The algebraic face of minimality | Zendy

Frank Wolter | Zendy

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The algebraic face of minimality

Author(s) -

Frank Wolter

Publication year - 2004

Publication title -

logic and logical philosophy

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.416

H-Index - 10

eISSN - 2300-9802

pISSN - 1425-3305

DOI - 10.12775/llp.1998.013

Subject(s) - mathematics , representation theorem , basis (linear algebra) , intuitionistic logic , set (abstract data type) , representation (politics) , algebraic number , heyting algebra , pure mathematics , algebra over a field , modal operator , monotonic function , modal , algebraic semantics , modal logic , discrete mathematics , propositional calculus , computer science , mathematical analysis , political science , polymer chemistry , law , programming language , chemistry , geometry , politics

Operators which map subsets of a given set to the set of their minimal elements with respect to some relation R form the basis of a semantic approach in non-monotonic logic, belief revision, conditional logic and updating. In this paper we investigate operators of this type from an algebraic viewpoint. A representation theorem is proved and various properties of the resulting algebras are investigated. It is shown that they behave quite differently from known algebras related to logics, e.g. modal algebras and Heyting algebras.

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