College Publications logo   College Publications title  
View Basket
Homepage Contact page
   
 
AiML
Academia Brasileira de Filosofia
Algorithmics
Arts
Cadernos de Lógica e Computação
Cadernos de Lógica e Filosofia
Cahiers de Logique et d'Epistemologie
Communication, Mind and Language
Computing
Comptes Rendus de l'Academie Internationale de Philosophie des Sciences
Cuadernos de lógica, Epistemología y Lenguaje
DEON
Dialogues
Economics
Encyclopaedia of Logic
Filosofia
Handbooks
Historia Logicae
IfColog series in Computational Logic
Journal of Applied Logics - IfCoLog Journal
Journals
Landscapes
Logics for New-Generation AI
Logic and Law
Logic and Semiotics
Logic PhDs
Logic, Methodology and Philosophy of Science
The Logica Yearbook
Neural Computing and Artificial Intelligence
Philosophy
Research
The SILFS series
Studies in Logic
History of Logic
Logic and cognitive systems
Mathematical logic and foundations
Studies in Logic and Argumentation
Logic and Bounded Rationality
Studies in Talmudic Logic
Student Publications
Systems
Texts in Logic and Reasoning
Texts in Mathematics
Tributes
Other
Digital Downloads
Information for authors
About us
Search for Books
 



Studies in Logic


Back

Logic and Conditional Probability

A Synthesis

Philip Calabrese

This monograph develops an algebra of Boolean fractions, (a|b) - ordered pairs of propositions or events - "a if b", "event a given event b". In nine chapters, the author shows that these conditional propositions (together with their associated instantiations or models):

Provide logical elements that better represent and more faithfully facilitate manipulation of certain and uncertain conditional information

Extend the Boole's algebra of 2-valued statements to a 3-valued system that includes inapplicable statements - those whose condition may be false in some or all instances (examples, cases, models...)

Allow a definition of the probability of an arbitrary Boolean proposition

Non-trivially combine Boolean logic with standard conditional probability theory

Provide a complete and adequate development of the crucial 4th operation for Boolean logic, namely conditioning, including iterated conditioning

Provide an expanded theory of deduction defined in terms of the extended operations on the Boolean fractions

Admit a variety of deduction relations, and that the deductively closed sets generated by some initial set of conditionals can be calculated

Extend the ordinary function operations of sum, difference, product & quotient to real-valued functions with possibly different or overlapping domains of definition

Represent & simplify complex conditional statements in Bayesian expert systems used to calculate maximum information entropy solutions

Explicate the logic of quantum measurements by better expressing the changing conditions in quantum mechanics

25 October 2017

978-1-84890-258-9

Buy from Amazon: UK   US   


Review






© 2005–2024 College Publications / VFH webmaster