About insufficiency of grammars for semantic validity of computer programs and ontologies as an alternative approach

Main Article Content

Laurence R. Ugalde


The Rice theorem proves that semantic properties of computer programs are not decidable. In this paper it will be proved that grammars are not a sufficient mean to provide semantic validity on computer programs, first as a corollary of the Rice theorem and then as an independent theorem. Once that is proved that they are not sufficient, the use of ontologies are presented as a viable alternative to grammars and the additional benefits they offer. Finally, an implementation of a programming language is presented which is not based in any grammar, but in an ontology.


Download data is not yet available.

Article Details



Benson, D. C. (1999), “The moment of proof: Mathematical epiphanies,†Oxford University Press, 1st. edition.

Chaitin, G. J. (2007), “Thinking about Gödel and Turing: Essays on complexity 1970-2007,†World Scientific Publishing.

Ferreirós, J. (2007), “Labyrinth of thought: A history of set theory and its role in mathematical thought,†Birkhuser, 2nd revised edition.

Feyerabend, P. (2010), “Against Method,†Verso, 4th. edition.

Gödel, K. (1992), “On the formally undecidable propositions of Principia Mathematica and related systems,†Oxford University Press.

Hawkings, S. W. & Mlodinow, L. (2010), “The grand design,†Bantam Books, 1st. edition.

Hofstadter, D. R. (1999) “Gödel, Escher, Bach: an eternal golden braid,†Basic Books, 20th anniversary edition.

Nagel, T. (1981), “Introduction to number theory,†Chelsea Pub Co, 2nd. edition.

Pelletier, F. J. (1994), “The principle of semantic compositionality,†Topoi, Vol. 13, pp. 11–24.

Pelletier, F. J. (2001), “Did Frege believe Frege’s principle?,†Journal of Logic, Language, and Information, pp. 87–114.

Rice, H. G. (1953), “Classes of recursively enumerable sets and their decision problems,†Trans. Amer. Math. Soc., Vol. 74, pp. 358366.

Scott, D. & Strachey, C. (1971), “Towards a mathematical semantics for computer languages,†Oxford Programming Research Group Technical Monograph.

Sebesta, R. W. (2010), “Concepts of programming languages,†Addison-Wesley, 9th edition.

Staab, S. & Studer, R. (2009), “Handbook on ontologies,†chapter “What is an ontology?,†Springer Publishing Company, Incorporated, 2nd edition.

Turing, A. (1938), “On computable numbers, with an application to the entscheidungsproblem,†A correction. Proceedings of the London Mathematical Society, Vol. 43, No. 6, pp. 544546.

Ugalde, L. R. (2015), “Cooperative development and human interface of a computer algebra system with the FÅrmulæ framework,†21st Confer ence on Applications of Computer Algebra (ACA 2015), pp. 38–41. http://www.singacom.uva.es/ACA2015/latex/ACAproc.pdf.

Ugalde, L. R. (2015), The FÅrmulæ website. http://www.formulae.org.

Ugalde, L. R. (2018), The “Rosetta code†website, task “Universal turing machineâ€, section “FÅrmulæâ€. http://rosettacode.org/wiki/Universal_Turing_machine#F.C5.8Drmul.C3.A6.