Many-sorted logic

Many-sorted logic can reflect formally our intention, not to handle the universe as a homogenous collection of objects, but to partition them in a way that is similar to types in typeful programming. Both functional and assertive “parts of speech” in the language of the logic reflect this typeful partitioning of the universe even on the syntax level: substitution and argument passing can be done only accordingly, respecting the “sorts”.

There are more ways to formalize the intention mentioned above. A many-sorted logic is any package of information which fulfills it. In most cases, the followings are given:

• a set of sorts, S
• an approriate generalization of the notion of signature to be able to handle all the surplus information which is caused by the introduction of more sorts.

Algebraization

The algebraization of many-sorted logic is explained in the following book: On the algebraization of many-sorted logics, written by Carlos Caleiro and Ricardo Gonçalves. The book generalizes abstract algebraic logic to the many-sorted case, but it can be used also as an introductory material.

External links

• Many-Sorted Logic, the first chapter in Lecture notes on Decision Procedures, written by Calogero G. Zarba

See also

• Higher-order logic