On Complexity of DeLP through Game Semantics On the Complexity of DeLP through Game Semantics ∗

Defeasible Logic Programming (DeLP) is a general argumentation based system for knowledge representation and reasoning. Its proof theory is based on a dialectical analysis where arguments for and against a literal interact in order to determine whether this literal is believed by a reasoning agent. The semantics GS is a declarative trivalued game-based semantics for DeLP that is sound and complete for DeLP proof theory. Complexity theory is an important tool for comparing different formalism and for helping to improve implementations whenever it is possible. In this work we address the problem of studying the complexity of some important decision problems in DeLP. Thus, we characterize the relevant decision problems in the context of DeLP and GS, and we define data and combined complexity for DeLP. Since DeLP computes every argument from a set of defeasible rules, it is of central importance to analyze the complexity of two decision problems. The first one can be defined as “Is a set of defeasible rules an argument for a literal under a defeasible logic program?”. We prove that this problem is P-complete. The second decision problem is “Does there exist an argument for a literal under a defeasible logic program?”. We prove that this problem is in NP. Furthermore, we study data complexity of query answering in the context of DeLP. As far as we know, data complexity has not been introduced in the context of argumentation systems.

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