Many-sorted logic

Many-sorted logic can reflect formally our intention, not to handle the universe as a homogeneous collection of objects, but to partition it 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 following are given:

• a set of sorts, S
• an appropriate generalization of the notion of signature to be able to handle the additional information that comes with the sorts.

The domain of discourse of any structure of that signature is then fragmented into disjoint subsets, one for every sort.

Algebraization

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

External links

• "Many-sorted Logic", the first chapter in Lecture Notes on Decision Procedures by Calogero G. Zarba

See also

• Categorical logic

This mathematical logic-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Systems of formal logic Mathematical logic stubs Wikimedia Foundation. 2010. Игры ⚽ Нужно сделать НИР? Doña Ana Mountains 49th Military Police Brigade (United States) Look at other dictionaries: many-sorted logic — A logic in which the variables range over different domains. In classical predicate calculus a proposition like ‘All Fs are G’ is represented as saying: take anything; if it is F, it is G. In a many sorted logic the representation will be: take… …   Philosophy dictionary many-sorted logic — noun A logic that directly supports classification of entities into disjunct sorts …   Wiktionary Logic — For other uses, see Logic (disambiguation). Philosophy …   Wikipedia Logic simulation — is the use of a computer program to simulate the operation of a digital circuit. Logic simulation is the primary tool used for verifying the logical correctness of a hardware design. In many cases logic simulation is the first activity performed… …   Wikipedia First-order logic — is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic (a less… …   Wikipedia Structure (mathematical logic) — In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations and relations which are defined on it. Universal algebra studies structures that generalize the algebraic structures such as… …   Wikipedia Interpretation (logic) — An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until …   Wikipedia Signature (logic) — In logic, especially mathematical logic, a signature lists and describes the non logical symbols of a formal language. In universal algebra, a signature lists the operations that characterize an algebraic structure. In model theory, signatures… …   Wikipedia Higher-order logic — In mathematics, higher order logic is distinguished from first order logic in a number of ways.One of these is the type of variables appearing in quantifications; in first order logic, roughly speaking, it is forbidden to quantify over predicates …   Wikipedia List of mathematical logic topics — Clicking on related changes shows a list of most recent edits of articles to which this page links. This page links to itself in order that recent changes to this page will also be included in related changes. This is a list of mathematical logic …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”