## An Equational Re-Engineering of Set Theories (1998)

Venue: | Automated Deduction in Classical and Non-Classical Logics, LNCS 1761 (LNAI |

Citations: | 6 - 6 self |

### BibTeX

@INPROCEEDINGS{Formisano98anequational,

author = {Andrea Formisano and Eugenio Omodeo},

title = {An Equational Re-Engineering of Set Theories},

booktitle = {Automated Deduction in Classical and Non-Classical Logics, LNCS 1761 (LNAI},

year = {1998},

pages = {175--190},

publisher = {Springer}

}

### OpenURL

### Abstract

New successes in dealing with set theories by means of state-of-the-art theoremprovers may ensue from terse and concise axiomatizations, such as can be moulded in the framework of the (fully equational) Tarski-Givant map calculus. In this paper we carry out this task in detail, setting the ground for a number of experiments. Key words: Set theory, relation algebras, first-order theorem-proving, algebraic logic. 1 Introduction Like other mature fields of mathematics, Set Theory deserves sustained efforts that bring to light richer and richer decidable fragments of it [5], general inference rules for reasoning in it [23, 2], effective proof strategies based on its domain-knowledge, and so forth. Advances in this specialized area of automated reasoning tend, in spite of their steadiness, to be slow compared to the overall progress in the field. Many experiments with set theories have hence been carried out with standard theorem-proving systems. Still today such experiments pose consider...