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Is it possible to define logic programming for every logic that has implication and conjunction connectives? Does logic programming adds something new to the usual inference process. By usual inference process I mean the construction of the consequence set from the axioms - deriving all true statements. Does logic programming simply adds directionality/focus the the usual inference process or does logic programming add something more?

I am trying to model the beliefs, intentions and the goals of the BDI agent using substructural logic and for BDI agent implementation one is required to implement logic programming of the underlying logic. So - I am trying to understand what it means to implement logic programming for substructural modal logic with multiple modalities.

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