Various types of everyday arguments are represented as argumentation schemes, originating from the Legal Argumentation literature. The recent achievements in this domain can be applied to multi-agent settings to enrich the paradigmatic aspects of communication and reasoning. Agents typically populate complex environments where incompleteness and inconsistency of information is rather a rule than exception. Although the problem how to tackle inconsistencies is already present in argumentation, a paraconsistent (that is, tolerating inconsistency) approach is still missing from the literature. The contribution of this research is a computationally-friendly framework for formalizing paraconsistent argumentation schemes. This is achieved by extending agent’s reasoning capabilities with non-deductive methods rooted in argumentation. To this end we provide a generic paraconsistent program template for implementation of various argumentation schemes. Our methodology is strongly influenced by ideas underlying 4QL: a four-valued, rule-based, Datalog ¬¬ -like query language. Thanks to its properties, the tractability of the solution (so hardly obtainable in logical modeling) has been reached. The paper concludes with examples of several paraconsistent argumentation schemes implemented in 4QL.