147 research outputs found
Anytime Computation of Cautious Consequences in Answer Set Programming
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.Comment: To appear in Theory and Practice of Logic Programmin
A Preference-Based Approach to Backbone Computation with Application to Argumentation
The backbone of a constraint satisfaction problem consists of those variables that take the same value in all solutions. Algorithms for determining the backbone of propositional formulas, i.e., Boolean satisfiability (SAT) instances, find various real-world applications. From the knowledge representation and reasoning (KRR) perspective, one interesting connection is that of backbones and the so-called ideal semantics in abstract argumentation. In this paper, we propose a new backbone algorithm which makes use of a "SAT with preferences" solver, i.e., a SAT solver which is guaranteed to output a most preferred satisfying assignment w.r.t. a given preference over literals of the SAT instance at hand. We also show empirically that the proposed approach is specifically effective in computing the ideal semantics of argumentation frameworks, noticeably outperforming an other state-of-the-art backbone solver as well as the winning approach of the recent ICCMA 2017 argumentation solver competition in the ideal semantics track.Peer reviewe
Exploiting the Enumeration of All Feature Model Configurations
.Feature models are widely used to encode the configurations of a software product line in terms of mandatory, optional and exclusive features as well as propositional constraints over the features. Numerous computationally expensive procedures have been developed to model check, test, configure, debug, or compute relevant information of feature models. In this paper we explore the possible improvement of relying on the enumeration of all configurations when performing automated analysis operations. We tackle the challenge of how to scale the existing enumeration techniques by relying on distributed computing. We show that the use of distributed computing techniques might offer practical solutions to previously unsolvable problems and opens new perspectives for the automated analysis of software product lines.Junta de Andalucía P12-TIC-1867Ministerio de Economía y Competitividad TIN2015- 70560-
Externally Supported Models for Efficient Computation of Paracoherent Answer Sets
Answer Set Programming (ASP) is a well established formalism for nonmonotonic reasoning. While incoherence, the non-existence of answer sets for some programs, is an important feature of ASP, it has frequently been criticised and indeed has some disadvantages, especially for query answering. Paracoherent semantics have been suggested as a remedy, which extend the classical notion of answer sets to draw meaningful conclusions also from incoherent programs. In this paper we present an alternative characterization of the two major paracoherent semantics in terms of (extended) externally supported models. This definition uses a transformation of ASP programs that is more parsimonious than the classic epistemic transformation used in recent implementations. A performance comparison carried out on benchmarks from ASP competitions shows that the usage of the new transformation brings about performance improvements that are independent of the underlying algorithms
On SAT representations of XOR constraints
We study the representation of systems S of linear equations over the
two-element field (aka xor- or parity-constraints) via conjunctive normal forms
F (boolean clause-sets). First we consider the problem of finding an
"arc-consistent" representation ("AC"), meaning that unit-clause propagation
will fix all forced assignments for all possible instantiations of the
xor-variables. Our main negative result is that there is no polysize
AC-representation in general. On the positive side we show that finding such an
AC-representation is fixed-parameter tractable (fpt) in the number of
equations. Then we turn to a stronger criterion of representation, namely
propagation completeness ("PC") --- while AC only covers the variables of S,
now all the variables in F (the variables in S plus auxiliary variables) are
considered for PC. We show that the standard translation actually yields a PC
representation for one equation, but fails so for two equations (in fact
arbitrarily badly). We show that with a more intelligent translation we can
also easily compute a translation to PC for two equations. We conjecture that
computing a representation in PC is fpt in the number of equations.Comment: 39 pages; 2nd v. improved handling of acyclic systems, free-standing
proof of the transformation from AC-representations to monotone circuits,
improved wording and literature review; 3rd v. updated literature,
strengthened treatment of monotonisation, improved discussions; 4th v. update
of literature, discussions and formulations, more details and examples;
conference v. to appear LATA 201
Trading inference effort versus size in CNF Knowledge Compilation
Knowledge Compilation (KC) studies compilation of boolean functions f into
some formalism F, which allows to answer all queries of a certain kind in
polynomial time. Due to its relevance for SAT solving, we concentrate on the
query type "clausal entailment" (CE), i.e., whether a clause C follows from f
or not, and we consider subclasses of CNF, i.e., clause-sets F with special
properties. In this report we do not allow auxiliary variables (except of the
Outlook), and thus F needs to be equivalent to f.
We consider the hierarchies UC_k <= WC_k, which were introduced by the
authors in 2012. Each level allows CE queries. The first two levels are
well-known classes for KC. Namely UC_0 = WC_0 is the same as PI as studied in
KC, that is, f is represented by the set of all prime implicates, while UC_1 =
WC_1 is the same as UC, the class of unit-refutation complete clause-sets
introduced by del Val 1994. We show that for each k there are (sequences of)
boolean functions with polysize representations in UC_{k+1}, but with an
exponential lower bound on representations in WC_k. Such a separation was
previously only know for k=0. We also consider PC < UC, the class of
propagation-complete clause-sets. We show that there are (sequences of) boolean
functions with polysize representations in UC, while there is an exponential
lower bound for representations in PC. These separations are steps towards a
general conjecture determining the representation power of the hierarchies PC_k
< UC_k <= WC_k. The strong form of this conjecture also allows auxiliary
variables, as discussed in depth in the Outlook.Comment: 43 pages, second version with literature updates. Proceeds with the
separation results from the discontinued arXiv:1302.442
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