Results 1 
7 of
7
Reducing propositional theories in equilibrium logic to logic programs
 PROGRESS IN ARTIFICIAL INTELLIGENCE, PROC. OF THE 12TH PORTUGUESE CONF. ON ARTIFICIAL INTELLIGENCE, EPIA’05
, 2005
"... The paper studies reductions of propositional theories in equilibrium logic to logic programs under answer set semantics. Specifically we are concerned with the question of how to transform an arbitrary set of propositional formulas into an equivalent logic program and what are the complexity const ..."
Abstract

Cited by 14 (7 self)
 Add to MetaCart
(Show Context)
The paper studies reductions of propositional theories in equilibrium logic to logic programs under answer set semantics. Specifically we are concerned with the question of how to transform an arbitrary set of propositional formulas into an equivalent logic program and what are the complexity constraints on this process. We want the transformed program to be equivalent in a strong sense so that theory parts can be transformed independent of the wider context in which they might be embedded. It was only recently established [2] that propositional theories are indeed equivalent (in a strong sense) to logic programs. Here this result is extended with the following contributions. (i) We show how to effectively obtain an equivalent program starting from an arbitrary theory. (ii) We show that in general there is no polynomial transformation if we require the resulting program to share precisely the vocabulary or signature of the initial theory. (iii) Extending previous work we show how polynomial transformations can be achieved if one allows the resulting program to contain new atoms. The program obtained is still in a strong sense equivalent to the original theory, and the answer sets of the theory can be retrieved from it.
Complexity of Clausal Constraints Over Chains
"... We investigate the complexity of the satisfiability problem of constraints over finite totally ordered domains. In our context, a clausal constraint is a disjunction of inequalities of the form x ≥ d and x ≤ d. We classify the complexity of constraints based on clausal patterns. A pattern abstracts ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
We investigate the complexity of the satisfiability problem of constraints over finite totally ordered domains. In our context, a clausal constraint is a disjunction of inequalities of the form x ≥ d and x ≤ d. We classify the complexity of constraints based on clausal patterns. A pattern abstracts away from variables and contains only information about the domain elements and the type of inequalities occurring in a constraint. Every finite set of patterns gives rise to a (clausal) constraint satisfaction problem in which all constraints in instances must have an allowed pattern. We prove that every such problem is either polynomially decidable or NPcomplete, and give a polynomialtime algorithm for recognizing the tractable cases. Some of these tractable cases are new and have not been previously identified in the literature.
Efficient algorithms for constraint description problems over finite totally ordered domains (Extended Abstract)
 PROCEEDINGS 2ND INTERNATIONAL JOINT CONFERENCE ON AUTOMATED REASONING (IJCAR'04). CORK (IRELAND), VOLUME 3097 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2004
"... Given a finite set of vectors over a finite totally ordered domain, we study the problem of computing a constraint in conjunctive normal form such that the set of solutions for the produced constraint is identical to the original set. We develop an efficient polynomialtime algorithm for the general ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
Given a finite set of vectors over a finite totally ordered domain, we study the problem of computing a constraint in conjunctive normal form such that the set of solutions for the produced constraint is identical to the original set. We develop an efficient polynomialtime algorithm for the general case, followed by specific polynomialtime algorithms producing Horn, dual Horn, and bijunctive constraints for sets of vectors closed under the operations of conjunction, disjunction, and median, respectively. We also consider the affine constraints, analyzing them by means of computer algebra. Our results generalize the work of Dechter and Pearl on relational data, as well as the papers by Hébrard and Zanuttini. They also complete the results of Hähnle et al. on multivalued logics and Jeavons et al. on the algebraic approach to constraints. We view our work as a step toward a complete complexity classification of constraint satisfaction problems over finite domains.
Approximability of Clausal Constraints
, 2006
"... We study a family of problems, called Maximum Solution (Max Sol), where the objective is to maximise a linear goal function over the feasible integer assignments to a set of variables subject to a set of constraints. When the domain is Boolean (i.e. restricted to {0, 1}), the maximum solution prob ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
We study a family of problems, called Maximum Solution (Max Sol), where the objective is to maximise a linear goal function over the feasible integer assignments to a set of variables subject to a set of constraints. When the domain is Boolean (i.e. restricted to {0, 1}), the maximum solution problem is identical to the wellstudied Max Ones problem, and the complexity and approximability is completely understood for all restrictions on the underlying constraints. We continue this line of research by considering the Max Sol problem for relations defined by regular signed logic over finite subsets of the natural numbers; the complexity of the corresponding decision problem has recently been classified by Creignou et al. [Theory of Computing Systems, 42(2):239– 255, 2008]. We give sufficient conditions for when such problems are polynomialtime solvable and we prove that they are APXhard otherwise. Similar dichotomies are also obtained for variants of the Max Sol problem.
Manyvalued Horn Logic is Hard
"... Fuzzy Description Logics (FDLs) have been introduced to reason about vague or imprecise knowledge in application domains. In recent years, reasoning in many FDLs based on infinitely many values has been proved to be undecidable [3,15] and systematic studies have been undertaken on this topic [8]. On ..."
Abstract
 Add to MetaCart
(Show Context)
Fuzzy Description Logics (FDLs) have been introduced to reason about vague or imprecise knowledge in application domains. In recent years, reasoning in many FDLs based on infinitely many values has been proved to be undecidable [3,15] and systematic studies have been undertaken on this topic [8]. On the other