A quantitative-informational approach to logical consequence

In Jean-Yves Beziau (ed.), The Road to Universal Logic (Studies in Universal Logic). Switzerland: Springer International Publishing. pp. 105-24 (2015)
Download Edit this record How to cite View on PhilPapers
In this work, we propose a definition of logical consequence based on the relation between the quantity of information present in a particular set of formulae and a particular formula. As a starting point, we use Shannon‟s quantitative notion of information, founded on the concepts of logarithmic function and probability value. We first consider some of the basic elements of an axiomatic probability theory, and then construct a probabilistic semantics for languages of classical propositional logic. We define the quantity of information for the formulae of these languages and introduce the concept of informational logical consequence, identifying some important results, among them: certain arguments that have traditionally been considered valid, such as modus ponens, are not valid from the informational perspective; the logic underlying informational logical consequence is not classical, and is at the least paraconsistent sensu lato; informational logical consequence is not a Tarskian logical consequence.
PhilPapers/Archive ID
Upload history
Archival date: 2017-12-06
View other versions
Added to PP index

Total views
251 ( #26,264 of 64,251 )

Recent downloads (6 months)
47 ( #16,497 of 64,251 )

How can I increase my downloads?

Downloads since first upload
This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.