Supracompact inference operations

Studia Logica 52 (3):457 - 481 (1993)
When a proposition is cumulatively entailed by a finite setA of premisses, there exists, trivially, a finite subsetB ofA such thatB B entails for all finite subsetsB that are entailed byA. This property is no longer valid whenA is taken to be an arbitrary infinite set, even when the considered inference operation is supposed to be compact. This leads to a refinement of the classical definition of compactness. We call supracompact the inference operations that satisfy the non-finitary analogue of the above property. We show that for any arbitrary cumulative operationC, there exists a supracompact cumulative operationK(C) that is smaller thenC and agrees withC on finite sets. Moreover,K(C) inherits most of the properties thatC may enjoy, like monotonicity, distributivity or disjunctive rationality. The main part of the paper concerns distributive supracompact operations. These operations satisfy a simple functional equation, and there exists a representation theorem that provides a semantic characterization for this family of operations. We examine finally the case of rational operations and show that they can be represented by a specific kind of model particularly easy to handle.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1007/BF01057658
 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: 15,904
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

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

7 ( #292,059 of 1,725,474 )

Recent downloads (6 months)

5 ( #134,647 of 1,725,474 )

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.