Probabilities defined on standard and non-standard cylindric set algebras

Cylindric set algebras are algebraizations of certain logical semantics. The topic surveyed here, i.e. probabilities defined on cylindric set algebras, is closely related, on the one hand, to probability logic (to probabilities defined on logical formulas), on the other hand, to measure theory. The set algebras occuring here are associated, in particular, with the semantics of first order logic and with non-standard analysis. The probabilities introduced are partially continous, they are continous with respect to so-called cylindric sums.

[1]  A. Tarski,et al.  Cylindric Set Algebras , 1981 .

[2]  Alfred Tarski,et al.  Measures in Boolean algebras , 1948 .

[3]  C. J. Everett,et al.  Projective Algebra I , 1946 .

[4]  J. Hintikka,et al.  Aspects of Inductive Logic. , 1968 .

[5]  Existence Theorems in Probability Theory , 1996 .

[6]  I. Németi,et al.  Cylindric-like algebras and algebraic logic , 2013 .

[7]  A. Robinson.  Non-standard analysis , 1966 .

[8]  Ian Hacking,et al.  An Introduction to Probability and Inductive Logic: Contents , 2001 .

[9]  J. Fenstad.  Representations of Probabilities Defined on First Order Languages , 1967 .

[10]  M. Ferenczi.  Probabilities on first order models , 2005 .

[11]  Miklós Ferenczi.  Non-standard Stochastics with a First Order Algebraization , 2010, Stud Logica.

[12]  D. Scott,et al.  Assigning Probabilities to Logical Formulas , 1966 .

[13]  Tarek Sayed Ahmed,et al.  Algebraic Logic, Where Does it Stand Today? , 2005, Bulletin of Symbolic Logic.

[14]  J. D. Monk,et al.  Mathematical Logic , 1976 .

[15]  Robert Goldblatt,et al.  Lectures on the hyperreals , 1998 .

[16]  M. Ferenczi,et al.  Measures on cylindric algebras , 1983 .

[17]  M. Ferenczi.  The polyadic generalization of the Boolean axiomatization of fields of sets , 2012 .

[18]  Martin Davis,et al.  Applied Nonstandard Analysis , 1977 .

[19]  Martin Meier,et al.  An infinitary probability logic for type spaces , 2012 .

[20]  D. A. Vladimirov,et al.  Boolean algebras in analysis , 2002 .

[21]  María Manzano,et al.  Extensions of First-Order Logic , 1996 .

[22]  H. Gaifman.  Concerning measures in first order calculi , 1964 .

[23]  Zoran Ognjanovic,et al.  A first-order conditional probability logic , 2012, Log. J. IGPL.

[24]  J. Łoś.  On the axiomatic treatment of probability , 1955 .

[25]  I. Hacking.  An Introduction to Probability and Inductive Logic , 2001 .