An important limitation of traditional logic programming as a knowledge representation tool, in comparison with classical logic, is that logic programming does not allow us to deal directly with incomplete information. In order to overcome this limitation, we extend the class of general logic programs by including classical negation, in addition to negation-as-failure. The semantics of such extended programs is based on the method of stable models. The concept of a disjunctive database can be extended in a similar way. We show that some facts of commonsense knowledge can be represented by logic programs and disjunctive databases more easily when classical negation is available. Computationally, classical negation can be eliminated from extended programs by a simple preprocessor. Extended programs are identical to a special case of default theories in the sense of Reiter. 1 Introduction An important limitation of traditional logic programming as a knowledge representation tool, in comp...

The idea of circumscription can be explained on a simple example. We would like to represent information about the locations of blocks in a blocks world, using the "default":

We survey here various approaches which were proposed to incorporate negation in logic programs. We concentrate on the proof-theoretic and model-theoretic issues and the relationships between them.

Well Founded Semantics is adequate to capture nonmonotonic reasoning if we interpret the Well Founded model of a program P as a (possibly incomplete) view of the world. Thus the Well Founded model may be accepted to be a definite view of the world and the extended stable models as alternative enlarged consistent belief models an agent may have about the world. Our purpose is to exhibit a modular systematic method of representing nonmonotonic problems with the Well Founded semantics of logic programs. In this paper we use this method to represent and solve some classical nonmonotonic problems. This leads us to consider our method quite generic. 1 Introduction Well Founded Semantics (WFS) [15] is adequate to capture nonmonotonic reasoning if we interpret the Well Founded model (WFM) of a program P as a (possibly incomplete) view of the world. Thus the WFM may be accepted to be a definite view of the world and the eXtended Stable Models (XSMs) as alternative enlarged consistent belief mo...

Abstract not found

The purpose of this paper is to compare three types of non-monotonic semantics: (a) proof-theoretic semantics based on the closed world assumption, (b) model-theoretic semantics based on the notion of a minimal model and (c) model-theoretic semantics based on the notion of a minimal Herbrand model. All of these semantics capture the non-monotonicity of common sense reasoning, i.e. the ability to withdraw conclusions after some new information is added to the original theories, and proved to be powerful enough to handle most examples of such reasoning presented in the literature. However, since these formalizations are based on different intuitions and often produce different results, the problem of understanding the relationship between them is especially important. In the first part of the paper we concentrate on the class of positive logic programs, also called definite theories. Although the three semantics usually differ for universal sentences, our main result shows that they alwa...

Truth maintenance systems have been studied by many authors and have become powerful tools in AI reasoning systems. From the viewpoint of commonsense reasoning, Doyle's TMS seems most interesting, for it allows nonmonotonic justifications. Its semantics, however, has remained unclear. In this paper, we shall give its declarative description in terms of autoepistemic logic, a kind of nonmonotonic logic. That is, we shall exhibit a one-to-one correspondence between states acceptable to the TMS and stable expansions of autoepistemic formulas attached to justifications. Thus, the TMS turns out to be a theorem prover of autoepistemic logic. For the practical interest, our result also suggests the possibility of implementing better TMS algorithms by using the theorem proving method of autoepistemic logic. 1

One of the problems in non-monotonic reasoning is the existence of multiple extensions for a given theory. Certain classes of theories have been identified where a unique extension may be selected and inferences made using such an extension is considered `natural '. However,there are several cases where there is no other alternative and several or all extensions of a theory have to be considered when performing inferences. In such cases we want to be skeptical, that is we are unwilling to believe some statement without conclusive evidence but we are willing to be uncertain in our beliefs. In this paper, we model skepticism as indefinite information. We first present some examples which show the need for skeptical beliefs and show how such information can be represented naturally by disjunctive programs. We also present a proof procedure which can be used to infer answers from these programs. 1 Introduction One of the problems in non-monotonic reasoning is the existence of multiple ex...

this paper, we study the computation of circumscription for non-Horn axioms consisting of disjunctive (indefinite) clauses and positive and negative disjuctive queries. The semantics of positive and negative consequences from a disjunctive logic program can be characterized with the minimal model semantics (MMS) and the Generalized Closed World Assumption (GCWA) [22]. The minimal model semantics (MMS) states that a positive disjunctive clause can be inferred from a disjunctive logic program if it is true in every minimal model of the program. A ground literal :p can be inferred to be true under the GCWA if p is false in every minimal model of the disjunctive database. That is, the MMS and the GCWA capture the same minimality criterion as does circumscription. This connection has been made use of by Przymusinski [35], who developed an algorithm, based on the proof-theoretic definition of the GCWA, for computing circumscription from function-free positive indefinite theories. Gelfond, Przymusinska and Przymusinski [10] developed the concept of the iterated closed world assumption for stratified disjunctive theories and showed that it is equivalent to prioritized circumscription when the indefinite function-free theories are prioritized approriately. Przymusinski [35] shows that by using the algorithm developed for computing circumscription from ground positive indefinite theories 3 recursively one can compute prioritized circumscription. In this paper, we provide a fixpoint characterization for prioritized circumscription of stratified disjunctive theories [27] that may contain function symbols. The fixpoint construction, using a nonmonotonic operator T

In this paper we present the class of general logic programs which has a special kind of stratifications, called the locally finite stratification. For the class, good properties of propositional logic programs, such as termination and safeness, are preserved. Using these properties, we show the completeness of a kind of SLDNF-resolution that use a depth bound, called depth bounded resolution, with respect to the perfect model semantics. Finally we syntactically characterize a subclass of the class, called weakly reducing programs and show that the depth bounded resolution is complete and effective for weakly reducing programs. 1 Introduction The completeness of a derivation procedure with respect to the perfect model semantics is important in both logic programming and non-monotonic reasoning. Perfect model semantics were introduced by Przymisinski [13], Apt, Blair and Walker [3] and by Van Gelder [23] as the declarative semantics for the class of stratified logic programs [3, 23] a...