David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Studia Logica 92 (2):265 - 280 (2009)
In their useful logic for a computer network Shramko and Wansing generalize initial values of Belnap’s 4-valued logic to the set 16 to be the power-set of Belnap’s 4. This generalization results in a very specific algebraic structure — the trilattice SIXTEEN 3 with three orderings: information, truth and falsity. In this paper, a slightly different way of generalization is presented. As a base for further generalization a set 3 is chosen, where initial values are a — incoming data is asserted, d — incoming data is denied, and u — incoming data is neither asserted nor denied, that corresponds to the answer “don’t know”. In so doing, the power-set of 3, that is the set 8 is considered. It turns out that there are not three but four orderings naturally defined on the set 8 that form the tetralattice EIGHT 4 . Besides three ordering relations mentioned above it is an extra uncertainty ordering. Quite predictably, the logics generated by a –order (truth order) and d –order (falsity order) coincide with first-degree entailment. Finally logic with two kinds of operations ( a –connectives and d –connectives) and consequence relation defined via a –ordering is considered. An adequate axiomatization for this logic is proposed.
|Keywords||Generalized truth values Dunn–Belnap logic Shramko–Wansing logic bilattice trilattice tetralattice first-degree entailment|
|Categories||categorize this paper)|
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
Alan Anderson, Belnap R., D. Nuel & J. Michael Dunn (1992). Entailment: The Logic of Relevance and Necessity, Vol. Ii. Princeton University Press.
Ofer Arieli & Arnon Avron (1996). Reasoning with Logical Bilattices. Journal of Logic, Language and Information 5 (1):25--63.
N. D. Belnap (1977). A Useful Four-Valued Logic. In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
Nuel Belnap (1977). How a Computer Should Think. In G. Ryle (ed.), Contemporary Aspects of Philosophy. Oriel Press Ltd..
J. Michael Dunn (1976). Intuitive Semantics for First-Degree Entailments and 'Coupled Trees'. Philosophical Studies 29 (3):149-168.
Citations of this work BETA
Dmitry Zaitsev & Yaroslav Shramko (2013). Bi-Facial Truth: A Case for Generalized Truth Values. Studia Logica 101 (6):1299-1318.
Similar books and articles
Didier Dubois & Henri Prade (1996). New Trends and Open Problems in Fuzzy Logic and Approximate Reasoning. Theoria 11 (3):109-121.
Nicholas J. J. Smith (2012). Many-Valued Logics. In Gillian Russell & Delia Graff Fara (eds.), The Routledge Companion to Philosophy of Language. Routledge. 636--51.
Henri Prade (1996). New Trends and Open Problems in Fuzzy Logic and Approximate Reasoning. Theoria 11 (3):109-121.
Helena Rasiowa (1994). Axiomatization and Completeness of Uncountably Valued Approximation Logic. Studia Logica 53 (1):137 - 160.
Richard DeWitt (2005). On Retaining Classical Truths and Classical Deducibility in Many-Valued and Fuzzy Logics. Journal of Philosophical Logic 34 (5/6):545 - 560.
Fred Seymour Michael (2002). Entailment and Bivalence. Journal of Philosophical Logic 31 (4):289-300.
A. Avron & B. Konikowska (2008). Rough Sets and 3-Valued Logics. Studia Logica 90 (1):69 - 92.
Yaroslav Shramko & Heinrich Wansing (2006). Hyper-Contradictions, Generalized Truth Values and Logics of Truth and Falsehood. Journal of Logic, Language and Information 15 (4):403-424.
Yaroslav Shramko & Heinrich Wansing (2005). Some Useful 16-Valued Logics: How a Computer Network Should Think. [REVIEW] Journal of Philosophical Logic 34 (2):121 - 153.
Added to index2009-07-11
Total downloads14 ( #129,263 of 1,410,137 )
Recent downloads (6 months)2 ( #107,954 of 1,410,137 )
How can I increase my downloads?