936 research outputs found
On the Semantics of Gringo
Input languages of answer set solvers are based on the mathematically simple
concept of a stable model. But many useful constructs available in these
languages, including local variables, conditional literals, and aggregates,
cannot be easily explained in terms of stable models in the sense of the
original definition of this concept and its straightforward generalizations.
Manuals written by designers of answer set solvers usually explain such
constructs using examples and informal comments that appeal to the user's
intuition, without references to any precise semantics. We propose to approach
the problem of defining the semantics of gringo programs by translating them
into the language of infinitary propositional formulas. This semantics allows
us to study equivalent transformations of gringo programs using natural
deduction in infinitary propositional logic.Comment: Proceedings of Answer Set Programming and Other Computing Paradigms
(ASPOCP 2013), 6th International Workshop, August 25, 2013, Istanbul, Turke
A computability theoretic equivalent to Vaught's conjecture
We prove that, for every theory which is given by an sentence, has less than many countable
models if and only if we have that, for every on a cone of
Turing degrees, every -hyperarithmetic model of has an -computable
copy. We also find a concrete description, relative to some oracle, of the
Turing-degree spectra of all the models of a counterexample to Vaught's
conjecture
Infinitary Tableau for Semantic Truth
Acknowledgements I would like to thank Philip Welch for his assistance and acknowledge the late Greg Hjorth for the time he spent in helping me learn how to use the tools used in the paper. I would also like to thank Hannes Leitgeb for giving me the opportunity to present this material and for providing me with valuable feedback. And I would like to thank Benedict Eastaugh and Marcus Holland for helping make the final sections of this paper more accessible in the way it was intended.Peer reviewedPostprin
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