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A Coalgebraic Approach to Unification Semantics of Logic Programming

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Book cover The Art of Modelling Computational Systems: A Journey from Logic and Concurrency to Security and Privacy

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11760))

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Abstract

In the version of logic programming (LP) based on interpretations where variables occur in atoms, a goal reduction via unification can be seen as a transition labelled by the most general unifier. Categorically, it is thus natural to model a logic program as a coalgebra. In the paper we represent: (i) goals as the substitutive monoid freely generated by the predicate symbols; (ii) the LTS as the structured coalgebra defined by the SOS rules implicit in the LP semantics; (iii) the bisimulation semantics of a logic program as its image on the final coalgebra.

Research supported by the MIUR PRINs 201784YSZ5 ASPRA: Analysis of program analyses and by University of Pisa PRA_2018_66 DECLWARE: Metodologie dichiarative per la progettazione e il deployment di applicazioni.

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References

  1. Adamek, J., Rosicky, J.: Locally Presentable and Accessible Categories. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (1994)

    Book  MATH  Google Scholar 

  2. Amato, G., Lipton, J., McGrail, R.: On the algebraic structure of declarative programming languages. Theor. Comp. Sci. 410(46), 4626–4671 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. Barr, M.: Terminal coalgebras in well-founded set theory. Theor. Comp. Sci. 114(2), 299–315 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bonchi, F., Montanari, U.: Reactive systems, (semi-)saturated semantics and coalgebras on presheaves. Theor. Comput. Sci. 410(41), 4044–4066 (2009). Festschrift for Mogens Nielsen’s 60th birthday

    Article  MathSciNet  MATH  Google Scholar 

  5. Bonchi, F., Zanasi, F.: Bialgebraic semantics for logic programming. Logical Methods Comput. Sci. 11(1), 1–47 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  6. Bonsangue, M.M., Hansen, H.H., Kurz, A., Rot, J.: Presenting distributive laws. In: Heckel, R., Milius, S. (eds.) CALCO 2013. LNCS, vol. 8089, pp. 95–109. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40206-7_9

    Chapter  Google Scholar 

  7. Bruni, R., Montanari, U., Rossi, F.: An interactive semantics of logic programming. Theory Pract. Logic Program. 1(6), 647–690 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  8. Corradini, A., Asperti, A.: A categorical model for logic programs: indexed monoidal categories. In: de Bakker, J.W., de Roever, W.-P., Rozenberg, G. (eds.) REX 1992. LNCS, vol. 666, pp. 110–137. Springer, Heidelberg (1993). https://doi.org/10.1007/3-540-56596-5_31

    Chapter  Google Scholar 

  9. Corradini, A., Heckel, R., Montanari, U.: From SOS specifications to structured coalgebras: how to make bisimulation a congruence. ENTCS 19, 118–141 (1999)

    MathSciNet  MATH  Google Scholar 

  10. Corradini, A., Montanari, U.: An algebraic semantics for structured transition systems and its applications to logic programs. Theor. Comput. Sci. 103(1), 51–106 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  11. de Simone, R.: Higher-level synchronising devices in meije-sccs. Theor. Comput. Sci. 37, 245–267 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  12. Falaschi, M., Levi, G., Palamidessi, C., Martelli, M.: Declarative modeling of the operational behavior of logic languages. Theor. Comput. Sci. 69(3), 289–318 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  13. Finkelstein, S.E., Freyd, P., Lipton, J.: Logic programming in tau categories. In: Pacholski, L., Tiuryn, J. (eds.) CSL 1994. LNCS, vol. 933, pp. 249–263. Springer, Heidelberg (1995). https://doi.org/10.1007/BFb0022261

    Chapter  MATH  Google Scholar 

  14. Gray, J.: The category of sketches as a model for algebraic semantics. In: Categories in Computer Science and Logic. Contemporary Mathematics, vol. 92. AMS (1989)

    Google Scholar 

  15. Komendantskaya, E., Power, J.: Coalgebraic semantics for derivations in logic programming. In: Corradini, A., Klin, B., Cîrstea, C. (eds.) CALCO 2011. LNCS, vol. 6859, pp. 268–282. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22944-2_19

    Chapter  MATH  Google Scholar 

  16. Komendantskaya, E., Power, J.: Logic programming: laxness and saturation. J. Log. Algebr. Meth. Program. 101, 1–21 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  17. Komendantskaya, E., Power, J., Schmidt, M.: Coalgebraic logic programming: from semantics to implementation. J. Log. Comput. 26(2), 745–783 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  18. Kowalski, R.A.: Algorithm = logic + control. Comm. ACM 22(7), 424–436 (1979)

    Article  MATH  Google Scholar 

  19. Lanese, I., Montanari, U.: Mapping fusion and synchronized hyperedge replacement into logic programming. Theory Pract. Logic Program. 7(1–2), 123–151 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  20. Leifer, J.J., Milner, R.: Deriving bisimulation congruences for reactive systems. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 243–258. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-44618-4_19

    Chapter  Google Scholar 

  21. Levi, G., Palamidessi, C.: Contributions to the semantics of logic perpetual processes. Acta Inf. 25(6), 691–711 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  22. Lloyd, J.W.: Foundations of Logic Programming, 2nd edn. Springer, Heidelberg (1987). https://doi.org/10.1007/978-3-642-83189-8

    Book  MATH  Google Scholar 

  23. Montanari, U., Rossi, F.: Perfect relaxation in constraint logic programming. In: ICLP 1991, pp. 223–237. MIT Press (1991)

    Google Scholar 

  24. Montanari, U., Sammartino, M., Tcheukam, A.: Decomposition structures for soft constraint evaluation problems: an algebraic approach. In: Heckel, R., Taentzer, G. (eds.) Graph Transformation, Specifications, and Nets. LNCS, vol. 10800, pp. 179–200. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-75396-6_10

    Chapter  Google Scholar 

  25. Turi, D., Plotkin, G.D.: Towards a mathematical operational semantics. In: LICS 1997, pp. 280–291. IEEE Computer Society (1997)

    Google Scholar 

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Acknowledgement

We thank Andrea Corradini who read a preliminary version of this paper and helped us to improve the presentation. We also thank the anonymous referees for their useful remarks and pointers to the literature.

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Authors and Affiliations

  1. Dipartimento di Informatica, Università di Pisa, Pisa, Italy

    Roberto Bruni & Ugo Montanari

  2. Dipartimento di Matematica, Università di Pisa, Pisa, Italy

    Giorgio Mossa

Authors
  1. Roberto Bruni
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  2. Ugo Montanari
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  3. Giorgio Mossa
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Correspondence to Roberto Bruni .

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Editors and Affiliations

  1. Universidade Federal de Minas Gerais, Belo Horizonte, Brazil

    Mário S. Alvim

  2. University of Athens, Athens, Greece

    Kostas Chatzikokolakis

  3. Federal University of Rio Grande do Norte - UFRN, Natal, Brazil

    Carlos Olarte

  4. CNRS & University Javeriana Cali, Palaiseau, France

    Frank Valencia

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Bruni, R., Montanari, U., Mossa, G. (2019). A Coalgebraic Approach to Unification Semantics of Logic Programming. In: Alvim, M., Chatzikokolakis, K., Olarte, C., Valencia, F. (eds) The Art of Modelling Computational Systems: A Journey from Logic and Concurrency to Security and Privacy. Lecture Notes in Computer Science(), vol 11760. Springer, Cham. https://doi.org/10.1007/978-3-030-31175-9_13

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  • DOI: https://doi.org/10.1007/978-3-030-31175-9_13

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-030-31175-9

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