Representation of inferential contexts may need logical systems that could be different from classical ones, particularly when the pretension is to model how inferences are in concrete scientific practices. Such contexts will be represented by means of different consequence relations, the so called consequence modulo X, for X as a set of formulas, a set of models or a set of additional rules, which are defined by following (in part) Makinson's method. Structural rules of the classical relation leads us to consider a variety of contexts that share a closure relation, though compactness may fail and uniform substitution is not accomplished. Taking into account such inferential contexts, abduction could be tackled in two ways: to define abductive problems in a given context or, transversally, considering a class of possible contexts, then a modal framework could be proposed to interpret abductive processes. The first will be developed when a set of sentences is the modulo of the corresponding consequence relation, then the process of constructing inferential contexts is studied as the result of applying abductive norms. To define calculi that could be used to search abductive solutions, a criterion of compactness/completeness is given, though problems arise when the semantics is considered w.r.t. the class of finite models and, on the other hand, when the language is a second order one. The second perspective will be pointed out. References [1] Aliseda, A.: Abductive Reasoning: Logical Investigations into Discovery and Explanation. Volume 330 of Synthese Library. Springer (2006) [2] Amor, J. A.: Compacidad en la logica de primer orden y su relacion con el Toerema de Completud Facultad de Ciencias de la U. N. A. M. (2006) [3] Hintikka, J.: "What is abduction? The fundamental problem of contemporary epistemology". Transactions of the Charles S. Peirce Society, 34 (3) (1998) 503 - 533.[4] Makinson, D.: "Bridges between Classical Logic and Nonmonotonic Logic", Logic Journal of the IGPL 11, 1 (2003) [5] Nepomuceno, A., Soler, F., Aliseda, A.: "Searching the Unity of Science: from Classical Logic to Abductive Logical Systems" Selected paper Lisbon Colloquium for the Philosophy of Science. To appear (2008)"