On the Decidability of Formulae Involving Continuous and Closed Functions

Cantone, Domenico; Omodeo, Eugenio G.

On the Decidability of Formulae Involving Continuous and Closed Functions

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Proceedings of the Eleventh International Joint Conference on Artificial Intelligence. Automated Deduction. 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.

Domenico Cantone, and Eugenio G. Omodeo. 1989. On the Decidability of Formulae Involving Continuous and Closed Functions. In Proceedings of the Eleventh International Joint Conference on Artificial Intelligence, IJCAI-89. IJCAI, 425–429. https://ijcai.org/proceedings/1989/68

@inproceedings{ijcai1989p68,
  title     = {On the Decidability of Formulae Involving Continuous and Closed Functions},
  author    = {Cantone, Domenico and Omodeo, Eugenio G.},
  booktitle = {Proceedings of the Eleventh International Joint Conference on
               Artificial Intelligence, {IJCAI-89}},
  publisher = {International Joint Conferences on Artificial Intelligence},
  editor    = {N. S. Sridharan},
  pages     = {425--429},
  year      = {1989},
  month     = {8},
  note      = {Automated Deduction},
  url       = {https://ijcai.org/proceedings/1989/68},
}

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TI  - On the Decidability of Formulae Involving Continuous and Closed Functions
AU  - Cantone, Domenico
AU  - Omodeo, Eugenio G.
T2  - Proceedings of the Eleventh International Joint Conference on Artificial Intelligence, IJCAI-89
PB  - International Joint Conferences on Artificial Intelligence
PY  - 1989
SP  - 425
EP  - 429
UR  - https://ijcai.org/proceedings/1989/68
ER  -