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List of paradoxes. Outline of public relations – Overview of and topical guide to public relations. Map–territory relation – Relationship between an object and a representation of that object (confusing map with territory, menu with meal) Mathematical fallacy – Certain type of mistaken proof.
Logical reasoning is a mental activity that aims to arrive at a conclusion in a rigorous way. It happens in the form of inferences or arguments by starting from a set of premises and reasoning to a conclusion supported by these premises. The premises and the conclusion are propositions, i.e. true or false claims about what is the case.
These two definitions of formal logic are not identical, but they are closely related. For example, if the inference from p to q is deductively valid then the claim "if p then q" is a logical truth. [16] Formal logic needs to translate natural language arguments into a formal language, like first-order logic, to assess whether they are valid.
A logic that extends first-order logic to allow for more nuanced expressions of quantifier scope and dependence, particularly in contexts of game-theoretical semantics. independent Referring to a pair of propositions that are not contrary , subcontrary , contradictory , logically equivalent , or implied one by the other (either the first by the ...
In logic, the logical form of a statement is a precisely-specified semantic version of that statement in a formal system. Informally, the logical form attempts to formalize a possibly ambiguous statement into a statement with a precise, unambiguous logical interpretation with respect to a formal system. In an ideal formal language, the meaning ...
Logical truth is one of the most fundamental concepts in logic. Broadly speaking, a logical truth is a statement which is true regardless of the truth or falsity of its constituent propositions. In other words, a logical truth is a statement which is not only true, but one which is true under all interpretations of its logical components (other ...
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, so that rather than ...
propositional logic, Boolean algebra, first-order logic. ⊥ {\displaystyle \bot } denotes a proposition that is always false. The symbol ⊥ may also refer to perpendicular lines. The proposition. ⊥ ∧ P {\displaystyle \bot \wedge P} is always false since at least one of the two is unconditionally false. ∀.