China 
Africa 
Explore chapters and articles related to this topic
Propositional logic
Published in Richard E. Neapolitan, Xia Jiang, Artificial Intelligence, 2018
Richard E. Neapolitan, Xia Jiang
The syntax of propositional logic is only concerned with developing propositions; it has nothing to do with attaching meaning to them. As mentioned previously, we need not even associate statements about the world with the propositions. The semantics of propositional logic gives meaning to the propositions. The semantics consists of rules for assigning either the value T (true) or F (false) to every proposition. Such an assignment is called the truth value of the proposition. If a proposition has truth value T, we say it is true; otherwise, we say it is false.
B
Published in Carl W. Hall, Laws and Models, 2018
The law is a linearization of the power law over a certain range of density. This law is used as a tool for design and construction of earth models. Keywords: compressional wave, density, earth, geophysical wave, velocity BIRCH, Francis, 1903-1992, American geologist Sources: Science 177:261-262, 21, July 1972; Science 257:66-67, 3 July 1992. See also RICHTER BIVALENCE, PRINCIPLE OF OR LAW OF Every statement is either true or false, that is, every statement has a truth-value, and there are only two truth values. It does not consider the "excluded middle." The principle or law
Miscellaneous
Published in Dan Zwillinger, CRC Standard Mathematical Tables and Formulas, 2018
A statement such as (p → (q ∧ r)) ∨ ¬p is a compound statement composed of the atomic propositions p, q, and r. The letters P, Q, and R are used to designate compound statements. A tautology is a compound statement which always is true, regardless of the truth values of the atomic statements used to define it. For example, a simple tautology is (¬¬p) ↔ p. Tautologies are logical truths. More examples:
A Method for Backward Failure Propagation in Conceptual System Design
Published in Nuclear Science and Engineering, 2023
Ali Mansoor, Xiaoxu Diao, Carol Smidts
As discussed earlier, the forward application of the ISFA method relies on logic-based rules, i.e., BRs and FFL. However, it is imperative to derive a reversed version of the rules for their application to the backward propagation. The derivation of the reverse rules is performed using PL (Ref. 42). This mathematical technique is widely used in computer science to verify software and design computing and artificial intelligence systems. It is a branch of mathematical logic that combines simple propositions to make more complicated propositions and studies the logical relationships and properties derived from manipulating the statements. The propositions are the simplest statements that cannot be further subdivided. A proposition can be either true or false but cannot have both truth values simultaneously. The value of a complex statement depends on the truth values of the comprising propositions. The simple propositions are combined using connectives to make complex statements (some connectives are shown in Table I). These complex statements can be studied based on the axioms of PL and the rules of inference of PL. A set of statements, called premise, can be used to derive a new statement or a new set of statements. For the sake of simplicity and improved readability of the logical expressions used later in this paper, we introduce a logic connective called multi-XOR, , which is defined as follows: