Well-founded semantics and stratification for ordered logic programs

1993 ◽  
Vol 12 (1) ◽  
pp. 91-121 ◽  
Author(s):  
N. Leone ◽  
G. Rossi
Keyword(s):  
Logic Programs ◽  
Ordered Logic

scholarly journals A framework for compiling preferences in logic programs

2003 ◽  
Vol 3 (2) ◽  
pp. 129-187 ◽  
Author(s):  
JAMES P. DELGRANDE ◽  
TORSTEN SCHAUB ◽  
HANS TOMPITS
Keyword(s):  
Logic Program ◽  
Logic Programs ◽  
Wide Range ◽  
Dynamic Case ◽  
General Preference ◽  
Reasoning With Preferences ◽  
Answer Set Semantics ◽  
Ordered Logic ◽  
Answer Sets ◽  
General Dynamic

We introduce a methodology and framework for expressing general preference information in logic programming under the answer set semantics. An ordered logic program is an extended logic program in which rules are named by unique terms, and in which preferences among rules are given by a set of atoms of form s [pr ] t where s and t are names. An ordered logic program is transformed into a second, regular, extended logic program wherein the preferences are respected, in that the answer sets obtained in the transformed program correspond with the preferred answer sets of the original program. Our approach allows the specification of dynamic orderings, in which preferences can appear arbitrarily within a program. Static orderings (in which preferences are external to a logic program) are a trivial restriction of the general dynamic case. First, we develop a specific approach to reasoning with preferences, wherein the preference ordering specifies the order in which rules are to be applied. We then demonstrate the wide range of applicability of our framework by showing how other approaches, among them that of Brewka and Eiter, can be captured within our framework. Since the result of each of these transformations is an extended logic program, we can make use of existing implementations, such as dlv and smodels. To this end, we have developed a publicly available compiler as a front-end for these programming systems.

Preferred answer sets for ordered logic programs

2006 ◽  
Vol 6 (1-2) ◽  
pp. 107-167 ◽  
Author(s):  
DAVY VAN NIEUWENBORGH ◽  
DIRK VERMEIR
Keyword(s):  
Natural Order ◽  
Logic Programs ◽  
Minimal Elements ◽  
Classical Negation ◽  
Answer Set Semantics ◽  
Ordered Logic ◽  
The Cost ◽  
Answer Sets ◽  
Rule Order ◽  
Answer Set

We extend answer set semantics to deal with inconsistent programs (containing classical negation), by finding a “best” answer set. Within the context of inconsistent programs, it is natural to have a partial order on rules, representing a preference for satisfying certain rules, possibly at the cost of violating less important ones. We show that such a rule order induces a natural order on extended answer sets, the minimal elements of which we call preferred answer sets. We characterize the expressiveness of the resulting semantics and show that it can simulate negation as failure, disjunction and some other formalisms such as logic programs with ordered disjunction. The approach is shown to be useful in several application areas, e.g. repairing database, where minimal repairs correspond to preferred answer sets.

Efficient evaluation of a class of ordered logic programs

1997 ◽  
Vol 23 (2) ◽  
pp. 185-214 ◽  
Author(s):  
Nicola Leone ◽  
Clara Pizzutit ◽  
Pasquale Rullo
Keyword(s):  
Logic Programs ◽  
Ordered Logic

Generalized Disjunctive Well-Founded Semantics for Logic Programs

1990 ◽  
Author(s):  
Chitta Baral ◽  
Jorge Lobo ◽  
Jack Minker
Keyword(s):  
Logic Programs

Logical Decision Problems and Complexity of Logic Programs

1987 ◽  
Vol 10 (1) ◽  
pp. 1-33
Author(s):  
Egon Börger ◽  
Ulrich Löwen
Keyword(s):  
Fixed Point ◽  
Computational Complexity ◽  
Decision Problem ◽  
Decision Problems ◽  
Complexity Classes ◽  
Logic Programs ◽  
Finite Structures ◽  
Syntactic Restrictions

We survey and give new results on logical characterizations of complexity classes in terms of the computational complexity of decision problems of various classes of logical formulas. There are two main approaches to obtain such results: The first approach yields logical descriptions of complexity classes by semantic restrictions (to e.g. finite structures) together with syntactic enrichment of logic by new expressive means (like e.g. fixed point operators). The second approach characterizes complexity classes by (the decision problem of) classes of formulas determined by purely syntactic restrictions on the formation of formulas.

Y-Logic: A Framework for Reasoning About Chameleonic Programs with Inconsistent Completions

1990 ◽  
Vol 13 (4) ◽  
pp. 465-483
Author(s):  
V.S. Subrahmanian
Keyword(s):  
Classical Logic ◽  
Logic Program ◽  
Logic Programs ◽  
Large Subset ◽  
General Logic ◽  
Traditional Sense

Large logic programs are normally designed by teams of individuals, each of whom designs a subprogram. While each of these subprograms may have consistent completions, the logic program obtained by taking the union of these subprograms may not. However, the resulting program still serves a useful purpose, for a (possibly) very large subset of it still has a consistent completion. We argue that “small” inconsistencies may cause a logic program to have no models (in the traditional sense), even though it still serves some useful purpose. A semantics is developed in this paper for general logic programs which ascribes a very reasonable meaning to general logic programs irrespective of whether they have consistent (in the classical logic sense) completions.

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