scholarly journals Well-Founded Semantics for Extended Logic Programs with Dynamic Preferences

1996 ◽  
Vol 4 ◽  
pp. 19-36 ◽  
Author(s):  
G. Brewka
Keyword(s):  
Polynomial Time ◽  
Legal Reasoning ◽  
Predicate Symbol ◽  
Logic Programs ◽  
Preference Information ◽  
Logical Language ◽  
Dynamic Preferences

The paper describes an extension of well-founded semantics for logic programs with two types of negation. In this extension information about preferences between rules can be expressed in the logical language and derived dynamically. This is achieved by using a reserved predicate symbol and a naming technique. Conflicts among rules are resolved whenever possible on the basis of derived preference information. The well-founded conclusions of prioritized logic programs can be computed in polynomial time. A legal reasoning example illustrates the usefulness of the approach.

Reasoning about Dynamic Preferences in Circumscriptive Theory by Logic Programming

1997 ◽  
Vol 1 (2) ◽  
pp. 121-129 ◽  
Author(s):  
Toshiko Wakaki ◽  
◽  
Ken Satoh ◽  
Katsumi Nitta ◽  
◽  
...  
Keyword(s):  
Logic Programming ◽  
Logic Program ◽  
Legal Reasoning ◽  
Preference Information ◽  
Normal Logic ◽  
Object Level ◽  
Normal Logic Program ◽  
Dynamic Preferences

To treat dynamic preferences correctly is inevitably required in legal reasoning. In this paper, we present a method which enables us to handle some class of dynamic preferences in the framework of circumscription and to consistently compute its metalevel and object-level reasoning by expressing them in an extended logic program. This is achieved on the basis of policy axioms and priority axioms which permit as to describe circumscription policy by axioms and play a role in intervening between metalevel and object-level reasoning. Not only the preference information among rules and metarules but also relations between dynamic preferences and priority axioms in circumscription are represented by a normal logic program. Thus, priorities can be derived from the preferences dynamically, which allows us to compute objectlevel circumscriptive theory using logic programming based on Wakaki and Satoh’s method.

Polynomial-time MAT learning of multilinear logic programs

1993 ◽  
pp. 63-74
Author(s):  
Kimihito Ito ◽  
Akihiro Yamamoto
Keyword(s):  
Polynomial Time ◽  
Logic Programs

Recurrence with affine level mappings is P-time decidable for CLP

2007 ◽  
Vol 8 (01) ◽  
pp. 111-119 ◽  
Author(s):  
FRED MESNARD ◽  
ALEXANDER SEREBRENIK
Keyword(s):  
Polynomial Time ◽  
Logic Programs ◽  
Constraint Logic Programs

AbstractIn this paper we introduce a class of constraint logic programs such that their termination can be proved by using affine level mappings. We show that membership to this class is decidable in polynomial time.

scholarly journals Pac-Learning Recursive Logic Programs: Efficient Algorithms

1995 ◽  
Vol 2 ◽  
pp. 501-539 ◽  
Author(s):  
W. W. Cohen
Keyword(s):  
Polynomial Time ◽  
Companion Paper ◽  
Efficient Algorithms ◽  
Pac Learning ◽  
Logic Programs ◽  
Constant Depth ◽  
Learning Problem ◽  
Equivalence Queries ◽  
Recursive Programs ◽  
Natural Way

We present algorithms that learn certain classes of function-free recursive logic programs in polynomial time from equivalence queries. In particular, we show that a single k-ary recursive constant-depth determinate clause is learnable. Two-clause programs consisting of one learnable recursive clause and one constant-depth determinate non-recursive clause are also learnable, if an additional ``basecase'' oracle is assumed. These results immediately imply the pac-learnability of these classes. Although these classes of learnable recursive programs are very constrained, it is shown in a companion paper that they are maximally general, in that generalizing either class in any natural way leads to a computationally difficult learning problem. Thus, taken together with its companion paper, this paper establishes a boundary of efficient learnability for recursive logic programs.

scholarly journals CP-logic: A language of causal probabilistic events and its relation to logic programming

2009 ◽  
Vol 9 (3) ◽  
pp. 245-308 ◽  
Author(s):  
JOOST VENNEKENS ◽  
MARC DENECKER ◽  
MAURICE BRUYNOOGHE
Keyword(s):  
Logic Programming ◽  
Formal Semantics ◽  
Probabilistic Logic ◽  
Logic Programs ◽  
Causal Knowledge ◽  
Fundamental Study ◽  
Logical Language ◽  
Logical Representation ◽  
Causal Laws ◽  
Probability Trees

