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Lukaszewicz-style Answer Set Programming: A Preliminary Report

The correspondence between Reiter’s default reasoning and logic programming has been exhaustively studied (e.g. [1], [2], [3]). A Contrario the relation with the many variants of the initial theory of Reiter seems far less known. This paper aims to present a preliminary investigation on applying a variant of default reasoning proposed by Witold Łukaszewicz [5] to extended logic programs. We show that the modification made to the notion of extension by Łukaszewicz has its counterpart as a relaxed notion of answer set of an extended logic program. As can be expected from this correspondence: (1) any extended logic program has always at least one relaxed answer set; (2) classical answer sets can be completely characterized among the set of relaxed answer sets of an extended logic program.