Chiaki Sakama

Prioritized logic programming and its application to commonsense reasoning

Representing and reasoning with priorities are important in commonsense reasoning. This paper introduces a framework of prioritized logic programming (PLP), which has a mechanism of explicit representation of priority information in a program. When a program contains incomplete or indefinite information, PLP is useful for specifying preference to reduce non-determinism in logic programming. Moreover, PLP can realize various forms of commonsense reasoning in AI such as abduction, default reasoning, circumscription, and their prioritized variants. The proposed framework increases the expressive power of logic programming and exploits new applications in knowledge representation.

Negation as failure in the head

The class of logic programs with negation as failure in the head is a subset of the logic of MBNF introduced by Lifschitz and is an extension of the class of extended disjunctive programs. An interesting feature of such programs is that the minimality of answer sets does not hold. This paper considers the class of general extended disjunctive programs (GEDPs) as logic programs with negation as failure in the head. First, we discuss that the class of GEDPs is useful for representing knowledge in various domains in which the principle of minimality is too strong. In particular, the class of abductive programs is properly included in the class of GEDPs. Other applications include the representation of inclusive disjunctions and circumscription with fixed predicates. Secondly, the semantic nature of GEDPs is analyzed by the syntax of programs. In acyclic programs, negation as failure in the head can be shifted to the body without changing the answer sets of the program. On the other hand, supported sets of any program are always preserved by the same transformation. Thirdly, the computational complexity of the class of GEDPs is shown to remain in the same complexity class as normal disjunctive programs. Through the simulation of negation as failure in the head, computation of answer sets and supported sets is realized using any proof procedure for extended or positive disjunctive programs. Finally, a simple translation of GEDPs into autoepistemic logic is presented.

An alternative approach to the semantics of disjunctive logic programs and deductive databases

In this paper, we study a new semantics of logic programming and deductive databases. Thepossible model semantics is introduced as a declarative semantics of disjunctive logic programs. The possible model semantics is an alternative theoretical framework to the classical minimal model semantics and provides a flexible inference mechanism for inferring negation in disjunctive logic programs. We also present a proof procedure for the possible model semantics and show that the possible model semantics has an advantage from the computational complexity point of view.

Updating Extended Logic Programs through Abduction

This paper introduces techniques for updating knowledge bases represented in extended logic programs. Three different types of updates, view updates, theory updates, and inconsistency removal, are considered. We formulate these updates through abduction, and provide methods for computing them with update programs. An update program is an extended logic program which specifies changes on abductive hypotheses, then updates are computed by the U-minimal answer sets of an update program. The proposed technique provides a uniform framework for these different types of updates, and each update is computed using existing procedures of logic programming.

Paraconsistent Stable Semantics for Extended Disjunctive Programs

This paper presents declarative semantics of possibly inconsistent disjunctive logic programs. We introduce the paraconsistent minimal and stable model semantics for extended disjunctive programs, which can distinguish inconsistent information from other information in a program. These semantics are based on lattice-structured multi-valued logics, and are characterized by a new fixpoint semantics of extended disjunctive programs. Applications of the paraconsistent semantics for reasoning in inconsistent programs are also presented.

An abductive framework for computing knowledge base updates

This paper introduces an abductive framework for updating knowledge bases represented by extended disjunctive programs. We first provide a simple transformation from abductive programs to update programs which are logic programs specifying changes on abductive hypotheses. Then, extended abduction, which was introduced by the same authors as a generalization of traditional abduction, is computed by the answer sets of update programs. Next, different types of updates, view updates and theory updates are characterized by abductive programs and computed by update programs. The task of consistency restoration is also realized as special cases of these updates. Each update problem is comparatively assessed from the computational complexity viewpoint. The result of this paper provides a uniform framework for different types of knowledge base updates, and each update is computed using existing procedures of logic programming.

Possible Model Semantics for Disjunctive Databases

Abstract This paper introduce the class of possible models for a declarative semantics of deductive databases. The possible model semantics is an extension of the minimal model semantics of databases and provides both inclusive and exclusive interpretations for disjunctive deductive databases. We characterize it by giving a new fixpoint semantics of databases and then introduce a rule, called the GCW A P for inferring negation from a database. We also present the proof procedure, called SLD P -resolution and show its soundness and completeness with respect to possible model semantics.

A fixpoint characterization of abductive logic programs

A new fixpoint semantics for abductive logic programs is provided, in which the belief models of an abductive program are characterized as the fixpoint of a disjunctive program obtained by a suitable program transformation. In the transformation, both negative hypotheses through negation as failure and positive hypotheses from the abducibles are dealt with uniformly. The result is further generalized to a fixpoint semantics for abductive extended disjunctive programs. These characterizations allow us to have a parallel bottom-up model generation procedure for computing abductive explanations from any (range-restricted and function-free) normal, extended, and disjunctive programs with integrity constraints.

Speculative computation by abduction under incomplete communication environments

We present a method of problem solving in multi-agent systems when communication between agents is not guaranteed. To solve the problem of incomplete communication, we propose a method using abduction. The idea is as follows. When communication is delayed or failed, then we use a default hypothesis as a tentative answer and continue computation. When some response is obtained, we check consistency of the response and the current computation. If the response is consistent, then we continue the current computation, or else if the response is inconsistent, we seek an alternative computation. This way of computation is called speculative computation, since computation using a tentative answer would lead to a significant advantage if it succeeds. In this paper, we restrict our attention to a master-slave multi-agent system and propose an implementation of speculative computation and show that abduction plays an important role in speculative computation.

Induction from answer sets in nonmonotonic logic programs

Inductive logic programming (ILP) realizes inductive machine learning in computational logic. However, the present ILP mostly handles classical clausal programs, especially Horn logic programs, and has limited applications to learning nonmonotonic logic programs. This article studies a method for realizing induction in nonmonotonic logic programs. We consider an extended logic program as a background theory, and introduce techniques for inducing new rules using answer sets of the program. The produced new rules explain positive/negative examples in the context of inductive logic programming. The proposed methods extend the present ILP techniques to a syntactically and semantically richer framework, and contribute to a theory of nonmonotonic ILP.