AbstractThis paper develops a logical language for representing probabilistic causal laws. Our interest in such a language is two-fold. First, it can be motivated as a fundamental study of the representation of causal knowledge. Causality has an inherent dynamic aspect, which has been studied at the semantical level by Shafer in his framework of probability trees. In such a dynamic context, where the evolution of a domain over time is considered, the idea of a causal law as something which guides this evolution is quite natural. In our formalization, a set of probabilistic causal laws can be used to represent a class of probability trees in a concise, flexible and modular way. In this way, our work extends Shafer's by offering a convenient logical representation for his semantical objects. Second, this language also has relevance for the area of probabilistic logic programming. In particular, we prove that the formal semantics of a theory in our language can be equivalently defined as a probability distribution over the well-founded models of certain logic programs, rendering it formally quite similar to existing languages such as ICL or PRISM. Because we can motivate and explain our language in a completely self-contained way as a representation of probabilistic causal laws, this provides a new way of explaining the intuitions behind such probabilistic logic programs: we can say precisely which knowledge such a program expresses, in terms that are equally understandable by a non-logician. Moreover, we also obtain an additional piece of knowledge representation methodology for probabilistic logic programs, by showing how they can express probabilistic causal laws.

scholarly journals Polynomial-time learnability of logic programs with local variables from entailment

2001 ◽  
Vol 268 (2) ◽  
pp. 179-198 ◽  
Author(s):  
M.R.K. Krishna Rao ◽  
A. Sattar
Keyword(s):  
Polynomial Time ◽  
Logic Programs

scholarly journals A correct, precise and efficient integration of set-sharing, freeness and linearity for the analysis of finite and rational tree languages

2004 ◽  
Vol 4 (3) ◽  
pp. 289-323 ◽  
Author(s):  
PATRICIA M. HILL ◽  
ENEA ZAFFANELLA ◽  
ROBERTO BAGNARA
Keyword(s):  
Polynomial Time ◽  
Redundant Information ◽  
Logic Programs ◽  
Finite Tree ◽  
Domain Combination ◽  
Efficient Integration ◽  
Tree Languages ◽  
Set Sharing

It is well known that freeness and linearity information positively interact with aliasing information, allowing both the precision and the efficiency of the sharing analysis of logic programs to be improved. In this paper, we present a novel combination of set-sharing with freeness and linearity information, which is characterized by an improved abstract unification operator. We provide a new abstraction function and prove the correctness of the analysis for both the finite tree and the rational tree cases. Moreover, we show that the same notion of redundant information as identified in Bagnara et al. (2000) and Zaffanella et al. (2002) also applies to this abstract domain combination: this allows for the implementation of an abstract unification operator running in polynomial time and achieving the same precision on all the considered observable properties.

scholarly journals On the problem of computing the well-founded semantics

2001 ◽  
Vol 1 (5) ◽  
pp. 591-609 ◽  
Author(s):  
ZBIGNIEW LONC ◽  
MIROSŁAW TRUSZCZYŃSKI
Keyword(s):  
Polynomial Time ◽  
Wide Class ◽  
Logic Program ◽  
Logic Programs ◽  
Top Down ◽  
Asymptotically Optimal ◽  
Semantics Of Logic Programs

The well-founded semantics is one of the most widely studied and used semantics of logic programs with negation. In the case of finite propositional programs, it can be computed in polynomial time, more specifically, in O([mid ]At(P)[mid ] × size(P)) steps, where size(P) denotes the total number of occurrences of atoms in a logic program P. This bound is achieved by an algorithm introduced by Van Gelder and known as the alternating-fixpoint algorithm. Improving on the alternating-fixpoint algorithm turned out to be difficult. In this paper we study extensions and modifications of the alternating-fixpoint approach. We then restrict our attention to the class of programs whose rules have no more than one positive occurrence of an atom in their bodies. For programs in that class we propose a new implementation of the alternating-fixpoint method in which false atoms are computed in a top-down fashion. We show that our algorithm is faster than other known algorithms and that for a wide class of programs it is linear and so, asymptotically optimal.

Everyday Legal Reasoning: A Behavioral Intention Measure of Legal Reasoning

2013 ◽  
Author(s):  
Lindsey Marie Cole
Keyword(s):  
Behavioral Intention ◽  
Legal Reasoning
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