Some useful 16-valued logics: How a computer network should think [Book Review]

Journal of Philosophical Logic 34 (2):121 - 153 (2005)
In Belnap's useful 4-valued logic, the set 2 = {T, F} of classical truth values is generalized to the set 4 = (2) = {Ø, {T}, {F}, {T, F}}. In the present paper, we argue in favor of extending this process to the set 16 = ᵍ (4) (and beyond). It turns out that this generalization is well-motivated and leads from the bilattice FOUR₂ with an information and a truth-and-falsity ordering to another algebraic structure, namely the trilattice SIXTEEN₃ with an information ordering together with a truth ordering and a (distinct) falsity ordering. Interestingly, the logics generated separately by the algebraic operations under the truth order and under the falsity order in SIXTEEN₃ coincide with the logic of FOUR₂, namely first degree entailment. This observation may be taken as a further indication of the significance of first degree entailment. In the present setting, however, it becomes rather natural to consider also logical systems in the language obtained by combining the vocabulary of the logic of the truth order and the falsity order. We semantically define the logics of the two orderings in the extended language and in both cases axiomatize a certain fragment comprising three unary operations: a negation, an involution, and their combination. We also suggest two other definitions of logics in the full language, including a bi-consequence system. In other words, in addition to presenting first degree entailment as a useful 16-valued logic, we define further useful 16-valued logics for reasoning about truth and (non-)falsity. We expect these logics to be an interesting and useful instrument in information processing, especially when we deal with a net of hierarchically interconnected computers. We also briefly discuss Arieli's and Avron's notion of a logical bilattice and state a number of open problems for future research
Keywords bi-consequence logic  first degree entailment  generalized truth values  (logical) bilattices  trilattices  multilattices
Categories (categorize this paper)
DOI 10.2307/30226835
 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: 16,667
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

View all 19 references / Add more references

Citations of this work BETA
Heinrich Wansing (2008). Constructive Negation, Implication, and Co-Implication. Journal of Applied Non-Classical Logics 18 (2-3):341-364.

View all 14 citations / Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

39 ( #85,374 of 1,726,991 )

Recent downloads (6 months)

8 ( #84,758 of 1,726,991 )

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.