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Subalternation [1] [2] is an immediate inference which is only made between A (All S are P) and I (Some S are P) categorical propositions and between E (No S are P or originally, No S is P) and O (Some S are not P or originally, Not every S is P) categorical propositions of the traditional square of opposition and the original square of opposition. [3]
In modern logic, this is not assumed so the faded ones do not hold. (There can be no element in the faded red areas in the modern logic.) Depiction from the 15th century. In term logic (a branch of philosophical logic), the square of opposition is a diagram representing the relations between the four basic categorical propositions.
Cases of the incorrect application of the contrary, subcontrary and subalternation relations (these hold in the traditional square of opposition, not the modern square of opposition) are syllogistic fallacies called illicit contrary, illicit subcontrary, and illicit subalternation, respectively. Cases of incorrect application of the ...
Subalternation, going from a universal proposition to a particular proposition in logic "A Subaltern", the author listed in William Cobbett's "The Soldier's Friend"
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 .
Logic Journal of the IGPL, 12, 111–124. Curry, H. B. (1952) On the definition of substitution, replacement and allied notions in an abstract formal system. Revue philosophique de Louvain 50, 251–269. Hunter, G. (1971). Metalogic: An Introduction to the Metatheory of Standard First Order Logic. University of California Press. ISBN 0-520-01822-2
Categorical logic is the branch of mathematics in which tools and concepts from category theory are applied to the study of mathematical logic. It is also notable for its connections to theoretical computer science. [1] In broad terms, categorical logic represents both syntax and semantics by a category, and an interpretation by a functor.
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.