Authors: Perović, Aleksandar
Doder, Dragan
Ognjanović, Zoran 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: On real-valued evaluation of propositional formulas
Journal: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume: 7153 LNCS
First page: 264
Last page: 277
Conference: 7th International Symposium on Foundations of Information and Knowledge Systems, FoIKS 2012; Kiel; Germany; 5 March 2012 through 9 March 2012
Issue Date: 15-Mar-2012
Rank: M33
ISBN: 978-3-642-28472-4
ISSN: 0302-9743
DOI: 10.1007/978-3-642-28472-4_15
Arguably, [0,1]-valued evaluation of formulas is dominant form of representation of uncertainty, believes, preferences and so on despite some theoretical issues - most notable one is incompleteness of any unrestricted finitary formalization. We offer an infinitary propositional logic (formulas remain finite strings of symbols, but we use infinitary inference rules with countably many premises, primarily in order to address the incompleteness issue) which is expressible enough to capture finitely additive probabilistic evaluations, some special cases of truth functionality (evaluations in Lukasiewicz, product, Gödel and logics) and the usual comparison of such evaluations. The main technical result is the proof of completeness theorem (every consistent set of formulas is satisfiable).
Keywords: Completeness theorems | Finite strings | Inference rules | Probabilistic evaluation | Propositional formulas | Propositional logic
Publisher: Springer Link

Show full item record


checked on Jul 13, 2024

Page view(s)

checked on May 9, 2024

Google ScholarTM




Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.