Skip to main content
Log in

Simplified handling of iterated term schemata

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

Abstract

We propose an extension of primal grammars (Hermann and Galbavý, Theor Comp Sci 176(1–2):111–158, 1997), called P-grammars. Primal grammars are term grammars with a high expressive power and good computational properties. P-grammars have exactly the same properties but are more modular, more concise, and easier to use, as shown by some examples. We prove that P-grammars are exponentially more concise than primal grammars. An algorithm, called p2primal, transforming any P-grammar into an equivalent primal grammar is provided, thus making the original formalism much easier to handle from a practical point of view.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Amaniss, A., Hermann, M., Lugiez, D.: Etude comparative des méthodes de schématisation de séquences infinies de termes du premier ordre. Research Report 93-R-114, Centre de Recherche en Informatique de Nancy (1993)

  2. Aravantinos, V.: Schémas de preuves et de formules: vers plus de structure et d’efficacité en déduction automatique. Master thesis, Institut National Polytechnique de Grenoble & Université Joseph Fourier (2007). http://membres-lig.imag.fr/aravantinos

  3. Aravantinos, V., Caferra, R., Peltier, N.: A schemata calculus for propositional logic. In: Giese, M., Waaler, A. (eds.) TABLEAUX. Lecture Notes in Computer Science, vol. 5607, pp. 32–46. Springer (2009)

  4. Bensaid, H., Caferra, R., Peltier, N.: Dei: a theorem prover for terms with integer exponents. In: Schmidt, R.A. (ed.) CADE. Lecture Notes in Computer Science, vol. 5663, pp. 146–150. Springer (2009)

  5. Bensaid, H., Caferra, R., Peltier, N.: Perfect discrimination graphs: indexing terms with integer exponents. In: Giesl, J., Hähnle, R. (eds.) International Joint Conference on Automated Reasoning. Lecture Notes in Computer Science. Springer (2010, to appear)

  6. Chen, H., Hsiang, J., Kong, H.: On finite representations of infinite sequences of terms. In: Conditional and Typed Rewriting Systems. LNCS 516, pp. 100–114. Springer (1990)

  7. Comon, H.: On unification of terms with integer exponents. Math. Syst. Theory 28, 67–88 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  8. Comon, H., Dauchet, M., Gilleron, R., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree automata techniques and applications. http://www.grappa.univ-lille3.fr/tata (2005). Release 12 October 2007

  9. Hermann, M.: Divergence des systèmes de réécriture et schématisation des ensembles infinis de termes. Habilitation, Université Henri Poincaré Nancy 1 (1994)

  10. Hermann, M.: Overview of existing recurrent schematizations. In: Proc. of the CADE-13 Workshop on Term Schematization and their Applications (1996)

  11. Hermann, M., Galbavý, R.: Unification of infinite sets of terms schematized by primal grammars. Theor. Comp. Sci. 176(1–2), 111–158 (1997)

    Article  MATH  Google Scholar 

  12. Peltier, N.: The first order theory of primal grammars is decidable. Theor. Comp. Sci. 323, 267–320

  13. Salzer, G.: The unification of infinite sets of terms and its applications. In: Logic Programming and Automated Reasoning (LPAR’92). LNAI 624, pp. 409–429. Springer (1992)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vincent Aravantinos.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aravantinos, V., Caferra, R. & Peltier, N. Simplified handling of iterated term schemata. Ann Math Artif Intell 58, 155–183 (2010). https://doi.org/10.1007/s10472-010-9200-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10472-010-9200-3

Keywords

Mathematics Subject Classification (2010)

Navigation