Surya Mantha

Preference queries in deductive databases

Traditional database query languages such as datalog and SQL allow the user to specify only mandatory requirements on the data to be retrieved from a database. In many applications, it may be natural to express not only mandatory requirements but also preferences on the data to be retrieved. Lacroix and Lavency10) extended SQL with a notion of preference and showed how the resulting query language could still be translated into the domain relational calculus. We explore the use of preference in databases in the setting of datalog. We introduce the formalism of preference datalog programs (PDPs) as preference logic programs without uninterpreted function symbols for this purpose. PDPs extend datalog not only with constructs to specify which predicate is to be optimized and the criterion for optimization but also with constructs to specify which predicate to be relaxed and the criterion to be used for relaxation. We can show that all of the soft requirements in Reference10) can be directly encoded in PDP. We first develop anaively-pruned bottom-up evaluation procedure that is sound and complete for computing answers to normal and relaxation queries when the PDPs are stratified, we then show how the evaluation scheme can be extended to the case when the programs are not necessarily stratified, and finally we develop an extension of themagic templates method for datalog14) that constructs an equivalent but more efficient program for bottom-up evaluation.

Optimization and relaxation in constraint logic languages

Optimization and relaxation are two important operations that naturally arise in many applications involving constraints, e.g., engineering design, scheduling, decision support, etc. In optimization, we are interested in finding the optimal (i.e., best) solutions to a set of constraints with respect to an objective function. In many applications, optimal solutions may be difficult or impossible to obtain, and hence we are interested in finding suboptimal solutions, by either relaxing the constraints or relaxing the objective function. The contribution of this paper lies in providing a logical framework for performing optimization and relaxation in a constraint logic programming language. Our proposed framework is called preference logic programming (PLP), and its use for optimization was discussed in [8]. Essentially, in PLP we can designate certain predicates as optimization predicates, and we can specify the objective function by stating preference criteria for determining the optimal solutions to these predicates. This paper extends the PLP paradigm with facilities to formulate relaxation problems in a natural manner. We introduce the concept of a relaxation goal, and discuss its use for preference relaxation. Our model-theoretic semantics of relaxation is based on simple concepts from modal logic: Essentially, each world in the possible-worlds semantics for a preference logic program is a model for the constraints of the program, and an ordering over these worlds is determined by the objective function. Optimization can then be expressed as truth in strongly optimal worlds, while relaxation becomes truth in suitably-defined suboptimal worlds. We also present an operational semantics for relaxation as well as correctness results. Our conclusion is that the concept of preference provides a unifying framework for formulating optimization as well as relaxation problems.

Preference logics: Towards a unified approach to nonmonotonicity in deductive reasoning

The notion ofpreference is central to most forms of nonmonotonic reasoning. Shoham, in his dissertation, used this notion to give a single semantical point of view from which most nonmonotonic reasoning systems could be studied. In this paper, we study the notion of preference closely and devise a class of logics of preference that extract the logicalcore of the notion of preference. Earlier attempts have been largely unsuccessful, because of adoption as matters of logic of certain theory-specific preference principles such asasymmetry andtransitivity. Soundness, completeness and decidability proofs for the logics are given. We define the notion of a preferential theory and reframe nonmonotonicity as a symbolic optimization problem where defaults are coded aspreference criteria which place preference orders on the models of a first-order theory. We study the relationship between normal default theories and show the correspondence between models of extensions and optimal worlds. We give a preferential account of some forms of circumscription. Thelocal nature of preference logic is contrasted with the global notion of normality and preference that is used by conditional logics of normality and cumulative inference operations. In related papers, we give a completely declarative semantics for the stable models of normal logic programs, a deontic logic based on preferences that is free of the anomalies of standard deontic logic, and extend Horn clause logic programming to impose partial orders on the bodies of clauses as declarative specification of the relaxation criteria for the truth-hood of the heads.

