Abstract
We contend that the well-founded semantics (WFS), for normal program, and similarly the well-founded semantics with explicit negation (WFSX), for extended ones are, by design, overly careful in deciding about the falsity of some atoms, by leaving them undefined.
We've dealt with this issue in normal programs and have previously defined the O-semantics, one that extends WFS by addjoining to it more negative assumptions, at the expense of undefined literals. The goal of this paper is to generalize that work to extended programs, and define a semantics for such programs that enlarges WFSX with more negative assumptions.
To achieve this we view default literals as arguments a rational agent can sustain along with the program. As our goal is to enlarge WFSX, we consider the latter as the common reasoning ground and argumentation tool of agents.
With this basis, and in order to define the semantics, we first formalize the concepts of consistent and non-refutable sets of arguments (or of hypotheses). In general several such sets may exist. So, and in order to define a unique semantics, given by a single set of additional assumptions, we introduce an additional non-refutability of arguments criterium — tenability — for always and finally preferring just one set of arguments over another.
We thank Esprit BR project Compulog 2 (no. 6810) for its support.
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Alferes, J.J., Pereira, L.M. (1995). An argumentation theoretic semantics based on non-refutable falsity. In: Dix, J., Pereira, L.M., Przymusinski, T.C. (eds) Non-Monotonic Extensions of Logic Programming. NMELP 1994. Lecture Notes in Computer Science, vol 927. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030657
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