Fuzzy Positive Primitive Formulas
Can non-classical logic contribute to the analysis of complexity in computer science? In this paper, we give a step towards the solution of this open problem, taking a logical model-theoretic approach to the analysis of complexity in fuzzy constraint satisfaction. We study fuzzy positive-primitive sentences, and we present an algebraic characterization of classes axiomatized by this kind of sentences in terms of homomorphisms and finite direct products. The ultimate goal is to study the expressiveness and reasoning mechanisms of non-classical languages, with respect to constraint satisfaction problems and, in general, in modelling decision scenarios.
KeywordsFuzzy constraint satisfaction Preference modeling Fuzzy logics Model theory
The research leading to these results has received funding from RecerCaixa. This project has also received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement No 689176 (SYSMICS project), and by the projects RASO TIN2015-71799-C2-1-P, CIMBVAL TIN2017-89758-R, and the grant 2017SGR-172 from the Generalitat de Catalunya. The author would like to thank the reviewers for their comments, and the Algorithmic Decision Theory Group of Data61 (UNSW, Sydney) for hosting me during this research.
- 10.Dubois, D., Fargier, H., Prade, H.: The calculus of fuzzy restrictions as a basis for flexible constraint satisfaction. In: 2nd IEEE International Conference on Fuzzy Systems, IEEE (1993)Google Scholar
- 16.Kolmogorov, V., Krokhin, A., Rolinek, M.: The Complexity of General-Valued CSPs. In: FOCS, pp. 1246–1258 (2015)Google Scholar
- 17.Krokhin, A.A., Zivny, S.: The Complexity of Valued CSPs. The Constraint Satisfaction Problem, pp. 233–266 (2017)Google Scholar
- 19.Moura J., Prade, H.: Logical analysis of fuzzy constraint satisfaction problems. In: 7nd IEEE International Conference on Fuzzy Systems. IEEE (1993)Google Scholar
- 20.Pini, M.S., Rossi, F., Venable, K.B.: Compact preference representation via fuzzy constraints in stable matching problems. In: Rothe, J. (ed.) Compact Preference Representation via Fuzzy Constraints in Stable Matching Problems. LNCS (LNAI), vol. 10576, pp. 333–338. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-67504-6_23CrossRefGoogle Scholar
- 21.Rossi, F., Brent, K., Walsh, T.: A short introduction to preferences. In: Synthesis Lectures on Artificial Intelligence and Machine Learning. Morgan and Claypool Pub (2011)Google Scholar
- 22.Horcík, R., Moraschini, T., Vidal, A.: An algebraic approach to valued constraint satisfaction. In: 26th EACSL Annual Conference on Computer Science Logic, pp. 42:1–42:20 (2017)Google Scholar
- 25.Ruttkay, Z.: Fuzzy constraint satisfaction. In: 3rd IEEE International Conference on Fuzzy Systems. IEEE (1994)Google Scholar
- 26.Schiex, T., Fargier, H., Verfaillie, G.: Valued constraint satisfaction problems: Hard and easy problems. In: Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence (IJCAI 95), pp. 631–639 (1995)Google Scholar