Toshiro Wakayama

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.

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.

Case-free programs: an abstraction of definite horn programs

We consider a form of linear resolution (called SEI) that requires no factoring and no ancestor resolution. Thus, SEI behaves just like SLD, but it can tolerate certain non-Horn clauses and negative clauses. We prove that the class of case-free programs (a program here is a finite set of any clauses with the consistency requirement) is the largest class of programs for which SEI is sound and complete. Intuitively, a case-free program is a program in which no case analyses are required for computing correct query answers. The class of case-free programs is significantly larger than that of definite Horn programs. In particular, it is large enough to allow extensive manipulation of negative information, including non-allowed clauses: recall that negation-as-failure in SLDNF is essentially a test, and the allowedness is an essential requirement for the completeness of SLDNF[3]. We then prove a result that strongly indicates that SLDNF has some fundamental difficulties when and only when it deals with non-case-free programs. This result may open the possibility of obtaining better completeness results of SLDNF by restricting our attention to case-free programs.

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.

A formal specification of document processing

We propose a computational model of structured documents and their processing based on preferential attribute grammar schemes and grammar coordinations. Our grammar-based model can be viewed as a specification of composable structure transformations. The main novel features are declarative specification of preferential constraints, and specification of structure transformations at the level of meta-data through coordination schemes. The preferential constraints may express constraints to guide computations as in dynamic programming, as well as constraints to control declaratively the outcome of transformation. A coordination is essentially a partial substitution map from the vocabulary of a grammar to languages over the vocabulary of another grammar. Although our grammar-based coordination schemes are designed to capture various types of document processing (such as view processing and query processing), we focus on the document layout application in this work. Our first main result shows that when the coordination map satisfies the uniformity condition, the two grammars (of the layout coordination scheme) are syntactically coordinated in the sense that trees of the first grammar are always transformable to trees of the second grammar, while satisfying the constraints imposed by the coordination. We then show that the elementary uniformity is a decidable property when the coordination is regular, thereby establishing a decidable class of coordinated grammar schemes.