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We now turn out attention to search algorithms underlying ASP technology. In particular, we will focus on the techniques employed by answer set solver such as clasp. Recall that clasp is only one building block of an answer set system clingo that also incorporates grounder called gringo. In the scope of this course we ignore the details behind grounders, but note that these are highly nontrivial systems solving a complex and computationally intense task of intelligent instantiation. The algorithms behind majority answer set solvers fall into group of so called backtracking search algorithms. Backtracking is a general algorithm for finding all (or some) solutions to some computational problem, that incrementally builds candidates to the solutions, and abandons each partial candidate c (”backtracks”) as soon as it determines that c cannot possibly be completed to a valid solution. (Wikipedia) The Davis-Putnam-Logemann-Loveland (DPLL) procedure is a classic example of backtracking search algorithms. DPLL is a method for deciding the satisfiability of propositional logic formula in conjunctive normal form, or, in other words, for solving the propositional satisfiability problem. Algorithms used by answer set solvers share a lot in common with DPLL. In this handout, we thus begin by presenting DPLL procedure. We then discuss its extensions suitable for computing answer sets of a program in place.
Publication Date
3-2020
Publisher
University of Nebraska at Omaha
City
Omaha, Nebraska
Recommended Citation
Lierler, Yuliya, "Handout on Algorithms in Backtracking Search behind SAT and ASP" (2020). Computer Science Faculty Books and Monographs. 3.
https://digitalcommons.unomaha.edu/compscifacbooks/3
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Parts of this handout follow • the lecture notes on Logic-based AI course, UT, Spring 20111 by Vladimir Lifschitz. • What is answer set programming to propositional satisfiability, Yuliya Lierler, Constraints, July 2017, Volume 22, Issue 3, pp 307337 available at https://link.springer.com/ article/10.1007/s10601-016-9257-7. In class discussions of Fall 2020 course on Introduction to AI at UNO contributed to several examples listed in these notes.