An Overview of a Formal Framework for Managing Mathematics
Annals of Mathematics and Artificial Intelligence
Understanding expression simplification
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
A computational approach to reflective meta-reasoning about languages with bindings
Proceedings of the 3rd ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding
A Rational Reconstruction of a System for Experimental Mathematics
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
A Rational Reconstruction of a System for Experimental Mathematics
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
CTP-based programming languages?: considerations about an experimental design
ACM Communications in Computer Algebra
Formalizing and operationalizing industrial standards
FASE'11/ETAPS'11 Proceedings of the 14th international conference on Fundamental approaches to software engineering: part of the joint European conferences on theory and practice of software
MathScheme: project description
MKM'11 Proceedings of the 18th Calculemus and 10th international conference on Intelligent computer mathematics
The formalization of syntax-based mathematical algorithms using quotation and evaluation
CICM'13 Proceedings of the 2013 international conference on Intelligent Computer Mathematics
A universal machine for biform theory graphs
CICM'13 Proceedings of the 2013 international conference on Intelligent Computer Mathematics
| Hi-index | 0.00 |
An axiomatic theoryrepresents mathematical knowledge declaratively as a set of axioms. An algorithmic theoryrepresents mathematical knowledge procedurally as a set of algorithms. A biform theoryis simultaneously an axiomatic theory and an algorithmic theory. It represents mathematical knowledge both declaratively and procedurally. Since the algorithms of algorithmic theories manipulate the syntax of expressions, biform theories--as well as algorithmic theories--are difficult to formalize in a traditional logic without the means to reason about syntax. Chironis a derivative of von-Neumann-Bernays-Gödel (nbg) set theory that is intended to be a practical, general-purpose logic for mechanizing mathematics. It includes elements of type theory, a scheme for handling undefinedness, and a facility for reasoning about the syntax of expressions. It is an exceptionally well-suited logic for formalizing biform theories. This paper defines the notion of a biform theory, gives an overview of Chiron, and illustrates how biform theories can be formalized in Chiron.