, and the compound proposition "P and Q" (or "P and Q") is called the conjunction of P and Q, marked as P ∧ Q, and "∧" is the conjunction. P ∧ Q is true if and only if both p and q are true.
∧ "is the logical abstraction of" harmony ","both … and …… ","Dan ","harmony ","although … but …… "and" one side …… "in natural language. But not all "he" and "he" should be expressed by conjunctions, and should be analyzed according to the semantics of the sentence.
Let p and q be any two propositions, and the compound proposition "p or q" is called disjunction of p and q, marked as P ∨ Q, and "∨" is disjunctive conjunction. P∞Q is true if and only if at least one of p and q is true.
The conjunction "∨" is the logical abstraction of "or" and "or" in natural language. In natural language, "or" has "combinable"
Or "(or the same or)," not both or "(that is, XOR). Strictly speaking, disjunctive conjunctions actually mean -and-or, and XOR sometimes uses separate XOR conjunctions "⊕" or "∨? "To show it.
Let P and Q be any two propositions, and the compound proposition "If P, then Q" is called the implication of P and Q, marked as P → Q, and "→" is the implication conjunction. P → Q is false if and only if P is true and Q is false. Generally, P in the implication formula P → Q is called the antecedent of the implication formula, and Q is called the afterpart of the implication formula.
Let p and q be any two propositions, and the compound proposition "p if and only if q" is called the equivalence of p and q, and is denoted as p? Ask, "?" It is an equivalent conjunction (also known as a double conditional conjunction). p？ Q is true if and only if both P and Q are true and false.
Conjunction is the connection between the truth values of two propositions, not the content of propositions, so the truth values of compound propositions only depend on the truth values of simple propositions that constitute them, and have nothing to do with their content and whether there is a relationship between them.
A specific proposition is a constant proposition, which has either the value "t" ("1") or the value "f" ("0").
An arbitrary atomic proposition with no specific content is a variable proposition, which is usually called propositional variable. The propositional variable has no specific truth value, and its variable domain is set to {T, F} (or {0, 1}).
A table composed of the truth values of formula G under all its possible explanations is called the truth table of G.
Necessity: If G = H, then G and H are both true or false under their arbitrary interpretation I, so use "?" Change the meaning of knowledge, formula g? H in any of its explanations I, its truth value is "true", that is, G? H is an eternal formula.
Adequacy: suppose the formula g? H is an eternal formula, and I is its arbitrary interpretation. Under I, g? H is true, so both G and H are true or false. Because of the arbitrariness of I, there is G = H. ..