Premium
Classification of Boolean Algebras of Logic and Probabilities Defined on them by Classical Models
Author(s) -
Amer Mohamed A.
Publication year - 1985
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19850313106
Subject(s) - citation , order (exchange) , mathematics , boolean algebra , computer science , library science , algebra over a field , artificial intelligence , discrete mathematics , pure mathematics , finance , economics
L, t 1, bc a formal language of a logical spstom estcnding classical sentential logic, ant1 let S(L) be the set of all L-sentences. The relat'ioii defined on S(L) by oI o2 iff (o, f-) 02) is a thcoreni of an arbitrary. but fixed. L-theory, is an cquivalence relation. S(L)/is a Boolean alge1)ra (see 171 for basic dtfinitions and properties) under tlic. operations induced by A . v. and 1. The sniallest and greatest elements of a Boolean nlpl, ia shall he dcnoted l)y 0 a.nd 1. respect,ively. Also, 0 and 1 shall denote. respectiwly. the truth values "false" and "true".