College Publications logo   College Publications title  
View Basket
Homepage Contact page
Cadernos de Lógica e Computação
Cadernos de Lógica e Filosofia
Cahiers de Logique et d'Epistemologie
Communication, Mind and Language
Cuadernos de lógica, Epistemología y Lenguaje
Encyclopaedia of Logic
IfColog series in Computational Logic
Law and Society
Logic PhDs
Logic, Methodology and Philosophy of Science
The Logica Yearbook
Neural Computing and Artificial Intelligence
The SILFS series
Studies in Logic
History of Logic
Logic and cognitive systems
Mathematical logic and foundations
Studies in Logic and Argumentation
Studies in Talmudic Logic
Texts in Mathematics
Digital Downloads
Information for authors
About us
Search for Books

Logic and cognitive systems


Automated Reasoning in Higher-Order Logic

Set Comprehension and Extensionality in Church's Type Theory

Chad E. Brown

Many mathematical and computational concepts can be represented in a natural way using higher-order logic. Consequently, higher-order logic has become an important topic of research. Automated Reasoning in Higher-Order Logic presents both a theoretical analysis of fragments of higher-order logic as well as a complete automated search procedure for an extensional form of higher-order logic.

The first part of the book provides a detailed presentation of the theory (syntax and semantics) of fragments of higher-order logic. The fragments differ in the amount of extensionality and set comprehension principles included. Three families of sequent calculi are defined and proven sound and complete with respect to appropriate model classes. Using the model constructions in the book, different versions of Cantor's theorem are determined to not be provable in certain fragments. In fact, some versions of Cantor's theorem are independent of other versions (in sufficiently weak fragments).

In the second part of the book, an automated proof procedure for extensional type theory is described. Proving completeness of such a higher-order search procedure is a nontrivial task. The book provides such a completeness proof by first proving completeness of the ground case and then proving appropriate lifting results.

Automated Reasoning in Higher-Order Logic is an essential document for researchers in higher-order logic and higher-order theorem proving. The book is also essential reading for programmers implementing or extending higher-order search procedures.

Users of higher-order theorem provers can use the book to improve their understanding of the underlying logical systems.


Buy from Amazon: UK   US   

© 2005–2017 College Publications / VFH webmaster