The study of the relationships between conjectures, hypotheses, refutations and speculations have been studied by Professor Enric Trillas and coworkers in the classical case to the point of having well clarified its main properties in rather general structures as the orthocomplemented lattices. In the framework of a possibilistic interpretation of fuzzy logic, these models have been studied from the point of view of a crisp reasoning. In this work these models defined by graduated consequences relations are studied under a fuzzy algebraic structure general enough that it can accommodate various common phenomena in natural language reasoning.
I would like to thank Professor Enric Trillas for their support in carrying out this work and for an enriching collaboration during my research career. Also I acknowledge the support of the Spanish Ministry for Economy and Innovation and the European Regional Development Fund (ERDF/FEDER) under grant TIN2011-29827-C02-02.
- 2.Itziar, G-H., Enric, T.: On an attempt to formalize guessing. In: Rudolf, S., González, V.S. (eds.) Soft Computing in Humanities and Social Sciences. Studies in Fuzziness and Soft Computing, vol 273, pp. 237–255, Springer, Berlin (2012)Google Scholar
- 4.Marvin, M.: The Emotion Machine. Commonsense Thinking, Artificial Intelligence, and the Future of the Human Mind. Simon and Schuster (2007)Google Scholar
- 5.Nilsson, N.J.: Human-level artificial intelligence? Be serious!. AI Mag. 26(4), 68 (2005)Google Scholar
- 6.Popper, K.R.: Conjectures and Refutations: The Growth of Scientific Knowledge. Harper and Row, New York (1968)Google Scholar
- 7.Tarski, A.: Methodology of deductive sciences. In: Logic, S. (ed.) Metamathematics, vol. 24, pp. 60–109. Clarendon Press, Oxford (1956)Google Scholar
- 9.Enric, T., Alsina, C., Pradera, A.: On a class of fuzzy set theories. In: IEEE International Fuzzy Systems Conference, 2007. July 2007, pp. 1-5 (2007)Google Scholar
- 10.Trillas, E., Sanchez, D.: Conjectures in de morgan algebras. In: 2012 Annual Meeting of the North American, Fuzzy Information Processing Society (NAFIPS), pp. 1–6 (2012)Google Scholar
- 11.Trillas, E.: Non contradiction, excluded middle, and fuzzy sets. In: Fuzzy Logic and Applications, pp. 1–11, Springer (2009)Google Scholar