NDLI: Algebraizable logics with a strong conjunction and their semi-lattice based companions

Content Provider	Springer Nature Link
Author	Jansana, Ramon
Copyright Year	2012
Abstract	The best known algebraizable logics with a conjunction and an implication have the property that the conjunction defines a meet semi-lattice in the algebras of their algebraic counterpart. This property makes it possible to associate with them a semi-lattice based deductive system as a companion. Moreover, the order of the semi-lattice is also definable using the implication. This makes that the connection between the properties of the logic and the properties of its semi-lattice based companion is strong. We introduce a class of algebraizable deductive systems that includes those systems, and study some of their properties and of their semi-lattice based companions. We also study conditions which, when satisfied by a deductive system in the class, imply that it is strongly algebraizable. This brings some information on the open area of research of Abstract Algebraic Logic which consists in finding interesting characterizations of classes of algebraizable logics that are strongly algebraizable.
Ending Page	861
Page Count	31
Starting Page	831
File Format	PDF
ISSN	09335846
e-ISSN	14320665
Journal	Archive for Mathematical Logic
Issue Number	7-8
Volume Number	51
Language	English
Publisher	Springer-Verlag
Publisher Date	2012-08-24
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Semilattices Algebra Algebraizable logics Logics based on semi-lattices Abstract deductive systems Mathematics Strongly algebraizable logics Abstract algebraic logic Abstract Algebraic logic Mathematical Logic and Foundations
Content Type	Text
Resource Type	Article
Subject	Philosophy Logic

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