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While the roots of formalized logic go back to Aristotle, the end of the 19th and early 20th centuries saw the development of modern logic and formalized mathematics. Frege's Begriffsschrift (1879) introduced both a complete propositional calculus and what is essentially modern predicate logic. [1]
The propositional calculus [a] is a branch of logic. [1] It is also called propositional logic, [2] statement logic, [1] sentential calculus, [3] sentential logic, [4] [1] or sometimes zeroth-order logic. [b] [6] [7] [8] Sometimes, it is called first-order propositional logic [9] to contrast it with System F, but it should not be confused with ...
The formulas of propositional calculus, also called propositional formulas, [14] are expressions such as (()).Their definition begins with the arbitrary choice of a set V of propositional variables.
Toggle Rules for propositional calculus subsection. 2.1 Rules for negations. ... Download QR code; Print/export Download as PDF; Printable version; In other projects
Propositional logic (also referred to as Sentential logic) refers to a form of logic in which formulae known as "sentences" can be formed by combining other simpler sentences using logical connectives, and a system of formal proof rules allows certain formulae to be established as theorems.
For propositional logic, systematically applying the resolution rule acts as a decision procedure for formula unsatisfiability, solving the (complement of the) Boolean satisfiability problem. For first-order logic , resolution can be used as the basis for a semi-algorithm for the unsatisfiability problem of first-order logic , providing a more ...
In propositional calculus, a propositional function or a predicate is a sentence expressed in a way that would assume the value of true or false, except that within the sentence there is a variable (x) that is not defined or specified (thus being a free variable), which leaves the statement undetermined.
In theoretical computer science, the modal μ-calculus (Lμ, L μ, sometimes just μ-calculus, although this can have a more general meaning) is an extension of propositional modal logic (with many modalities) by adding the least fixed point operator μ and the greatest fixed point operator ν, thus a fixed-point logic.