---
title: "On the Decidability of Formulae Involving Continuous and Closed Functions"
authors:
  - "Domenico Cantone"
  - "Eugenio G. Omodeo"
doi: ""
url: "https://ijcai.org/proceedings/1989/68"
pdf: "https://ijcai.org/proceedings/1989/0068.pdf"
venue: "Proceedings of the Eleventh International Joint Conference on Artificial Intelligence"
year: 1989
pages: "425-429"
track: "Automated Deduction"
keywords:
---

# On the Decidability of Formulae Involving Continuous and Closed Functions

Domenico Cantone, Eugenio G. Omodeo

*Proceedings of the Eleventh International Joint Conference on Artificial Intelligence*, pages 425-429.

## Abstract

The satisfiability problem for a syllogistic embracing E, \, Boolean set operations, the Kurato~ski topological closure operation -, and contmuous and closed maps between topological spaces, along with the operations of point evaluation , set image, and inverse set image, is solved for formulae that meet a particular syntactic non-circularity property. The unquantified interpreted language £ 2 • 00 to be considered has infinitely many sorts of variables, each corresponding to a different topological space. Three kinds of variables are available, namely, individual, set, and map variables. Individual variables of a given sort are supposed to range over the universe of that sort , whereas set variables range over the subsets of t~e appropriate universe. Finally , each map vanable ranges over the collection of continuous or closed maps between two appropriate topological spaces.