Preference logic grammars

Preference logic grammars (PLGs) are introduced in this paper as a concise, declarative, modular, and efficient means of resolving ambiguity in logic grammars. Preference logic grammars can be thought as extensions of definite clause grammars (DCGs) and definite-clause translation grammars (DCTGs). Just as DCGs and DCTGs can be directly translated into logic programs, PLGs can be translated into preference logic programs (PLPs), which we introduced in our earlier work. We discuss two applications of PLGs: optimal parsing, and ambiguity resolution in programming-language and natural-language grammars. Optimal parsing is an extension of parsing wherein costs are associated with the different (ambiguous) parses of a string and the preferred parse is the one with least cost. Many problems can be viewed as optimal parsing problems, e.g., code generation, document layout, etc. In the area of natural language parsing, we illustrate the use of preference clauses for resolution of prepositional phrase attachment ambiguities, and point out the growing consensus in the literature on the need to explicitly specify preference criteria for ambiguity resolution.

Exploiting the normative aspect of preference: A deontic logic without actions

This paper is an attempt to clear the following charge leveled against preference logics: preference logics rest upon the mistaken belief that concept construction can satisfactorily be carried out in isolation from theory construction (J. Mullen, Metaphilosophy 10(1979)247–255). We construct a logic of preference that is fundamental in the sense that it does notcommit itself to any allegedlyobvious or intuitive — and in actuality,theory specific — preference principles. A unique feature of our construction is that preference orderings are placed upon possible worlds. While this has been done before in the work of S.O. Hansson and N. Rescher, among others, we do not derive a binary preference relation — from these orders — that acts on individual propositions. Instead, we provide the syntactic means to impose the preference orderings among worlds. Thus, unlike Hansson, we do not need to assumea priori that our preference orderings be transitive. Such properties can be axiomatized. The close connections between preferences and obligations, in particular their normative nature, then allow us to derive a deontic logic that is free of the paradoxes of standard deontic logic. It is interesting to note here that this work arose in an attempt to provide a logical characterization of document description and layout Layout directives can be succinctly represented as preference criteria.

A Logical Reconstruction of Constraint Relaxation Hierarchies in Logic Programming

We propose an extension to Definite Horn Clauses by placing partial orders on the bodies of clauses. Such clauses are called relaxable clauses. These partial orders are interpreted as a specification of relaxation criteria in the proof of the consequent of a relaxable clause, i.e., the order in which to relax the conditions of truthhood of the consequent if all the goals in the body cannot be satisfied. We present a modal logic of preference that enables us to characterize these preference orders, both syntactically and semantically. The richer structure of the modal preference models reflects these preference orders; something that is absent in the essentially flat structure of traditional Herbrand models. A variant of SLD-resolution that generates solutions in the preferred order is presented. The notion of control as preference is introduced as a first step towards specifying control information in a logically coherent fashion. Relaxable Horn clauses can be used to succinctly specify constraint problems in formal design. It is worth noting that the development of preference logic was driven by the desire to characterize declaratively, problems in document layout. In [4] we give a completely declarative account of the stable models of a general logic program. The reader is referred to [3],[5]and [14] for a detailed account of nonmonotonicity as preferential reasoning,the soundness and completeness proofs for the logics and applicationsto Artificial Intelligence, such as deontic reasoning.

Preference logics and nonmonotonicity in logic programming

It is claimed that the notion of preference is a fundamental modality in computing and is a generalization of the notion of minimality. A logic of feasible preference is presented. The non-monotonic behavior of negation in logic programming is modeled as a symbolic optimization problem. As a case study, for the class of logic programs with one or more stable models, we give a preferential transformation of logic programs that identifies their stable models as the optimal worlds in the intended model of the corresponding preferential theory. Minimization and minimization orderings are given explicit syntactic representations and their due status in the model theory. Preference logics gives a very elegant model theory for defaults, without any mention of fixpoints. Further, nonmonotonic reasoning is carried out in a monotonic logic, since members of the optimal worlds are not identified with theorems of a preferential theory. Preference logics have great potential to bring the areas of Symbolic Computation, Knowledge Representation and Classical Optimization closer.