Mingyi Zhang

Knowledge forgetting in answer set programming

The ability of discarding or hiding irrelevant information has been recognized as an important feature for knowledge based systems, including answer set programming. The notion of strong equivalence in answer set programming plays an important role for different problems as it gives rise to a substitution principle and amounts to knowledge equivalence of logic programs. In this paper, we uniformly propose a semantic knowledge forgetting, called HT-and FLP-forgetting, for logic programs under stable model and FLP-stable model semantics, respectively. Our proposed knowledge forgetting discards exactly the knowledge of a logic program which is relevant to forgotten variables. Thus it preserves strong equivalence in the sense that strongly equivalent logic programs will remain strongly equivalent after forgetting the same variables. We show that this semantic forgetting result is always expressible; and we prove a representation theorem stating that the HT-and FLP-forgetting can be precisely characterized by Zhang-Zhous four forgetting postulates under the HT-and FLP-model semantics, respectively. We also reveal underlying connections between the proposed forgetting and the forgetting of propositional logic, and provide complexity results for decision problems in relation to the forgetting. An application of the proposed forgetting is also considered in a conflict solving scenario.

The loop formula based semantics of description logic programs

Description logic programs (dl-programs) proposed by Eiter et al. constitute an elegant yet powerful formalism for the integration of answer set programming with description logics, for the Semantic Web. In this paper, we generalize the notions of completion and loop formulas of logic programs to description logic programs and show that the answer sets of a dl-program can be precisely captured by the models of its completion and loop formulas. Furthermore, we propose a new, alternative semantics for dl-programs, called the canonical answer set semantics, which is defined by the models of completion that satisfy what are called canonical loop formulas. A desirable property of canonical answer sets is that they are free of circular justifications. Some properties of canonical answer sets are also explored and we compare the canonical answer set semantics with the FLP-semantics and the answer set semantics by translating dl-programs into logic programs with abstract constraints. We present a clear picture on the relationship among these semantics variations for dl-programs.

Weight Constraint Programs with Functions

In this paper we consider a new class of logic programs, called weight constraint programs with functions, which are lparse programs incorporating functions over non-Herbrand domains. We define answer sets for these programs and develop a computational mechanism based on loop completion. We present our results in two stages. First, we formulate loop formulas for lparse programs (without functions). Our result improves the previous formulations in that our loop formulas do not introduce new propositional variables, nor there is a need of translating lparse programs to nested expressions. Building upon this result we extend the work to weight constraint programs with functions. We show that the loop completion of such a program can be transformed to a Constraint Satisfaction Problem (CSP) whose solutions correspond to the answer sets of the program, hence off-the-shelf CSP solvers can be used for answer set computation. We show some preliminary experimental results.

Weight constraint programs with evaluable functions

In the current practice of Answer Set Programming (ASP), evaluable functions are represented as special kinds of relations. This often makes the resulting program unnecessarily large when instantiated over a large domain. The extra constraints needed to enforce the relation as a function also make the logic program less transparent. In this paper, we consider adding evaluable functions to answer set logic programs. The class of logic programs that we consider here is that of weight constraint programs, which are widely used in ASP. We propose an answer set semantics to these extended weight constraint programs and define loop completion to characterize the semantics. Computationally, we provide a translation from loop completions of these programs to instances of the Constraint Satisfaction Problem (CSP) and use the off-the-shelf CSP solvers to compute the answer sets of these programs. A main advantage of this approach is that global constraints implemented in such CSP solvers become available to ASP. The approach also provides a new encoding for CSP problems in the style of weight constraint programs. We have implemented a prototype system based on these results, and our experiments show that this prototype system competes well with the state-of-the-art ASP solvers. In addition, we illustrate the utilities of global constraints in the ASP context.

Logic Programs, Compatibility and Forward Chaining Construction

Logic programming under the stable model semantics is proposed as a non-monotonic language for knowledge representation and reasoning in artificial intelligence. In this paper, we explore and extend the notion of compatibility and the Λ operator, which were first proposed by Zhang to characterize default theories. First, we present a new characterization of stable models of a logic program and show that an extended notion of compatibility can characterize stable submodels. We further propose the notion of weak auto-compatibility which characterizes the Normal Forward Chaining Construction proposed by Marek, Nerode and Remmel. Previously, this construction was only known to construct the stable models of FC-normal logic programs, which turn out to be a proper subclass of weakly auto-compatible logic programs. We investigate the properties and complexity issues for weakly auto-compatible logic programs and compare them with some subclasses of logic programs.

Embedding Functions into Disjunctive Logic Programs

We extend the notions of completion and loop formulas of normal logic programs with functions to a class of nested expressions that properly include disjunctive logic programs. We show that answer sets for such a logic program can be characterized as the models of its completion and loop formulas. These results provide a basis for computing answer sets of disjunctive programs with functions, by solvers for the Constraint Satisfaction Problem. The potential benefit in answer set computations for this approach has been demonstrated previously in the implementation called fasp. We also present a formulation of completion and loop formulas for disjunctive logic programs with variables. This paper focuses on the theoretical development of these extensions.

Constructing first-order loops of normal logic programs

It is possible that a logic program has no finite complete sets of loops. For instance, the Hamiltonian circuit problem encoded by Nielemä is such a logic program. This means that the complete set of loops of a logic program is possibly infinite. In order to represent a possible infinite complete set of loops by a finite set of loops, we propose a constructive approach: (i) we introduce the notion of base loops which can be obtained from predicate positive dependency graphs of logic programs and show that every logic program has a finite complete set of base loops; (ii) we show that every loop of a logic program can be constructed from its base loops using substitution and union.