Many-sorted logic

Many-sorted logic can reflect formally our intention not to handle the universe as a <a href="/facts/Homogeneous/y84KQJxl">homogeneous</a> collection of objects, but to <a href="/facts/Partition_(number_theory)/LtyXWqwH">partition</a> it in a way that is similar to types in <a href="/facts/Type_system/Tz0bAMS9">typeful programming</a>. Both functional and assertive "<a href="/facts/Lexical_category/WbQ89MHX">parts of speech</a>" 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 various ways to formalize the intention mentioned above; a many-sorted logic is any package of information which fulfils it. In most cases, the following are given:

<ul><li>a set of sorts, S</li>
<li>an <a href="/facts/Signature_(logic)/C0YQCuce">appropriate generalization</a> of the notion of <a href="/facts/Signature_(logic)/C0YQCuce">signature</a> to be able to handle the additional information that comes with the sorts.</li></ul>
The <a href="/facts/Domain_of_discourse/T1WRQxx6">domain of discourse</a> of any <a href="/facts/Structure_(mathematical_logic)/GsMx1fEb">structure</a> of that signature is then fragmented into disjoint subsets, one for every sort.

Many-sorted logic open-in-new

Many-sorted logic