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In particular, the same formula may appear twice in the same sequence. The full set of sequent calculus inference rules contains rules to swap adjacent formulas on the left and on the right of the assertion symbol (and thereby arbitrarily permute the left and right sequences), and also to insert arbitrary formulas and remove duplicate copies ...
Nearly all sequential logic today is clocked or synchronous logic. In a synchronous circuit, an electronic oscillator called a clock (or clock generator) generates a sequence of repetitive pulses called the clock signal which is distributed to all the memory elements in the circuit.
Logical consequence (also entailment or logical implication) is a fundamental concept in logic which describes the relationship between statements that hold true when one statement logically follows from one or more statements.
Logic studies valid forms of inference like modus ponens. Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and ...
An infinite sequence of real numbers (in blue). This sequence is neither increasing, decreasing, convergent, nor Cauchy. It is, however, bounded. In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called elements, or terms).
Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language .
First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables.
The process of performing a sequence of calculations or logical operations systematically to obtain a result. concept An abstract idea representing the fundamental characteristics of what it describes. conclusion The statement that logically follows from the premises of an argument, serving as the argument's final claim. concrete object