Characterizing equivalential and algebraizable logics by the Leibniz operator

Studia Logica 58 (2):305-323 (1997)
In [14] we used the term finitely algebraizable for algebraizable logics in the sense of Blok and Pigozzi [2] and we introduced possibly infinitely algebraizable, for short, p.i.-algebraizable logics. In the present paper, we characterize the hierarchy of protoalgebraic, equivalential, finitely equivalential, p.i.-algebraizable, and finitely algebraizable logics by properties of the Leibniz operator. A Beth-style definability result yields that finitely equivalential and finitely algebraizable as well as equivalential and p.i.-algebraizable logics can be distinguished by injectivity of the Leibniz operator. Thus, from a characterization of equivalential logics we obtain a new short proof of the main result of [2] that a finitary logic is finitely algebraizable iff the Leibniz operator is injective and preserves unions of directed systems. It is generalized to nonfinitary logics. We characterize equivalential and, by adding injectivity, p.i.-algebraizable logics.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
Categories (categorize this paper)
DOI 10.1023/A:1004979825733
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 23,664
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA
J. Czelakowski & D. Pigozzi (2004). Fregean Logics. Annals of Pure and Applied Logic 127 (1-3):17-76.

View all 14 citations / Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

20 ( #231,734 of 1,903,041 )

Recent downloads (6 months)

1 ( #446,009 of 1,903,041 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.