Algorithms for computing backbones of propositional formulae

Answer Set Programming (ASP) is a logic-based knowledge representation framework, supporting-among other reasoning modes-the central task of query answering. In the propositional case, query answering amounts to computing cautious consequences of the input program among the atoms in a given set of candidates, where a cautious consequence is an atom belonging to all stable models. Currently, the most efficient algorithms either iteratively verify the existence of a stable model of the input program extended with the complement of one candidate, where the candidate is heuristically selected, or introduce a clause enforcing the falsity of at least one candidate, so that the solver is free to choose which candidate to falsify at any time during the computation of a stable model. This paper introduces new algorithms for the computation of cautious consequences, with the aim of driving the solver to search for stable models discarding more candidates. Specifically, one of such algorithms enforces minimality on the set of true candidates, where different notions of minimality can be used, and another takes advantage of unsatisfiable cores computation. The algorithms are implemented in WASP, and experiments on benchmarks from the latest ASP competitions show that the new algorithms perform better than the state of the art. (Under consideration for acceptance in TPLP).

Section: Introductionmentioning

confidence: 99%

Cautious reasoning in ASP via minimal models and unsatisfiable cores

Alviano¹,

Dodaro²,

Järvisalo³

et al. 2018

“…Figure 7 shows a possible path in FS Π for the program Π of Example 1. Chunking and core-based methods can be combined using our methodology to abstract Algorithm 7 from (Janota et al 2015). Such a combination will be employed in the experiments.…”

Section: Core-based Methodsmentioning

confidence: 99%

Abstract Solvers for Computing Cautious Consequences of ASP programs

Amendola¹,

Dodaro²,

Maratea³

2019

solvers are a method to formally analyze algorithms that have been profitably used for describing, comparing and composing solving techniques in various fields such as Propositional Satisfiability (SAT), Quantified SAT, Satisfiability Modulo Theories, Answer Set Programming (ASP), and Constraint ASP.In this paper, we design, implement and test novel abstract solutions for cautious reasoning tasks in ASP. We show how to improve the current abstract solvers for cautious reasoning in ASP with new techniques borrowed from backbone computation in SAT, in order to design new solving algorithms. By doing so, we also formally show that the algorithms for solving cautious reasoning tasks in ASP are strongly related to those for computing backbones of Boolean formulas. We implement some of the new solutions in the ASP solver WASP and show that their performance are comparable to state-of-the-art solutions on the benchmark problems from the past ASP Competitions. Under consideration for acceptance in TPLP. KEYWORDS:Answer Set Programming, Abstract solvers, Cautious reasoning solver, SUP (Lierler 2011); however, abstract solvers have been so far mainly applied to ASP solvers for brave reasoning tasks where, given an input query and a knowledge base expressed in ASP, answers are witnessed by ASP solutions, i.e., stable models (Baral 2003;Eiter et al. 1997;Gelfond and Lifschitz 1988;Gelfond and Lifschitz 1991;Marek and Truszczyński 1998;Niemelä 1999).However, in ASP, also cautious reasoning has been deeply studied in the literature: answers here must be witnessed by all stable models. This task has found a significant number of interesting applications as well, including consistent query answering (Arenas et al. 2003;Manna et al. 2013), data integration (Eiter 2005), multi-context systems (Brewka and Eiter 2007), and ontology-based reasoning (Eiter et al. 2008). Two well-known ASP solvers, i.e., DLV (Leone et al. 2006) and CLASP (Gebser et al. 2012), have been extended for computing cautious consequences of ASP programs. More recently, Alviano et al. (2014) presented a unified, high-level view of such solving procedures, and designed several algorithms for cautious reasoning in ASP, including those implemented in DLV and CLASP, borrowed from the backbone computation of Boolean formulas (Janota et al. 2015): all these techniques are implemented (and tested) on top of the ASP solver WASP (Alviano et al. 2015).In this paper we design, implement and test novel abstract solutions for cautious reasoning tasks in ASP. We show how to improve the current abstract solvers (Brochenin and Maratea 2015a) for cautious reasoning in ASP with further techniques borrowed from backbone computation in SAT, in order to design new solving algorithms. In particular, we import a technique called "chunk", which generalizes over-and under-approximation by testing a set soft atoms simultaneously for being added in the under-approximation, and core-based algorithms, which can be considered either a solution per se, or a way for pruning the set of atoms t...

“…In fact, the backbone of a propositional formula ϕ is the set of literals that are true in all models of ϕ. Several algorithms for computing backbones of propositional formulas are based on variants of the iterative consistency testing algorithm (Marques-Silva et al 2010;Janota et al 2014), which essentially corresponds to the iterative coherence testing algorithm analyzed in this paper. Backbone search algorithms usually feature additional techniques for removing candidates to be tested, such as implicant reduction and core-based chunking (Ravi and Somenzi 2004).…”

Section: Related Workmentioning

confidence: 99%

“…For example, backbone search algorithms can reduce their overestimate by removing all unassigned variables when a (partial) model is found; in our setting, ASP solvers always terminate with a complete assignment. Core-based chunking, instead, requires a portfolio of algorithms (Janota et al 2014) in order to be effective, which is beyond the scope of this paper.…”

Section: Related Workmentioning

confidence: 99%

Anytime Computation of Cautious Consequences in Answer Set Programming

Alviano

Dodaro

Ricca

2014

Query answering in Answer Set Programming (ASP) is usually solved by computing (a subset of) the cautious consequences of a logic program. This task is computationally very hard, and there are programs for which computing cautious consequences is not viable in reasonable time. However, current ASP solvers produce the (whole) set of cautious consequences only at the end of their computation. This paper reports on strategies for computing cautious consequences, also introducing anytime algorithms able to produce sound answers during the computation.