There is work on how we can (can we ?) justify deduction. Justification is in this context an epistemological notion : on what grounds can we reasonably believe that deductive inference is valid ? Michael Dummett's 'The Justification of Deduction' in Truth and Other Enigmas addresses these matters.
As for logical pluralism, the following is not entirely easy reading but it does convey the basic thrust of logical pluralism :
"Crudely put, a pluralist maintains that there is more than one relation of logical
consequence," say Beall and Restall (p.25). The less crude statements of their position
involve a general principle, GTT (short for Generalised Tarski Thesis) which they
advocate as providing the correct account of logical consequence.
GTT: An argument is VALIDx if and only if, in every CASEx in which the premises
are true, so is the conclusion.
Different logical consequence relations will result from employing different notions
of a case or a different understanding of "every case"; and by spelling out the notion
of a case, you produce an instance of GTT. Beall and Restall then state that "Logical
pluralism is the claim that at least two different instances of GTT provide admissible
precisifications of logical consequence" (p. 29). There are additional conditions on
admissible precisifications corresponding to crucial features of the notion of logical
consequence, namely the requirements that the relations display features of necessity, formality and normativity. Beall and Restall argue that various different logical
consequence relations each meet all the criteria and are all true logical consequence
relations. In particular classical logic, intuitionistic logic and relevance logic are all
defended as providing admissible instances of GTT, with cases captured by Tarskian
models, stages of constructions and situations (including incomplete and complete
ones), respectively. (Rosanna Keefe, 'What logical pluralism cannot be', Synthese, Vol. 191, No. 7 (May 2014), pp. 1375-1390 : 1376; Beall, J. C., & Restall. G. (2006). Logical pluralism. Oxford: Clarendon Press.
Dummett, M. Truth and Other Enigmas, ISBN 10: 0715616501 / ISBN 13: 9780715616505
Published by Gerald Duckworth & Co Ltd, 1998.
Beall, J. C., & Restall, G. (2000). Logical pluralism. Australasian Journal of Philosophy, 78, 475-93
Beall, J. C., & Restall, G. (2001). Defending logical pluralism. In Logical Consequence: Rival Approaches. In J. Woods, & B. Brown (Eds.), Proceedings of the 1999 conference of the society of exact philosophy (pp. 1-22). Stanmore: Hermes.
Beall, J. C., & Restall. G. (2006). Logical Pluralism.
Published by Oxford University Press, United Kingdom (2006)
ISBN 10: 0199288410 ISBN 13: 9780199288410
'VALIDx' and 'CASEx' : in their text B & G type 'valid' and 'case' in lower case and subscript 'x'. I am unable to insert subscripts here.