Negation as a Resource: a Novel View on Answer Set Semantics

In recent work, we provided a formulation of ASP programs in terms of linear logic theories. Answer sets were characterized in terms of maximal tensor conjunctions provable from such theories. In this paper, we propose a full comparison between Answer Set Semantics and its variation obtained by interpreting literals (including negative literals) as resources, which leads to a different interpretation of negation. We argue that this novel view can be of both theoretical and practical interest, and we propose a modified Answer Set Semantics that we call Resource-based Answer Set Semantics. One advantage is that of avoiding inconsistencies, so every program has a (possibly empty) resource-based answer set. This implies however the introduction of a different way of representing constraints.

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