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A proposition is a central concept in the philosophy of language, semantics, logic, and related fields, often characterized as the primary bearer of truth or falsity. Propositions are also often characterized as the type of object that declarative sentences denote. For instance, the sentence "The sky is blue" denotes the proposition that the ...
In this sense, propositional logic is the foundation of first-order logic and higher-order logic. Propositional logic is typically studied with a formal language, [c] in which propositions are represented by letters, which are called propositional variables. These are then used, together with symbols for connectives, to make propositional formula.
In propositional logic, a propositional formula is a type of syntactic formula which is well formed. If the values of all variables in a propositional formula are given, it determines a unique truth value. A propositional formula may also be called a propositional expression, a sentence, [1] or a sentential formula.
Stoic logic is the system of propositional logic developed by the Stoic philosophers in ancient Greece. It was one of the two great systems of logic in the classical world. It was largely built and shaped by Chrysippus , the third head of the Stoic school in the 3rd-century BCE.
Philosophy of logic is the philosophical discipline studying the scope and nature of logic. [59] It examines many presuppositions implicit in logic, like how to define its basic concepts or the metaphysical assumptions associated with them. [158]
Philosophy of logic is the area of philosophy that studies the nature of logic. [1] [2] Like many other disciplines, logic involves various philosophical presuppositions which are addressed by the philosophy of logic. [3]
In propositional logic, modus ponens (/ ˈ m oʊ d ə s ˈ p oʊ n ɛ n z /; MP), also known as modus ponendo ponens (from Latin 'method of putting by placing'), [1] implication elimination, or affirming the antecedent, [2] is a deductive argument form and rule of inference. [3]
propositional logic, Boolean algebra A ⇔ B {\displaystyle A\Leftrightarrow B} is true only if both A and B are false, or both A and B are true. Whether a symbol means a material biconditional or a logical equivalence , depends on the author’s style.